Physics II: Electricity & Magnetism Binomial Expansions, Riemann Sums, Sections 21.6 to 21.11

Thursday (Day 11)  Binomial Expansion

Warm-Up Thurs, Feb 5  Calculate the force acting on Q 2 at distance of 0.50 m.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 5)  Electrostatics Lab #2: Lab Report  Have you complete WebAssign Problems: ?  For future assignments - check online at Thurs, Feb 5  Calculate the force acting on Q 2 at distance of 0.50 m.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 5)  Electrostatics Lab #2: Lab Report  Have you complete WebAssign Problems: ?  For future assignments - check online at

Warm-Up Review  Calculate the force acting on Q 2 at distance of 0.50 m.

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 5) with answer guide.  Begin The Four Circles Graphic Organizer  DERIVATIVE PROOF USING BINOMIAL EXPANSION  Derivative practice  FRIDAY:  INTEGRAL PROOF USING RIEMANN SUMS  Integral Practice  MONDAY:  Discuss Electric Fields & Gravitational Field  Apply Electric Fields  Continue with The Four Circles Graphic Organizer  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 5) with answer guide.  Begin The Four Circles Graphic Organizer  DERIVATIVE PROOF USING BINOMIAL EXPANSION  Derivative practice  FRIDAY:  INTEGRAL PROOF USING RIEMANN SUMS  Integral Practice  MONDAY:  Discuss Electric Fields & Gravitational Field  Apply Electric Fields  Continue with The Four Circles Graphic Organizer

Topic #1: Determine the slope at point A for f(x)=x n y = 1/2 x WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Topic #1: Determine the slope at point A for f(x)=x n y = 1/4 x 2 WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Topic #1: Determine the slope at point A for f(x)=x n The something is determined by using binomial expansion. Binomial Expansion is defined as: The something is determined by using binomial expansion. Binomial Expansion is defined as: Slope “is defined as” the rise over the run. Trick #1: Factor out (b-a) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Aside #1: Binomial Expansion Practice Using binomial expansion: Expand b 1 -a 1 : WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Aside #2: Binomial Expansion Practice Using binomial expansion: Expand b 2 -a 2 : WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Aside #3: Binomial Expansion Practice Using binomial expansion: Expand b 3 -a 3 : WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Aside #4: Binomial Expansion Practice Using binomial expansion: Expand b 4 -a 4 : WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Aside #5: Binomial Expansion Practice Using binomial expansion: Expand b 5 -a 5 : WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Determination of Slope Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 1 The expansion of b 1 -a 1 = (b-a)(1) Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 1 The expansion of b 1 -a 1 = (b-a)(1) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Determination of Slope Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 2 The expansion of b 2 -a 2 = (b-a)(b+a) Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 2 The expansion of b 2 -a 2 = (b-a)(b+a) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Determination of Slope Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 3 The expansion of b 3 -a 3 = (b-a)(b 2 +ba+a 2 ) Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 3 The expansion of b 3 -a 3 = (b-a)(b 2 +ba+a 2 ) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Determination of Slope Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 4 The expansion of b 4 -a 4 = (b-a)(b 3 +b 2 a+ba 2 +a 3 ) Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 4 The expansion of b 4 -a 4 = (b-a)(b 3 +b 2 a+ba 2 +a 3 ) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Determination of Slope Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 5 The expansion of b 5 -a 5 = (b-a)(b 4 +b 3 a+b 2 a 2 +ba 3 +a 4 ) Recall: The definition for slope of a polynomial is now: Calculate the slope for f(x) = x 5 The expansion of b 5 -a 5 = (b-a)(b 4 +b 3 a+b 2 a 2 +ba 3 +a 4 ) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Determination of Slope  Now we can show that:  Now this is where it gets fun! It is time to decrease the distance between points a and b to get a more accurate slope at point a.  This is called taking the ‘limit’ as “b” approaches “a.”  All we have to do is change all “b’s” to “a’s”  Now we can show that:  Now this is where it gets fun! It is time to decrease the distance between points a and b to get a more accurate slope at point a.  This is called taking the ‘limit’ as “b” approaches “a.”  All we have to do is change all “b’s” to “a’s” WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Determination of Slope  The slope of any power is now: WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Method Determination Comparision  Checking the slope for f(a) = a n where n = 2  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree?  Checking the slope for f(a) = a n where n = 2  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree? WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Method Determination Comparision  Checking the slope for f(a) = a n where n = 1  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree?  Checking the slope for f(a) = a n where n = 1  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree? WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Method Determination Comparision  Checking the slope for f(a) = a n where n = 3  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree?  Checking the slope for f(a) = a n where n = 3  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree? WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Method Determination Comparision  Checking the slope for f(a) = a n where n = 4  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree?  Checking the slope for f(a) = a n where n = 4  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree? WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Method Determination Comparision  Checking the slope for f(a) = a n where n = 5  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree?  Checking the slope for f(a) = a n where n = 5  Using the binomial expansion method  Using the slope = n a n-1 method  Do they agree? WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Summary of Derivative  After adding the constant back in and changing a to the variable x we get f(x) =C x n Slope = n C x n-1  How is the derivative expressed?  After adding the constant back in and changing a to the variable x we get f(x) =C x n Slope = n C x n-1  How is the derivative expressed? WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Summary of Derivative  How is the derivative for a polynomial, represented?  What about finding the area under a curve (or line)? Find the integral. For a polynomial:  How is the derivative for a polynomial, represented?  What about finding the area under a curve (or line)? Find the integral. For a polynomial: WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

So what is the relationship...  between finding the slope and taking the first derivative?  They are the same.  Other derivative representations  between finding the slope and taking the first derivative?  They are the same.  Other derivative representations WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Summary  After comparing the force constants for electrostatics and gravity, identify which Force is stronger.  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 6)  Derivative Practice  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 3 classes)  After comparing the force constants for electrostatics and gravity, identify which Force is stronger.  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 6)  Derivative Practice  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 3 classes) How do we use Coulomb ’ s Law and the principle of superposition to determine the force that acts between point charges?

Friday (Day 12)  Riemann Sums

Warm-Up Fri, Feb 6  Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x m)  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 6)  Derivative Practice  For future assignments - check online at Fri, Feb 6  Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x m)  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 6)  Derivative Practice  For future assignments - check online at

Warm-Up Review  Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x m)

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the concept of electric field?  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the concept of electric field?  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 6) with answer guide.  Review Derivative Practice  INTEGRAL PROOF USING RIEMANN SUMS  Integral Practice  MONDAY:  Discuss Electric Fields & Gravitational Field  Apply Electric Fields  Continue with The Four Circles Graphic Organizer  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 6) with answer guide.  Review Derivative Practice  INTEGRAL PROOF USING RIEMANN SUMS  Integral Practice  MONDAY:  Discuss Electric Fields & Gravitational Field  Apply Electric Fields  Continue with The Four Circles Graphic Organizer

Topic #1: Determine the slope at point A for f(x)=x n y = 1/2 x WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Topic #1: Determine the slope at point A for f(x)=x n y = 1/4 x 2 WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Summary  Identify one section that in the Integral Proof using Riemann Sums that was confusing?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 7)  Go through the Riemann sum derivation - determine what you do not understand.  Integral Practice  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 3 classes)  Identify one section that in the Integral Proof using Riemann Sums that was confusing?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 7)  Go through the Riemann sum derivation - determine what you do not understand.  Integral Practice  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 3 classes) How do we use Coulomb ’ s Law and the principle of superposition to determine the force that acts between point charges?

Monday (Day 13)  Riemann Sums (Day II)  Section 21.6  Section 21.8  Riemann Sums (Day II)  Section 21.6  Section 21.8

Warm-Up Mon, Feb 9 1.If I measured the distance of each step I took and summed them all together, what would I have calculated? 2.If I was driving in a car on the turnpike at a constant speed and I multiplied my speed by the time I was traveling, what would I have calculated? 3.Now make it more complex, what if my speed was slowly changing and I 1.Wrote down my velocity and the amount of time I was traveling at that velocity; 2.Multiplied those two numbers together; 3.Added those new numbers together;  What would I have calculated?  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 7)  Integral Practice  For future assignments - check online at Mon, Feb 9 1.If I measured the distance of each step I took and summed them all together, what would I have calculated? 2.If I was driving in a car on the turnpike at a constant speed and I multiplied my speed by the time I was traveling, what would I have calculated? 3.Now make it more complex, what if my speed was slowly changing and I 1.Wrote down my velocity and the amount of time I was traveling at that velocity; 2.Multiplied those two numbers together; 3.Added those new numbers together;  What would I have calculated?  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 7)  Integral Practice  For future assignments - check online at

Warm-Up Mon, Feb 9 1.If I measured the distance of each step I took and summed them all together, what would I have calculated? 2.If I was driving in a car on the turnpike at a constant speed and I multiplied my speed by the time I was traveling, what would I have calculated? 3.Now make it more complex, what if my speed was slowly changing and I 1.Wrote down my velocity and the amount of time I was traveling at that velocity; 2.Multiplied those two numbers together; 3.Added those new numbers together;  What would I have calculated? Mon, Feb 9 1.If I measured the distance of each step I took and summed them all together, what would I have calculated? 2.If I was driving in a car on the turnpike at a constant speed and I multiplied my speed by the time I was traveling, what would I have calculated? 3.Now make it more complex, what if my speed was slowly changing and I 1.Wrote down my velocity and the amount of time I was traveling at that velocity; 2.Multiplied those two numbers together; 3.Added those new numbers together;  What would I have calculated?

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the concept of electric field?  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the concept of electric field?  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 7) with answer guide.  Complete the Integral Proof using Riemann Sums  Review Integral Practice  Discuss  Electric Fields  Gravitational Field  Field Lines  Continue with The Four Circles Graphic Organizer  Apply Electric Fields  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 7) with answer guide.  Complete the Integral Proof using Riemann Sums  Review Integral Practice  Discuss  Electric Fields  Gravitational Field  Field Lines  Continue with The Four Circles Graphic Organizer  Apply Electric Fields

Riemann Sums Proof  ADD RIEMANN SUMS PROOF HERE

Riemann Sums Riemann Sums Related to Reality

Big Picture Ideas and Relationships  If F(x) is written as x(t) (aka. Displacement as a function of time)  Then slope of the graph, F’(x), can be written as x’(t) (aka v(t), the velocity as a function of time)  And F(b) - F(a) is the really the just the x final - x initial.  This is also equal to the summation of all velocity x time calculations  [f(c i )(x i -x i-1 )] or rewritten as  [v(c i )(t i -t i-1 )]  If F(x) is written as x(t) (aka. Displacement as a function of time)  Then slope of the graph, F’(x), can be written as x’(t) (aka v(t), the velocity as a function of time)  And F(b) - F(a) is the really the just the x final - x initial.  This is also equal to the summation of all velocity x time calculations  [f(c i )(x i -x i-1 )] or rewritten as  [v(c i )(t i -t i-1 )]

The graph of y(x) Referred to as F(x) [or x(t)]

The graph of y ’ (x); Called F ’ (x); [or x ’ (t)]

The graph of F ’ (x) is renamed f(x); [or x ’ (t) is renamed v(t)]

Riemann Sum with only 1 approximation (  t: large)

Riemann Sum with only 2 approximations (  t: still large)

Riemann Sum with 9 approximations (  t: medium)

Riemann Sum with 17 approximations (  t: small)

Riemann Sum with only 33 approximations (  t: smaller)

Riemann Sums  Confusing Points:  x(c i ) is only a point of reference, not the “height” to which the  t is multiplied to get the area under the curve.  In fact, it is the area under the v(t) graph that we are trying to find in order to determine the total displacement.  Confusing Points:  x(c i ) is only a point of reference, not the “height” to which the  t is multiplied to get the area under the curve.  In fact, it is the area under the v(t) graph that we are trying to find in order to determine the total displacement.

Riemann Sums  As  t decreases, your approximations become more accurate.  Note: Summing up all of the “slope of x vs t times  t” (aka. “velocity x time”) calculations will equal the total displacement (aka. The final position minus the starting position).  As  t decreases, your approximations become more accurate.  Note: Summing up all of the “slope of x vs t times  t” (aka. “velocity x time”) calculations will equal the total displacement (aka. The final position minus the starting position).

Section 21.6  How do we describe and apply the concept of electric field?  How do we define electric fields in terms of the force on a test charge?  How do we describe and apply the concept of electric field?  How do we define electric fields in terms of the force on a test charge?

Section 21.6  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?  How do we use Coulomb ’ s Law to describe the electric field of a single point charge?  How do we use vector addition to determine the electric field produced by two or more point charges?  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?  How do we use Coulomb ’ s Law to describe the electric field of a single point charge?  How do we use vector addition to determine the electric field produced by two or more point charges?

21.6 The Electric Field The electric field is the force on a small charge, divided by the charge:

21.6 The Electric Field For a point charge:

21.6 The Electric Field Force on a point charge in an electric field: Superposition principle for electric fields:

21.6 The Electric Field Problem solving in electrostatics: electric forces and electric fields 1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions 2. Calculate forces using Coulomb’s law 3. Add forces vectorially to get result

Section 21.8  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?  How do we compare and contrast Coulomb ’ s Law and the Universal Law of Gravitation?  How do we describe and apply Coulomb ’ s Law and the Principle of Superposition?  How do we compare and contrast Coulomb ’ s Law and the Universal Law of Gravitation?

21.8 Field Lines The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.

Electric Field created by a spherically charged object

21.8 Field Lines The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge. The electric field is stronger where the field lines are closer together.

21.8 Field Lines Electric dipole: two equal charges, opposite in sign:

21.8 Field Lines Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line. 2. The magnitude of the field is proportional to the density of the lines. 3. Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge.

21.8 Field Lines Summary of field lines: 4. Field lines never cross because the electric field cannot have two values for the same point.

EM Field uses color to represent the field strength (ie. Red is stronger; blue is weaker). Each charge below is ±10q.

Summary  Using Newton’s Second Law, what the formula for force?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 16)  Web Assign  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 2 classes)  Using Newton’s Second Law, what the formula for force?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 16)  Web Assign  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 2 classes) How do we use Coulomb ’ s Law and the principle of superposition to determine the force that acts between point charges?

Tuesday (Day 14)  Section 21.9  Section  Section 21.9  Section 21.10

Warm-Up Tues, Feb 10  Each charge on the next slide is ±q. What will happen to the lines if a 3 rd charge of +q is added to the (1) right side and (2) left side?  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 16)  Web Assign  For future assignments - check online at Tues, Feb 10  Each charge on the next slide is ±q. What will happen to the lines if a 3 rd charge of +q is added to the (1) right side and (2) left side?  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 16)  Web Assign  For future assignments - check online at

Field Example #1: Each charge below is ±q. What will happen to the lines if a 3 rd charge of +q is added to the (1) right side and (2) left side?

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the nature of electric fields in and around conductors?  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we describe and apply the concept of electric fields?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the nature of electric fields in and around conductors?  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we describe and apply the concept of electric fields?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 16) with answer guide.  Discuss  Electric Fields and Conductors  Motion of a Charged Particle in an Electric Field  Work on Web Assign  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 16) with answer guide.  Discuss  Electric Fields and Conductors  Motion of a Charged Particle in an Electric Field  Work on Web Assign

Field Example #2: Each charge below is ±5q. What will happen to the lines if a 3 rd charge of +q is added to the (1) right side and (2) left side?

Field Example #3: Each charge below is ±10q. What will happen to the lines if a 3 rd charge of +q is added to the (1) right side and (2) left side?

Section 21.9  How do we describe and apply the nature of electric fields in and around conductors?  How do we explain the mechanics responsible for the absence of electric field inside of a conductor?  Why must all of the excess charge reside on the surface of a conductor?  How do we prove that all excess charge on a conductor must reside on its surface and the electric field outside of the conductor must be perpendicular to the surface?  How do we describe and apply the nature of electric fields in and around conductors?  How do we explain the mechanics responsible for the absence of electric field inside of a conductor?  Why must all of the excess charge reside on the surface of a conductor?  How do we prove that all excess charge on a conductor must reside on its surface and the electric field outside of the conductor must be perpendicular to the surface?

Section 21.9  How do we describe and apply the concept of induced charge and electrostatic shielding?  What is the significance of why there can be no electric field in a charge-free region completely surrounded by a single conductor?  How do we describe and apply the concept of induced charge and electrostatic shielding?  What is the significance of why there can be no electric field in a charge-free region completely surrounded by a single conductor?

21.9 Electric Fields and Conductors The static electric field inside a conductor is zero – if it were not, the charges would move. The net charge on a conductor is on its surface.

Charge ball suspended in a hollow metal sphere  Observations  The hollow sphere had a charge on the outside.  The charged ball still had a charge.  Conclusions  The charged ball on the inside induces an equal charge on the hollow sphere.  Observations  The hollow sphere had a charge on the outside.  The charged ball still had a charge.  Conclusions  The charged ball on the inside induces an equal charge on the hollow sphere.

21.9 Electric Fields and Conductors The electric field is perpendicular to the surface of a conductor – again, if it were not, charges would move.

Charge ball placed into a hollow metal sphere  Observations  The hollow sphere had a charge on the outside.  The charged ball no longer had a charge.  Conclusions  The charge resides on the outside of a conductor.  Observations  The hollow sphere had a charge on the outside.  The charged ball no longer had a charge.  Conclusions  The charge resides on the outside of a conductor.

Applications of E-fields and conductors: Faraday Cages  Faraday cages protect you from lightning because there is no electrical field inside the metal cage (Notice (1) it completely surrounds him and (2) the size of the gaps in the fence (it is not a solid piece of metal).

Section  How do we describe and apply the nature of electric fields in and around conductors?  How do we determine the direction of the force on a charged particle brought near an uncharged or grounded conductor?  How do we describe and apply the nature of electric fields in and around conductors?  How do we determine the direction of the force on a charged particle brought near an uncharged or grounded conductor?

Section  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we determine the direction of the force on a charged particle brought near an uncharged or grounded conductor?  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we determine the direction of the force on a charged particle brought near an uncharged or grounded conductor?

Section  How do we describe and apply the concept of electric field?  How do we calculate the magnitude and direction of the force on a positive or negative charge in an electric field?  How do we analyze the motion of a particle of known mass and charge in a uniform electric field?  How do we describe and apply the concept of electric field?  How do we calculate the magnitude and direction of the force on a positive or negative charge in an electric field?  How do we analyze the motion of a particle of known mass and charge in a uniform electric field?

Electron accelerated by an electric field  An electron is accelerated in the uniform field E (E=2.0x10 4 N/C) between two parallel charged plates. The separation of the plates is 1.5 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate. (a) With what speed does it leave the hole? (b) Show that the gravitational force can be ignored. [NOTE: Assume the hole is so small that it does not affect the uniform field between the plates]

Electron accelerated by an electric field (a) With what speed does it leave the hole?

Electron accelerated by an electric field (b) Show that the gravitational force can be ignored. Note that F E is times larger than the F G. Also note that the electric field due to the electron does not enter the problem since it cannot exert a force on itself.

Applications of an electron accelerated by an E-Field: Mass Spectrometer  Mass Spectrometers are used to separate isotopes of atoms.  The charged isotopes (a.k.a. ions) are accelerated to a velocity by the parallel plates (located from S to S 1 )  Mass Spectrometers are used to separate isotopes of atoms.  The charged isotopes (a.k.a. ions) are accelerated to a velocity by the parallel plates (located from S to S 1 )

Projectile Motion of a Charged Particle: Electron moving perpendicular to E  Suppose an electron is traveling with a speed, v 0 = 1.0x10 7 m/s, enters a uniform field E at right angles to v 0. Describe the motion by giving the equation of its path while in the electric field. Ignore gravity. This is the equation of a parabola (i.e. projectile motion).

Electrons moving perpendicular to E: The discovery of the electron: J.J. Thomson’s Experiment  J. J. Thomson’s famous experiment that allowed him to discover the electron.

Applications of an electron moving perpendicular to E: Cathode Ray Tube (CRT)  Television Sets & Computer Monitors (CRT)

Applications of an electron moving perpendicular to E: Mass Spectrometer  Mass Spectrometers are used to separate isotopes of atoms.  The charged isotopes (a.k.a. ions) are accelerated to a velocity by the parallel plates (located at the - & + plates)  Mass Spectrometers are used to separate isotopes of atoms.  The charged isotopes (a.k.a. ions) are accelerated to a velocity by the parallel plates (located at the - & + plates)

Applications of an electron moving perpendicular to E: e/m Apparatus  e/m Apparatus

Applications of an electron moving perpendicular to E: e/m Apparatus  e/m Apparatus

Summary  Using your kinematic equations, determine the equation that relates y to v 0, g, , and x?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 17)  Web Assign  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 1 class)  Using your kinematic equations, determine the equation that relates y to v 0, g, , and x?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 17)  Web Assign  Future assignments:  Electrostatics Lab #3: Lab Report (Due in 1 class) How do we use Coulomb ’ s Law and the principle of superposition to determine the force that acts between point charges?

Wednesday (Day 15)  Work Day

Warm-Up Wed, Feb 11  Write down the steps that you would use to explain how to open a door to a blind person?  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 17)  Web Assign  For future assignments - check online at Wed, Feb 11  Write down the steps that you would use to explain how to open a door to a blind person?  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 17)  Web Assign  For future assignments - check online at

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the nature of electric fields in and around conductors?  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we describe and apply the concept of electric fields?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the nature of electric fields in and around conductors?  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we describe and apply the concept of electric fields?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 17) with answer guide.  Work Day  Coulomb’s Law  Web Assign  REVISE: Complete Graphic Organizer (up to Sections 21.10)  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 17) with answer guide.  Work Day  Coulomb’s Law  Web Assign  REVISE: Complete Graphic Organizer (up to Sections 21.10)

Summary  Using Newton’s Second Law, what the formula for force?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 18)  Web Assign  Future assignments:  Using Newton’s Second Law, what the formula for force?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 18)  Web Assign  Future assignments: How do we use Coulomb ’ s Law and the principle of superposition to determine the force that acts between point charges?

Thursday (Day 16)  Section 21.11

Warm-Up Thurs, Feb 12  Complete Graphic Organizers for Sections 21-8 &  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 18)  Web Assign  For future assignments - check online at Thurs, Feb 12  Complete Graphic Organizers for Sections 21-8 &  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 18)  Web Assign  For future assignments - check online at

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we compare and contrast the basic properties of an insulator and a conductor?  How do we describe and apply the concept of electric field?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we compare and contrast the basic properties of an insulator and a conductor?  How do we describe and apply the concept of electric field?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 18) with answer guide.  Discuss  Torque, factors that affect torque, r X F  Electric Dipoles  Electric Dipoles in an Electric Field  The electric field produced by a dipole  Calculations: Dipoles in an electric field  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 18) with answer guide.  Discuss  Torque, factors that affect torque, r X F  Electric Dipoles  Electric Dipoles in an Electric Field  The electric field produced by a dipole  Calculations: Dipoles in an electric field

Section  How do we compare and contrast the basic properties of an insulator and a conductor?  What are characteristics and classification(s) of electrically...  conductive atoms?  insulative atoms?  semi-conductive atoms?  conductive compounds?  insulative compounds?  semi-conductive compounds?  How do we compare and contrast the basic properties of an insulator and a conductor?  What are characteristics and classification(s) of electrically...  conductive atoms?  insulative atoms?  semi-conductive atoms?  conductive compounds?  insulative compounds?  semi-conductive compounds?

Section  How do we describe and apply the concept of electric field?  How do we calculate the net force and torque on a collection of charges in an electric field?  How do we describe and apply the concept of electric field?  How do we calculate the net force and torque on a collection of charges in an electric field? How do we calculate the net force and torque on a collection of charges in an electric field?

Torque To make an object start rotating, a force is needed; the position and direction of the force matter as well. The perpendicular distance from the axis of rotation to the line along which the force acts is called the lever arm. How do we calculate the net force and torque on a collection of charges in an electric field?

Torque A longer lever arm is very helpful in rotating objects. How do we calculate the net force and torque on a collection of charges in an electric field?

Torque Here, the lever arm for F A is the distance from the knob to the hinge; the lever arm for F D is zero; and the lever arm for F C is as shown. How do we calculate the net force and torque on a collection of charges in an electric field?

Torque The torque is defined as:  = r  F or  = r F 

Torque,   Torque is perpendicular to the direction of the rotation.  Right-hand rule - The direction of the positive torque is in the direction of increasing angle)  In general, if we define torque as  = r x F = r F sin   Also, torque can be defined about any point using  net = (r i x F i )  where r i is the position vector of the i th particle and F i is the net force on the i th particle.  Torque is perpendicular to the direction of the rotation.  Right-hand rule - The direction of the positive torque is in the direction of increasing angle)  In general, if we define torque as  = r x F = r F sin   Also, torque can be defined about any point using  net = (r i x F i )  where r i is the position vector of the i th particle and F i is the net force on the i th particle. How do we calculate the net force and torque on a collection of charges in an electric field?

Electric Dipoles The combination of two equal charges of opposite sign, +Q and -Q, separated by a distance l, is referred to as an electric dipole. The quantity Ql is called the dipole moment, p. The dipole moment points from the negative to the positive charge. Many molecules have a dipole moment and are referred to as polar molecules. It is interesting to note that the value of the separated charges may be less than that of a single electron or proton but cannot be isolated. How do we calculate the net force and torque on a collection of charges in an electric field?

Electric Dipoles Electric Dipoles: The combination of two equal charges of opposite sign, +Q and -Q, separated by a distance l. The dipole moment, p: The quantity Ql. The dipole moment points from the negative to the positive charge. Many molecules have a dipole moment and are referred to as polar molecules. It is interesting to note that the value of the separated charges may be less than that of a single electron or proton, but they cannot be isolated. Electric Dipoles: The combination of two equal charges of opposite sign, +Q and -Q, separated by a distance l. The dipole moment, p: The quantity Ql. The dipole moment points from the negative to the positive charge. Many molecules have a dipole moment and are referred to as polar molecules. It is interesting to note that the value of the separated charges may be less than that of a single electron or proton, but they cannot be isolated.

Dipole in an External Field How do we calculate the net force and torque on a collection of charges in an electric field?  F± -q +q  F± A dipole, p = Ql, is placed in an electric field E. First, let us analyze the angle , for torque and about its bisector at point O.  Point O sin  Point O  F± sin  F± Note that the choice of the angle does not change our value for sin   point O will be used for all reference angles instead of the rxF angle to relate the direction of the dipole moment to the E-Field.

Dipole in an External Field A dipole, p = Ql, is placed in an electric field E. Next, let us analyze the direction of the torque force to the change angle , Note: By definition, positive torque always increases the value of  (I.e. move the dipole in the counterclockwise direction). How do we calculate the net force and torque on a collection of charges in an electric field? It is also important to note that the applied torque force will cause the angle  decrease (in the clockwise direction) instead of increase (counter- clockwise) about point O.   about point O is negative.

Dipole in an External Field A dipole p = Ql is placed in an electric field E. How do we calculate the net force and torque on a collection of charges in an electric field?

Dipole in an External Field The effect of the torque is to try to turn the dipole so p is parallel to E. The work done on the dipole by the electric field to change the angle  from   to  , is Because the direction of the torque is opposite to the direction of increasing , we write the torque as Then the dipole so p is parallel to E. The work done on the dipole by the electric field to change the angle  from   to  , is How do we calculate the net force and torque on a collection of charges in an electric field?

Dipole in an External Field Positive work done by the field decreases the potential energy, U, of the dipole in the field. If we choose U = 0 when p is perpendicular to E (that is choosing   = 90º so cos   = 0), and setting   =  then How do we calculate the net force and torque on a collection of charges in an electric field?

Torque with respect to the Dipole’s Orientation How do we calculate the net force and torque on a collection of charges in an electric field?

Electric Field Produced by a Dipole To determine the electric field produced by a dipole in the absence of an external field along the midpoint or perpendicular bisector of the dipole. hh h r – + How do we calculate the net force and torque on a collection of charges in an electric field? at r >> L

Electric Field Produced by a Dipole It is interesting to note that at r >> l, the electric field decreases more rapidly for a dipole (1/r 3 ) than for a single point charge (1/r 2 ). This is due to the fact that at large distances the two opposite charges neutralize each other due to their close proximity At distances where r >> l, this 1/r 3 dependence also applies for points that are not on the perpendicular bisector of the dipole. For a dipole at r >> l hh h r – + For a single point charge How do we calculate the net force and torque on a collection of charges in an electric field?

Table of Dipole Moment Values How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field The dipole moment of a water molecule is 6.1 x Cm. A water molecule is placed in a uniform electric field with magnitude 2.0 x 10 5 N/C. What is the magnitude of the maximum torque that electric field can exert on the molecule? What is the potential energy when the torque is at its maximum? What is the dipole moment, p 1 and p 2, for a single O-H bond (where 2  = 104.5°)? Note: Let How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field The dipole moment of a water molecule is 6.1 x Cm. A water molecule is placed in a uniform electric field with magnitude 2.0 x 10 5 N/C. In what position will the potential energy take on its greatest value? Why is this different than the position where the torque is maximized? The potential energy will be maximized when cos  = –1, so  = 180°, which means p and E are antiparallel. The potential energy is maximized when the dipole moment is oriented so that it has to rotate through the largest angle, 180°, to reach equilibrium at  = 0°. The torque is maximized when the electric forces are perpendicular to p. How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field The carbonyl group (C=O) dipole. The distance between the carbon (  + ) and oxygen (  – ) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x m and the dipole moment of this group is about 8.0 x Cm. A formaldehyde molecule, CH 2 O, is placed in a uniform electric field with magnitude 2.0 x 10 5 N/C. What the direction of the dipole moment, p? What is the magnitude of the maximum torque that electric field can exert on the molecule? What is the potential energy when the torque is at its maximum? How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field The carbonyl group (C=O) dipole. The distance between the carbon (  + ) and oxygen (  – ) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x m and the dipole moment of this group is about 8.0 x Cm. A formaldehyde molecule, CH 2 O, is placed in a uniform electric field with magnitude 2.0 x 10 5 N/C. What is the partial charge (  ± ) of the carbon (  + ) and oxygen (  – ) atoms in the carbonyl group? (a) How much of the quantized charge of an electron/proton is the partial charge of the carbonyl group to? (b) What is this value in percent? How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field The carbonyl group (C=O) dipole. The distance between the carbon (  + ) and oxygen (  – ) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x m and the dipole moment of this group is about 8.0 x Cm. A formaldehyde molecule, CH 2 O, is placed in a uniform electric field with magnitude 2.0 x 10 5 N/C. In what position will the potential energy take on its greatest value? Why is this different than the position where the torque is maximized? The potential energy will be maximized when cos  = –1, so  = 180°, which means p and E are antiparallel. The potential energy is maximized when the dipole moment is oriented so that it has to rotate through the largest angle, 180°, to reach equilibrium at  = 0°. The torque is maximized when the electric forces are perpendicular to p. How do we calculate the net force and torque on a collection of charges in an electric field?

Summary  How does positive torque relate to the change in the angle?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 19)  Web Assign  Future assignments:  How does positive torque relate to the change in the angle?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 19)  Web Assign  Future assignments: How do we calculate the net force and torque on a collection of charges in an electric field?

Supplementary Notes

Vector Cross Product  Known as the vector product or cross product  The cross product of two vectors A and B is defined as another vector C = A x B whose magnitude is C = |A x B| = AB sin  where  < 180º between A and B and whose direction is perpendicular to both A and B.  Right hand rules for cross products  Known as the vector product or cross product  The cross product of two vectors A and B is defined as another vector C = A x B whose magnitude is C = |A x B| = AB sin  where  < 180º between A and B and whose direction is perpendicular to both A and B.  Right hand rules for cross products

Vector Cross Product  The cross product of two vectors  A = A x i + A y j + A z k  B = B x i + B y j + B z k  Can be written as A x B = (A y B z -A z B y )i + (A z B x -A x B z )j + (A x B y - A y B x )k  The cross product of two vectors  A = A x i + A y j + A z k  B = B x i + B y j + B z k  Can be written as A x B = (A y B z -A z B y )i + (A z B x -A x B z )j + (A x B y - A y B x )k

Properties of Vector Cross Products  A x A = 0  A x B = -B x A  A x (B + C) = (A x B) + (A x C) .  A x A = 0  A x B = -B x A  A x (B + C) = (A x B) + (A x C) .

NOT FINISHED START HERE  Review Riemann Sums Proof (see notes)

Friday (Day 17)

Warm-Up Fri, Feb 13  Complete Graphic Organizer for Section  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 19)  Web Assign  For future assignments - check online at Fri, Feb 13  Complete Graphic Organizer for Section  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 19)  Web Assign  For future assignments - check online at

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we describe and apply the electric field created by uniformly charged objects?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we describe and apply the electric field created by uniformly charged objects?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 19) with answer guide.  Steps to Determine the E-Field Created by a Uniform Charge Distributions  Calculate the electric field for continuous charge distributions for the following:  Uniformly Charged Ring (  0  2  )  Uniformly Charged Vertical Wire ( – ∞  + ∞)  Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )  Distribute E-Field Derivation Rubrics  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 19) with answer guide.  Steps to Determine the E-Field Created by a Uniform Charge Distributions  Calculate the electric field for continuous charge distributions for the following:  Uniformly Charged Ring (  0  2  )  Uniformly Charged Vertical Wire ( – ∞  + ∞)  Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )  Distribute E-Field Derivation Rubrics

Section 21.7  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we use integration and the principle of superposition to calculate the electric field of a straight, uniform charge wire?  How do we use integration and the principle of superposition to calculate the electric field of a thin ring of charge on the axis of the ring?  How do we use integration and the principle of superposition to calculate the electric field of a semicircle of charge at its center?  How do we use integration and the principle of superposition to calculate the electric field of a uniformly charged disk on the axis of the disk?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we use integration and the principle of superposition to calculate the electric field of a straight, uniform charge wire?  How do we use integration and the principle of superposition to calculate the electric field of a thin ring of charge on the axis of the ring?  How do we use integration and the principle of superposition to calculate the electric field of a semicircle of charge at its center?  How do we use integration and the principle of superposition to calculate the electric field of a uniformly charged disk on the axis of the disk?

Section 21.7  How do we identify and apply the fields of highly symmetric charge distributions?  How do we identify situations in which the direction of the electric field produced by highly symmetric charge distributions can be deduced from symmetry considerations?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we identify situations in which the direction of the electric field produced by highly symmetric charge distributions can be deduced from symmetry considerations?

Section 21.7  How do we describe and apply the electric field created by uniformly charged objects?  How do we describe the electric field of parallel charged plates?  How do we describe the electric field of a long, uniformly charged wire?  How do we use superposition to determine the electric fields of parallel charged plates?  How do we describe and apply the electric field created by uniformly charged objects?  How do we describe the electric field of parallel charged plates?  How do we describe the electric field of a long, uniformly charged wire?  How do we use superposition to determine the electric fields of parallel charged plates?

21-7 The Field of a Continuous Distribution To find the field of a continuous distribution of charge, treat it as a collection of near-point charges: Summing over the infinitesimal fields: How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

21-7 The Field of a Continuous Distribution Finally, making the charges infinitesimally small and integrating rather than summing: How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

21-7 The Field of a Continuous Distribution Constant linear charge density : Some types of charge distribution are relatively simple. How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

21-7 The Field of a Continuous Distribution Constant surface charge density : How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

21-7 The Field of a Continuous Distribution Constant volume charge density : How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

Steps to Determine the E-Field Created by a Uniform Charge Distributions Graphical: 1.Draw a picture of the object and 3-D plane. 2.Label the partial length, area, or volume that is creating the partial E-field. 3.Determine the distance from the charged object to the location of the desired E-Field and label all components and lengths. Mathematical: 4.Write the formulas for dE and the component of the E-field that contributes to the net E-field (i.e. does not cancel due to symmetry). 5.Write the total charge density and solve it for Q. 6.Write the charge density in relation to the partial charge and solve it for the partial charge (dq). 7.Set up the integral by determining what key component(s) change. 8. † Solve the integral and write the answer in a concise manner. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook. Graphical: 1.Draw a picture of the object and 3-D plane. 2.Label the partial length, area, or volume that is creating the partial E-field. 3.Determine the distance from the charged object to the location of the desired E-Field and label all components and lengths. Mathematical: 4.Write the formulas for dE and the component of the E-field that contributes to the net E-field (i.e. does not cancel due to symmetry). 5.Write the total charge density and solve it for Q. 6.Write the charge density in relation to the partial charge and solve it for the partial charge (dq). 7.Set up the integral by determining what key component(s) change. 8. † Solve the integral and write the answer in a concise manner. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook.

Uniformly Charged Ring (  0  2  )

Uniformly Charged Vertical Wire ( – ∞  + ∞)

Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )

Summary  How did symmetry help to reduce our calculations?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 20)  For each of the following, complete 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  Uniformly Charged Ring (  0  2  )  Uniformly Charged Vertical Wire ( – ∞  + ∞)  *Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )  Web Assign  How did symmetry help to reduce our calculations?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 20)  For each of the following, complete 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  Uniformly Charged Ring (  0  2  )  Uniformly Charged Vertical Wire ( – ∞  + ∞)  *Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )  Web Assign How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

Tuesday (Day 18)

Warm-Up Tues, Feb 17  Identify the parts of the derivation that were confusing.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 20)  For each of the following, 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  Uniformly Charged Ring (  0  2  )  Uniformly Charged Vertical Wire ( – ∞  + ∞)  *Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )  Web Assign  For future assignments - check online at Tues, Feb 17  Identify the parts of the derivation that were confusing.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 20)  For each of the following, 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  Uniformly Charged Ring (  0  2  )  Uniformly Charged Vertical Wire ( – ∞  + ∞)  *Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )  Web Assign  For future assignments - check online at

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we describe and apply the electric field created by uniformly charged objects?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we describe and apply the electric field created by uniformly charged objects?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 20) with answer guide.  Calculate the electric field for continuous charge distributions for the following:  † Uniformly Charged Horizontal Wire (d  d+l)  Uniformly Charged Disk (0  R)  Complete 4 Derivations + Reasoning for the above problems  Complete Web Assign Problems  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 20) with answer guide.  Calculate the electric field for continuous charge distributions for the following:  † Uniformly Charged Horizontal Wire (d  d+l)  Uniformly Charged Disk (0  R)  Complete 4 Derivations + Reasoning for the above problems  Complete Web Assign Problems

Section 21.7  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we use integration and the principle of superposition to calculate the electric field of a straight, uniform charge wire?  How do we use integration and the principle of superposition to calculate the electric field of a thin ring of charge on the axis of the ring?  How do we use integration and the principle of superposition to calculate the electric field of a semicircle of charge at its center?  How do we use integration and the principle of superposition to calculate the electric field of a uniformly charged disk on the axis of the disk?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we use integration and the principle of superposition to calculate the electric field of a straight, uniform charge wire?  How do we use integration and the principle of superposition to calculate the electric field of a thin ring of charge on the axis of the ring?  How do we use integration and the principle of superposition to calculate the electric field of a semicircle of charge at its center?  How do we use integration and the principle of superposition to calculate the electric field of a uniformly charged disk on the axis of the disk?

Section 21.7  How do we identify and apply the fields of highly symmetric charge distributions?  How do we identify situations in which the direction of the electric field produced by highly symmetric charge distributions can be deduced from symmetry considerations?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we identify situations in which the direction of the electric field produced by highly symmetric charge distributions can be deduced from symmetry considerations?

Section 21.7  How do we describe and apply the electric field created by uniformly charged objects?  How do we describe the electric field of parallel charged plates?  How do we describe the electric field of a long, uniformly charged wire?  How do we use superposition to determine the electric fields of parallel charged plates?  How do we describe and apply the electric field created by uniformly charged objects?  How do we describe the electric field of parallel charged plates?  How do we describe the electric field of a long, uniformly charged wire?  How do we use superposition to determine the electric fields of parallel charged plates?

Steps to Determine the E-Field Created by a Uniform Charge Distributions Graphical: 1.Draw a picture of the object and 3-D plane. 2.Label the partial length, area, or volume that is creating the partial E-field. 3.Determine the distance from the charged object to the location of the desired E-Field and label all components and lengths. Mathematical: 4.Write the formulas for dE and the component of the E-field that contributes to the net E-field (i.e. does not cancel due to symmetry). 5.Write the total charge density and solve it for Q. 6.Write the charge density in relation to the partial charge and solve it for the partial charge (dq). 7.Set up the integral by determining what key component(s) change. 8. † Solve the integral and write the answer in a concise manner. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook. Graphical: 1.Draw a picture of the object and 3-D plane. 2.Label the partial length, area, or volume that is creating the partial E-field. 3.Determine the distance from the charged object to the location of the desired E-Field and label all components and lengths. Mathematical: 4.Write the formulas for dE and the component of the E-field that contributes to the net E-field (i.e. does not cancel due to symmetry). 5.Write the total charge density and solve it for Q. 6.Write the charge density in relation to the partial charge and solve it for the partial charge (dq). 7.Set up the integral by determining what key component(s) change. 8. † Solve the integral and write the answer in a concise manner. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook.

† Uniformly Charged Horizontal Wire (d  d+l)

Uniformly Charged Disk (0  R)

Summary  How did symmetry help to reduce our calculations?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 21)  For each of the following, complete 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  † Uniformly Charged Horizontal Wire (d  d+l)  Uniformly Charged Disk (0  R)  Web Assign  How did symmetry help to reduce our calculations?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 21)  For each of the following, complete 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  † Uniformly Charged Horizontal Wire (d  d+l)  Uniformly Charged Disk (0  R)  Web Assign How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

Wednesday (Day 19)

Warm-Up Wed, Feb 18  Identify the parts of the derivation that were confusing.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 21)  For each of the following, 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  † Uniformly Charged Horizontal Wire (d  d+l)  Uniformly Charged Disk (0  R)  Web Assign  For future assignments - check online at Wed, Feb 18  Identify the parts of the derivation that were confusing.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 21)  For each of the following, 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  † Uniformly Charged Horizontal Wire (d  d+l)  Uniformly Charged Disk (0  R)  Web Assign  For future assignments - check online at

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we describe and apply the electric field created by uniformly charged objects?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we describe and apply the electric field created by uniformly charged objects?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 21) with answer guide.  Calculate the electric field for continuous charge distributions for the following:  Uniformly Charged Disk (0  ∞)  Uniformly Charged Hoop (R 1  R 2 )  Uniformly Charged Infinite Plate  Complete 4 Derivations + Reasoning for the above problems  Complete Web Assign Problems  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 21) with answer guide.  Calculate the electric field for continuous charge distributions for the following:  Uniformly Charged Disk (0  ∞)  Uniformly Charged Hoop (R 1  R 2 )  Uniformly Charged Infinite Plate  Complete 4 Derivations + Reasoning for the above problems  Complete Web Assign Problems

Section 21.7  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we use integration and the principle of superposition to calculate the electric field of a straight, uniform charge wire?  How do we use integration and the principle of superposition to calculate the electric field of a thin ring of charge on the axis of the ring?  How do we use integration and the principle of superposition to calculate the electric field of a semicircle of charge at its center?  How do we use integration and the principle of superposition to calculate the electric field of a uniformly charged disk on the axis of the disk?  How do we apply integration and the Principle of Superposition to uniformly charged objects?  How do we use integration and the principle of superposition to calculate the electric field of a straight, uniform charge wire?  How do we use integration and the principle of superposition to calculate the electric field of a thin ring of charge on the axis of the ring?  How do we use integration and the principle of superposition to calculate the electric field of a semicircle of charge at its center?  How do we use integration and the principle of superposition to calculate the electric field of a uniformly charged disk on the axis of the disk?

Section 21.7  How do we identify and apply the fields of highly symmetric charge distributions?  How do we identify situations in which the direction of the electric field produced by highly symmetric charge distributions can be deduced from symmetry considerations?  How do we identify and apply the fields of highly symmetric charge distributions?  How do we identify situations in which the direction of the electric field produced by highly symmetric charge distributions can be deduced from symmetry considerations?

Section 21.7  How do we describe and apply the electric field created by uniformly charged objects?  How do we describe the electric field of parallel charged plates?  How do we describe the electric field of a long, uniformly charged wire?  How do we use superposition to determine the electric fields of parallel charged plates?  How do we describe and apply the electric field created by uniformly charged objects?  How do we describe the electric field of parallel charged plates?  How do we describe the electric field of a long, uniformly charged wire?  How do we use superposition to determine the electric fields of parallel charged plates?

Steps to Determine the E-Field Created by a Uniform Charge Distributions Graphical: 1.Draw a picture of the object and 3-D plane. 2.Label the partial length, area, or volume that is creating the partial E-field. 3.Determine the distance from the charged object to the location of the desired E-Field and label all components and lengths. Mathematical: 4.Write the formulas for dE and the component of the E-field that contributes to the net E-field (i.e. does not cancel due to symmetry). 5.Write the total charge density and solve it for Q. 6.Write the charge density in relation to the partial charge and solve it for the partial charge (dq). 7.Set up the integral by determining what key component(s) change. 8. † Solve the integral and write the answer in a concise manner. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook. Graphical: 1.Draw a picture of the object and 3-D plane. 2.Label the partial length, area, or volume that is creating the partial E-field. 3.Determine the distance from the charged object to the location of the desired E-Field and label all components and lengths. Mathematical: 4.Write the formulas for dE and the component of the E-field that contributes to the net E-field (i.e. does not cancel due to symmetry). 5.Write the total charge density and solve it for Q. 6.Write the charge density in relation to the partial charge and solve it for the partial charge (dq). 7.Set up the integral by determining what key component(s) change. 8. † Solve the integral and write the answer in a concise manner. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook.

Uniformly Charged Disk (0  ∞)

Uniformly Charged Hoop (R 1  R 2 )

Uniformly Charged Infinite Plate No radius?!? What does that mean?!?

21.8 Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant.

21-7 The Field of a Continuous Distribution From the electric field due to a uniform sheet of charge, we can calculate what would happen if we put two oppositely-charged sheets next to each other: The individual fields: The superposition: The result: How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

Summary  How does the result of the Uniformly Charged Disk (0  ∞) & the Uniformly Charged Infinite Plate compare? Why is this the case when one is circular and the other is a rectangle?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 8)  For each of the following, complete 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  *Uniformly Charged Disk (0  ∞)  *Uniformly Charged Hoop (R 1  R 2 )  Uniformly Charged Infinite Plate  Web Assign  How does the result of the Uniformly Charged Disk (0  ∞) & the Uniformly Charged Infinite Plate compare? Why is this the case when one is circular and the other is a rectangle?  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 8)  For each of the following, complete 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  *Uniformly Charged Disk (0  ∞)  *Uniformly Charged Hoop (R 1  R 2 )  Uniformly Charged Infinite Plate  Web Assign How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

Thursday (Day 20)

Warm-Up Thurs, Feb 19  Identify the parts of the derivation that were confusing.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 20)  For each of the following, 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  *Uniformly Charged Disk (0  ∞)  *Uniformly Charged Hoop (R 1  R 2 )  Uniformly Charged Infinite Plate  Web Assign  For future assignments - check online at Thurs, Feb 19  Identify the parts of the derivation that were confusing.  Place your homework on my desk:  “Foundational Mathematics’ Skills of Physics” Packet (Page 20)  For each of the following, 1 derivation with reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)  *Uniformly Charged Disk (0  ∞)  *Uniformly Charged Hoop (R 1  R 2 )  Uniformly Charged Infinite Plate  Web Assign  For future assignments - check online at

Essential Question(s)  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the nature of electric fields in and around conductors?  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we describe and apply the concept of electric fields?  WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?  HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?  How do we describe and apply the nature of electric fields in and around conductors?  How do we describe and apply the concept of induced charge and electrostatic shielding?  How do we describe and apply the concept of electric fields?

Vocabulary  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Static Electricity  Electric Charge  Positive / Negative  Attraction / Repulsion  Charging / Discharging  Friction  Induction  Conduction  Law of Conservation of Electric Charge  Non-polar Molecules  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment  Polar Molecules  Ion  Ionic Compounds  Force  Derivative  Integration (Integrals)  Test Charge  Electric Field  Field Lines  Electric Dipole  Dipole Moment

Foundational Mathematics Skills in Physics Timeline DayPg(s)DayPg(s)DayPg(s)DayPg(s) † WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 8) with answer guide.  Work Day  Web Assign Problems and Final Copy  Review “Foundational Mathematics’ Skills of Physics” Packet (Page 8) with answer guide.  Work Day  Web Assign Problems and Final Copy

Summary  On the Sheets, write down:  3 things you already knew about static electricity.  2 things that you learned about static electricity.  1 thing you would like to know about static electricity.  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 9)  Web Assign  Web Assign Final Copies  Future assignments:  Web Assign Final Copies are due in 2 classes  ALL “5 Derivations” are due in 2 classes TOMORROW: CHAPTER 22: ELECTRIC FLUX & GAUSS’S LAW  On the Sheets, write down:  3 things you already knew about static electricity.  2 things that you learned about static electricity.  1 thing you would like to know about static electricity.  HW (Place in your agenda):  “Foundational Mathematics’ Skills of Physics” Packet (Page 9)  Web Assign  Web Assign Final Copies  Future assignments:  Web Assign Final Copies are due in 2 classes  ALL “5 Derivations” are due in 2 classes TOMORROW: CHAPTER 22: ELECTRIC FLUX & GAUSS’S LAW How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions? How do we describe and apply the electric field created by uniformly charged objects?

Summary of Chapter 21 Charge is quantized in units of e Objects can be charged by conduction or induction Coulomb’s law: Electric field is force per unit charge:

Summary of Chapter 21 Electric field of a point charge: Electric field can be represented by electric field lines Static electric field inside conductor is zero; surface field is perpendicular to surface

CHAPTER 21 - el fin -

TEMPLATES FOR Derivations

Uniformly Charged Disk (0  R)

Uniformly Charged Ring (0  2  )

Uniformly Charged Vertical Wire ( – ∞  + ∞)

Uniformly Charged Vertical Wire ( –L / 2  +L / 2 )

Uniformly Charged Vertical Wire

Uniformly Charged Horizontal Wire