Physics II: Electricity & Magnetism Binomial Expansions, Riemann Sums, Sections 21.6 & 21.8

Friday (Day 12)

Warm-Up Fri, Feb 6 Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x 10-10 m) Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 6) Derivative Practice For future assignments - check online at www.plutonium-239.com

Warm-Up Review Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x 10-10 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?

Vocabulary 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

Foundational Mathematics Skills in Physics Timeline Day Pg(s) 1 2 6 3 11 16 21 13 14 7 4 12 17 8 22 23 5 18 9 24 †12 19 10 15 20 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

Topic #1: Determine the slope at point A for f(x)=xn 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)=xn y = 1/4 x2 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) How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?

Monday (Day 13)

Warm-Up Mon, Feb 9 If I measured the distance of each step I took and summed them all together, what would I have calculated? 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? Now make it more complex, what if my speed was slowly changing and I Wrote down my velocity and the amount of time I was traveling at that velocity; Multiplied those two numbers together; 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 www.plutonium-239.com

Warm-Up Mon, Feb 9 If I measured the distance of each step I took and summed them all together, what would I have calculated? 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? Now make it more complex, what if my speed was slowly changing and I Wrote down my velocity and the amount of time I was traveling at that velocity; Multiplied those two numbers together; 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?

Vocabulary 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

Foundational Mathematics Skills in Physics Timeline Day Pg(s) 1 2 6 3 11 16 21 13 14 7 4 12 17 8 22 23 5 18 9 24 †12 19 10 15 20 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

Riemann Sums Proof ADD RIEMANN SUMS PROOF HERE

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 xfinal - xinitial. This is also equal to the summation of all velocity x time calculations [f(ci)(xi-xi-1)] or rewritten as [v(ci)(ti-ti-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(ci) 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).

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?

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?

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 Draw a diagram; show all charges, with signs, and electric fields and forces with directions Calculate forces using Coulomb’s law 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?

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

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: Field lines indicate the direction of the field; the field is tangent to the line. The magnitude of the field is proportional to the density of the lines. 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 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 21.5 - 21.7 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?