Physics II: Electricity & Magnetism Sections 23.2 to 23.3

Monday (Day 2)

Warm-Up Mon, Mar 2 Our scenario: A positive test charge is being “dropped” in an electric field at location, a, and will hit the other plate, b. Using the following equations, derive an equation to calculate the work done by the electric field. What if the charge were negative? Place your homework on my desk: Web Assign Chapter 22 Final Copies For future assignments - check online at www.plutonium-239.com

Scenario #2: A charge in an electric field is being “dropped” from a point a, and will hit the plate at point b. Direction of E a b a b + -- Direction of Motion

Warm-up Review Our scenario: A positive test charge is being “dropped” in an electric field at location, a, and will hit the other plate, b. Using the following equations, derive an equation to calculate the work done by the electric field. What if the charge were negative?

*Recall: Electric Field and Energy Using your knowledge and the law of conservation of energy, make a chart to generally Identify the direction of the electric field. (I.e. up, down, left ,right, etc) The potential energy at (a) point a and (b) point b. (I.e. high, low, same) The potential to do work at (a) point a and (b) point b. (I.e. high, low, same) The kinetic energy at (a) point a and (b) point b. (I.e. high, low, same) The change in potential energy, potential to do work, and kinetic energy as it moves from a to b. (I.e. increase, decrease, constant) The work done by the electric field (I.e. positive, negative, none)

*Electric Field and Energy (Positive Charge) x:  cos = cos(0) =1 Initial Location (a)  x0 = 0 Final Location (b) Change Potential Energy High Low PE = U = Ub - Ua  – Decreases,  Potential to do Work Potential = V = Vb - Va  – Kinetic Energy KE = K = Kb - Ka  + Increases 

*Electric Field and Energy (Negative Charge) x:  cos(180) = –1 Initial Location (a)  x0 = 0 Final Location (b) Change Potential Energy High Low PE = U = Ub - Ua  – Decreases,  Potential to do Work Potential = V = Vb - Va  – Kinetic Energy KE = K = Kb - Ka  + Increases 

Essential Question(s) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? How do we calculate the electrical work done on a positive and negative charge that moves through a potential difference? How do we apply the Law of Conservation of Energy to determine the speed of a charged particle that has been accelerated through a potential difference? How do we describe and apply the concept of electric fields?

Vocabulary Electric Potential Potential Difference in Potential Volt Voltage Equipotential Lines Equipotential Surfaces Electric Dipole Dipole Moment Electron Volt Cathode Ray Tube Thermionic Emission Cathode Anode Cathode Rays Oscilloscope Scalar Quantity

Agenda Discuss Complete The Four Circles Graphic Organizers The relation between the electric potential and the electric field The relation between the potential energy and the electric force The relation between electric fields and gravitational fields Particles in uniform fields How to derive the potential from the known E-field Derive the electric potential(s) for point charges Complete The Four Circles Graphic Organizers Work on Web Assign

Electrostatic Potential Energy and Potential Difference HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Electrostatic Potential Energy and Potential Difference Thus far, we have identified the following important equations

Relation between Electric Potential and Electric Field HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Relation between Electric Potential and Electric Field By substituting equation (7) into (6): By dividing both sides by q gives:

Electrostatic Potential Energy and Potential Difference HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Electrostatic Potential Energy and Potential Difference From our warm-ups, it is interesting to note that the field will do the same amount of work as confirmed by our warm-up, regardless whether it is a positive charge moving with field or and a negative charge moving in the †opposite direction (†reestablished as a  b ): Work can then be related to the potential by:

Electrostatic Potential Energy and Potential Difference HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Electrostatic Potential Energy and Potential Difference We now have the following equations

Calculating the Potential Difference, Vba, in a Uniform Field HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Calculating the Potential Difference, Vba, in a Uniform Field (1) Because the field and the direction of motion are the same, cos  = 1, (2) Because E is uniform, it can be pulled out of the integral. (3) The negative sign implies that the potential is decreasing as it moves a distance, d, in the electric field.

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Relation to Gravity using the Potential Energy, Uba, in a Uniform Field (1) Because the field (the positive direction) and the direction of motion are the same, cos  = 1, (2) Because the Gravitational Field is uniform at the surface of the Earth, it can be pulled out of the integral. (3) By using the field direction as the positive direction, hi is higher above the surface of the Earth and hf is closer to the ground.

Application: Potential Difference in a Uniform E HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Application: Potential Difference in a Uniform E Two parallel plates are charged to a voltage (aka. potential difference) of 50 V. If the separation between the plates is 5.0 cm, calculate the electric field between them. Note that Va = 50 V and Vb = 0 V, therefore the E field is in the direction of the motion. We could have also established Va = 0 V and Vb = –50 V or Va = 25 V and Vb = –25 V, etc.

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Point Charge

Determination of E: Positive Point Charge HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of E: Positive Point Charge dAsphere A1 + r E

Determination of E: Negative Point Charge HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of E: Negative Point Charge dAsphere A1 – r E

Determination of V from E: Point Charge HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Point Charge + E dr

Electric Potential Due to Point Charges HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Electric Potential Due to Point Charges These plots show the potential due to (a) positive and (b) negative charge.

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Steps to Determine the Potential from the known E-Field Created by a Uniform Charge Distributions Graphical: In relation to the known E-field, determine and draw the initial and final displacement locations. Determine the angle between the direction of motion and the electric field (E•dl). Mathematical: Write the formula for E. Write the formula for potential (V= -∫E•dl ). Calculate the cos  between the direction of motion and the electric field . Set up the integral by determining location of the initial and final displacements. †Solve the integral by using the predetermined locations of the initial and final displacements Write the answer in a concise manner. Verify that the answer makes physical sense. If possible, set the one of the potential to zero at an infinite location away. (ex. Vb= 0 at rb = ∞). Also, note that the negative signs may cancel leaving a positive quantity. Write the answer for the new absolute potential. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook.

GO: The Four Circles (aka. You’re givin’ me fevu?) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? GO: The Four Circles (aka. You’re givin’ me fevu?) Relationships between F, E, V, and U

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Summary Using the following electrostatic equations, develop their gravitational counterparts for force, gravitational field, potential energy and gravitational potential. HW (Place in your agenda): Web Assign 23.3 - 23.4 Future assignments: Electrostatics Lab #4 Report (Due in 2 Classes)

Tuesday (Day 3)

Warm-Up Tues, Mar 3 Suppose an electron in the picture tube of a television set is accelerated from rest through a potential difference Vba = +5000 V. (a) What is the change in potential energy of the electron (me = 9.1 x 10-31 kg)? (b) What is the final speed of the electron? (c) Repeat for a proton (mp = 1.67 x 10-27 kg) that accelerates through a potential difference of Vba = -5000 V. Place your homework on my desk (if applicable): Web Assign: Problems 23.3 & 23.4 For future assignments - check online at www.plutonium-239.com

Application: TV Particles Suppose an electron in the picture tube of a television set is accelerated from rest through a potential difference Vba = +5000 V. (a) What is the change in potential energy of the electron (me = 9.1 x 10-31 kg)? (b) What is the final speed of the electron? (c) Repeat for a proton (mp = 1.67 x 10-27 kg) that accelerates through a potential difference of Vba = -5000 V.

Application: TV Particles (the electron) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Application: TV Particles (the electron) Suppose an electron in the picture tube of a television set is accelerated from rest through a potential difference Vba = +5000 V. (a) What is the change in potential energy of the electron (me = 9.1 x 10-31 kg)? (b) What is the final speed of the electron?

Application: TV Particles (the proton) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Application: TV Particles (the proton) Suppose a proton in the picture tube of a television set is accelerated from rest through a potential difference Vba = -5000 V. (a) What is the change in potential energy of the proton (mp = 1.67 x 10-27 kg)? (b) What is the final speed of the proton?

Essential Question(s) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? How do we calculate the electrical work done on a positive and negative charge that moves through a potential difference? How do we apply the Law of Conservation of Energy to determine the speed of a charged particle that has been accelerated through a potential difference? How do we describe and apply the concept of electric fields?

Vocabulary Electric Potential Potential Difference in Potential Volt Voltage Equipotential Lines Equipotential Surfaces Electric Dipole Dipole Moment Electron Volt Cathode Ray Tube Thermionic Emission Cathode Anode Cathode Rays Oscilloscope Scalar Quantity

Agenda Derive the electric potential(s) for a(n): Conducting sphere Concentric conducting spheres Discuss the determination of potential for multiple point charges Work on Web Assign

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Important Note #1 We will now have the ability to sum up all of the point charges to determine the total potential for any charge distribution. But we will save that for another day . . .

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Important Note #2 We will now have the ability to sum up all of the point charges to determine the total potential energy for any charge distribution. But again we will save that for another day . . .

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Spherical Conductor

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Spherical Conductor E + + dAsphere + A2 + r2 r0 + + r1 + + A1

Determination of V from E: Outside a Spherical Conductor (r > r0) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Outside a Spherical Conductor (r > r0) + + + + r0 + + + + E dr

Determination of V from E: Spherical Conductor Surface (r  r0) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Spherical Conductor Surface (r  r0) + + dAsphere + + r0 + + + + E dr

Determination of V from E: Inside a Spherical Conductor (r < r0) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Inside a Spherical Conductor (r < r0) + + Einside=0 + + r0 dr + + + + E

Plots of E vs. r and of V vs. r: for a single Spherical Conductor

Concentric Conducting Spherical Shells HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Concentric Conducting Spherical Shells

Concentric Conducting Spherical Shells HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Concentric Conducting Spherical Shells – – rb E + + dAsphere – – + A1 + r1 ra + + r2 – – + + A2 – r3 – A3

Determination of V from E: Outside Concentric Spheres (r ≥ rb) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Outside Concentric Spheres (r ≥ rb) – – rb + + – – + + ra + + – – E + + – – dr Eoutside=0

Determination of V from E: Between Concentric Spheres (r  rb) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Between Concentric Spheres (r  rb) – – rb + + – – Einside=0 + + ra E + + – – + + – – dr

Determination of V from E: Between Concentric Spheres (r  ra) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Between Concentric Spheres (r  ra) – – rb + + – – Einside=0 + + ra E + + dr – – + + – –

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Between Concentric Spheres (ra< r < rb) – – rb + + – – + + ra E + + – – dr + + dr – – Eoutside=0

Determination of V from E: Center of Concentric Spheres (r < ra) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Center of Concentric Spheres (r < ra) – – rb + + – – Einside=0 + + ra dr E + + – – + + – –

Determination of V from E: Between Concentric Spheres (r  rm) HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of V from E: Between Concentric Spheres (r  rm) – – rb + + – – Einside=0 + + ra E + + rm – – + + – – dr

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL? Determination of rm where V = 0: Between Concentric Spheres (ra< r < rb) – – rb + + – – + + ra E + + rm – – + + – – Eoutside=0

E(r) for Concentric Spherical Shells Ea Eb r ra rm rb

V(r) for Concentric Spherical Shells Va r ra rm rb Vb