1. Concepts 1. Coulomb ’ s law – direction and magnitude of force 2. Superposition – add forces (fields) vectorially Field lines & Flux 3. Gauss ’ law – application to find E 4. Gauss ’ law – consequences for charge on conductors 5. Superposition ‘ fails ’ with conductors & charge redistribution 6. Potential -> potential energy -> work done 7. Superposition of potentials – scalars 8. Field is – gradient of potential. Field may be zero when potential ≠ 0. & vice versa 9. Field can only be calculated if we know potential in the vicinity of p. 10. Capacitance & Field energy. What happens to voltage on plates if we change separation, insert a dielectric? Caps in series & parallel

2. If I put a charge ±Q on a parallel plate capacitor and increase the plate separation, what happens to V? A] it increases B] it decreases C] it stays the same

3. If I put a charge ±Q on a parallel plate capacitor and increase the plate separation, what happens to V? The field is the same, but the distance is larger. So V increases. What happens to the potential energy U? A] it increases B] it decreases C] it stays the same

4. If I put a charge ±Q on a parallel plate capacitor and increase the plate separation, what happens to V? The field is the same, but the distance is larger. So V increases. What happens to the potential energy U? A] it increases The energy density u is the same, but there is more volume. Where did this energy come from??

5. If I put a charge ±Q on a parallel plate capacitor and insert a dielectric, what happens to V? A] it increases B] it decreases C] it stays the same

6. If I put a charge ±Q on a parallel plate capacitor and insert a dielectric, what happens to V? The field in the dielectric is reduced by a factor of K. So the potential goes down. What happens to the potential energy? A] it goes up by a factor of K B] it goes up by a factor of K 2 C] it goes down by a factor of K D] it goes down by a factor of K 2 E] it stays the same.

7. If I put a charge ±Q on a parallel plate capacitor and insert a dielectric, what happens to V? What happens to the potential energy? It may be counterintuitive, but the potential energy goes down by a factor of K (not K 2 ). U=Q 2 /(2C); the capacitance goes up by a factor of K. Note: the energy density for a given E field in a dielectric is The field goes down by a factor of K, but epsilon adds a factor of K.

8. If the potential energy goes down, where does the energy go? The field pulls the dielectric into the capacitor, giving it kinetic energy. (Very small, here.) Application: Optical tweezers

9. Some review questions: An insulating sphere has charge +Q distributed uniformly throughout. Another charge +Q is located a distance r from the surface. (Note: you may ignore induced surface charges for these kinds of calculations. We call this a “perfect” insulator, K=0) What is the magnitude of the E field at point S?

10. Some review questions: Field at S = 0, by superposition. What is the potential at point S? Take potential = 0 at infinity.

11. Some review questions: Field at S = 0, by superposition. Potential at S = ans C, by superposition. What is the field at point T, at the center of the sphere??

12. Some review questions: Field at S = 0, by superposition. Potential at S = ans C, by superposition. Field at the center of the sphere = ans. B. Sphere gives 0 contribution.

13. Some review questions: Now, suppose the sphere is a conductor. What is the field at point S?

14. Some review questions: Now, suppose the sphere is a conductor. What is the field at point S? Answer=E. We cannot solve this problem, because the charge on the sphere will move around. What is the field at point T, the center of the sphere?

15. Some review questions: Now, suppose the sphere is a conductor. What is the field at point T, the center of the sphere? Answer = 0. It’s a conductor, so there is no field inside (at rest).