# Concepts 1. Coulomb's law - direction and magnitude of force ... Concepts 1. Coulombs 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 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 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 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??

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 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 K2 C] it goes down by a factor of K D] it goes down by a factor of K2 E] it stays the same.

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 K2). U=Q2/(2C); the capacitance goes up by a factor of K. Note: the energy density for a given E field in a dielectric is

u 12 E 2 The field goes down by a factor of K, but epsilon adds a factor of K. 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 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? Some review questions: Field at S = 0, by superposition. What is the potential at point S? Take potential = 0 at infinity. 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?? 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.

Some review questions: Now, suppose the sphere is a conductor. What is the field at point S? 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? Some review questions: Now, suppose the sphere is a conductor. What is the field at point T, the center of the sphere? Answer = 0. Its a conductor, so there is no field inside (at rest).