E&M, Fall '10, Homework 11

Problems from UP Chapter 31

1. Problem 11 ("Two parallel loops")

2. Problem 20 ("semicircle")

3. Problem 37 ("drop to zero")

4. Re-do problem 11 from Chapter 30 (finding the magnetic field produced by a straight wire of length L at a point a distance R from the perpindicular bisector of the wire), but by using Ampere's law instead of the Biot-Savart law. Note that both terms on the right hand side will contribute. Note that charge conservation requires that, if a current i flows through the wire, the endpoints of the wire must be building up charges (one negative, one positive) at a rate equal to i. So then there will be an electric field (whose magnitude depends on r, the distance from the wire) that you can figure out by superposing the contributions from the charges on the ends of the wire.

5. Try to finish the puzzle from the end of Wednesday's class. That is: start with Ampere's law (but without the displacement current term!) in differential form, and try to figure out what you could add to the RHS such that, when you take the divergence, you get something consistent with charge conservation. Hint: it will help to first work out the differential form of Gauss' law.