E&M, Fall '10, Homework 10

Problems from UP Chapter 30

1. Problem 11 ("straight wire")

2. Problem 30 ("idealized schematic")

3. Problem 41 ("conducting sheet")

4. Imagine a hollow cardboard cylinder (like a paper towel roll) with length L and radius R. Suppose it is given a total electric charge Q, uniformly distributed over its area. And suppose it is rotating around its symmetry axis with a period T. What is the *magnetic* field near the middle of it?

5. Consider a circular loop of wire, radius R, carrying current i. In class we talked about how the magnetic field in the plane of and inside the circle varies, but only a little, at different points within the circle. Use the Biot-Savart law to write an *exact* expression for the magnitude of the field at a point a distance d (d < R) from the center of the circle. This will be an integral, and I think you'll get an integral you can't do. So most of the point here is to work through trying to set it up carefully. In particular, try to get all of the stuff in the integrand in terms of a single independent variable such that it's really genuinely "just math" to do the integral. Maybe you can do the integral, or maybe not.