Chapter 31, Problem 42AP

You are working on an LC circuit for an experiment you are performing in your basement. You have an appropriate capacitor, but you need to build your own inductor. You wish to cut a wooden ring with a rectangular cross section, as shown in Figure P31.41, from wood with thickness h. You want to wrap N turns of wire around it to form a toroidal inductor. For your experiment, you need to have energy U_B stored in the inductor when it carries a current i. In order to cut the appropriate wooden ring, you need to determine the ratio b/a. Ignore any effect of the wood core on the magnetic field.