Introduction to Electrodynamics · Problem 10.24

Potentials and Fields — David J. Griffiths

Physics · retarded-potentials

Problem

Suppose you take a plastic ring of radius

a

and glue charge on it, so that the line charge density is

\lambda_0|\sin(\theta/2)|

. Then you spin the loop about its axis at an angular velocity

\omega

. Find the (exact) scalar and vector potentials at the center of the ring.

\left[Answer: \mathbf{A} = (\mu_0\lambda_0\omega a/3\pi)\left\{\sin[\omega(t-a/c)]\,\hat{\mathbf{x}} - \cos[\omega(t-a/c)]\,\hat{\mathbf{y}}\right\}\right]