Average of a magnetic field in D dimensions

I solve problem 5.57 in Griffiths, Introduction to Electrodynamics. This problem asks to calculate the average of a magnetic field over a ball; I solve it in \( D \ge 3 \) space dimensions.

A troublesome integral

I calculate an integral that I need when solving problem 5.57 in Griffiths, Introduction to Electrodynamics. I generalized the exercise to \( D \) dimensions.

Electromagnetic properties of a charged rotating sphere

I calculate some properties of the electromagnetic field of a charged rotating sphere.

Charged rotating sphere in Maxwell-Chern-Simons theory

I calculate the electromagnetic field of a charged rotating sphere in five dimensional Maxwell-Chern-Simons theory.