A magnetostatic exercise in 10 dimensions

I calculate the electromagnetic field generated by electrical currents in 10 spacetime dimensions (9 space and 1 time). The set up is as follows: the current flows down the positive $x_1$-axis, hits the origin and then spreads out isotropically in the $x_2 x_3 x_4$ subspace, see figure 1 and 2. I wanted to calculate this because in string theory a similar calculation is needed to obtain the Kalb-Ramond field generated by a string ending on a $D3$-brane [1]

A calculation in magnetostatics

I wanted to calculate the magnetic field generated by a current which flows down the positive $z$-axis, hits the origin and then spreads out radially over the $xy$ plane, see figure 1.

Properties of a charged rotating sphere in Maxwell-Chern-Simons theory

I calculate some properties of a charged rotating sphere in five dimensional Maxwell-Chern-Simons theory.

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.

Charged rotating sphere in five dimensions

I calculate the electromagnetic field of a charged rotating sphere in 4 + 1 dimensions. Griffiths calculates the magnetic field of a charged rotating sphere in 3 + 1 dimensions in example 5.11 in his book. In this post, I perform a similar calculation but in 4+1 dimensions.