Problem set 05

Problem 1

In the 5th chapter of the book is an example (Ex. 5.11 in the 4th edition) about how to calculate the vector potential $\mathbf{A}$ of a rotating uniformly charged spherical shell. Use the results of this example to calculate the magnetic field $\mathbf{B}$ inside a solid sphere with uniform charge distribution $\rho$. The sphere rotates with a constant angular velocity.

Problem 2

Flat conductor parallel to the $x$-$y$-plane with $z$-coordinates restricted between $z=-a$ and $z=a$ carries a free current density $\mathbf{J}=J_0\mathbf{a}_x$. The conductor has magnetic susceptibility $\chi_m =0$. Outside the conductor is a linear magnetic material with susceptibility $\chi_m\neq 0$. Find everywhere $\mathbf{H}$, $\mathbf{B}$, $\mathbf{M}$ and the equivalent magnetization currents.

The problem is due Monday February 17 2025 at 20:00