# More Vector Potential

1. May 30, 2007

### stunner5000pt

1. The problem statement, all variables and given/known data
Find the vector potential and magnetic field everyehere of a cylinder of radius R and length L which carries a magnetization $\vec{M} = ks^2 \hat{\phi}$ where k is a constant and s is the distance from the axis of the cylinder.

2. Relevant equations
$$A(r) = \frac{\mu_{0}}{4\pi}\int \frac{J_{b}(s')}{s'} d\tau' +\frac{mu_{0}}{4\pi} \int\frac{K_{b}(s')}{s'} da'$$

$$B = \nabla \times A$$
3. The attempt at a solution
Ok so lets consider the inside part
s<R
the surface charge is zero inside the cylinder
so
$$A(r) = \frac{\mu_{0}}{4\pi} \int\frac{J_{b}(s')}{s'} d\tau'$$

$$J_{b}(s) = \nabla \times M = 3ks \hat{z}$$

so $$A(r) = \frac{\mu_{0}}{4\pi} \int\frac{J_{b}(s')}{s'} d\tau'$$

$$A(r) = \frac{\mu_{0}}{4\pi} \hat{z}\int\frac{3ks'}{s'} s'ds'd\phi' dz'$$

is the setup right??