# Magnetic field of a cylinder with magnetization M=ks^2

1. Jan 28, 2012

### JFuld

1. The problem statement, all variables and given/known data[/b]

this is griffiths 6.8 fyi.

a long cylinder of radius R carries magnetization M=ks^2 $\hat{∅}$, k is a constant and s is the distance from the axis. $\hat{∅}$ is the azimuthal unit vector. find the magnetic field inside and outside the cylinder.

2. Relevant equations

bound volume current Jb= $\nabla$XM
bound surface current Kb=MX$\hat{n}$

A(r)=μo/4π∫Jb(r')/(script r) dV' + μo/4π∫Kb(r')/(script r) da'

script r = r' - r

3. The attempt at a solution

first thing i did was to find the bound currents.

Jb = 3ks $\hat{z}$,

Kb=ks^2 $\hat{s}$ (on the top surface)

Kb= -ks^2 $\hat{s}$ (on the bottom surface)

Kb = -kR^2 $\hat{z}$ (on the walls of the cylinder)

Now I am stuck. I was thinking I should plug the bound currents into the equation for A(r), and find B by taking the curl of A(r). However, I am confused on what r' or script r would be. If any body could help me out there I would apreciate it.

I am not sure if amperes law would work here, no single amperian loop would incorporate every bound current so maybe I should break the problem into multiple pieces?