# Cylinder parallel to a constant external B field

1. Dec 8, 2015

### sayebms

1. The problem statement, all variables and given/known data
A cylinder of permeability $\mu$ is placed in an external field $B_0$. find the strength and direction of magnetic field inside the cylinder for:
a) when axis of cylinder is parallel to external field.
b) when axis of cylinder makes an angle $\theta _0$ with external field.

2. Relevant equations
Conditions of magneto statics:$$\nabla \times H =0\\H=-\nabla{\phi}\\\nabla^2{\phi}=0$$
the Laplace operator is in cylindrical coordinates

3. The attempt at a solution
for part a I take B to be in x direction. its clear from the problem that there is a symmetry in the $\phi$ direction so this means that the magnetic scalar potential does not depend on $\phi$. hence the Laplace equation reduces to $$\frac{1}{\rho}\frac{\partial}{\partial{\rho}}(\rho \frac{\partial \phi}{\partial{\rho}})+\frac{\partial^2\phi}{\partial z^2}=0$$ but here is the problem; I know that the magnetic field outside and far from cylinder must be a constant ($B_0$) which means that potential must have a term first order in $z$ but as we see from the Laplace equation we don't get such a thing. what am I doing wrong here? is this even the right approach for solving this problem?

2. Dec 13, 2015