# Cylinder parallel to a constant external B field

## Homework Statement

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.

## Homework Equations

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

## 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? [/B]