Cylinder parallel to a constant external B field

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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]
 

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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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