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Homework Help: Cylinder parallel to a constant external B field

  1. Dec 8, 2015 #1
    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. jcsd
  3. Dec 13, 2015 #2
    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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