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Magnetic field in a cavity

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data
    We are given an infinitely long cylinder of radius b with an empty cylinder (not coaxial) cut out of it, of radius a. The system carries a steady current (direction along the cylinders) of size I. I am trying to find the magnetic field at a point in the hollow. I am told that the answer is that the magnetic field is uniform throughout the cavity. and is proportional to [itex]d\over b^2-a^2[/itex] where [itex]d[/itex] is the distance between the centers of the cylinders.

    3. The attempt at a solution

    I have found by using Ampere's law that the magnetic field at a point at distance r from the axis in a cylinder of radius R carrying a steady current, I, is given by [itex]\mu_0 I r\over 2\pi R^2[/itex]. So I thought I would use superposition. But what I get is [itex]{\mu_0 I \sqrt{(x-d)^2+y^2}\over 2\pi b^2}-{\mu_0 I \sqrt{(x)^2+y^2}\over 2\pi a^2}[/itex]. However this is not the given answer!
  2. jcsd
  3. Feb 29, 2012 #2
    You are on the right track, but you have to superpose the magnetic field vectors.
  4. Feb 29, 2012 #3
    @M Quack: Thank you. I don't know how to change these into vectors, could you please kindly give me another nudge? Thanks again.
  5. Feb 29, 2012 #4
    The magnetic field generated by a long wire goes right around the wire. So it is perpendicular to the raidal vector.

    If the wire is along (0,0,z) and your point at (x,y,z), you know that B_z=0 and that
    B is perpendicular to (x,y,0). What vector has these properties?
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