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Homework Help: Magnetic field of a hollow cylinder

  1. Dec 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Find an expression for the magnetic field of a hollow finite solenoid carrying uniform current with n turns (there is no top or bottom surfaces and the turns a very closely winded) at a point arbitrary P both inside and outside. Lets just say windings around a hollow pvc pipe.

    2. Relevant equations
    I can use either biot savarts law and/or magnetic vector potential for surface currents. I'll use griffiths notation 3rd edition equations 5.39 and 5.64 respectively.

    3. The attempt at a solution
    I'll attempt this in cylinderical coordinates. Since the current is uniform. I'll use the


    Current density [itex]\vec{K}[/itex] is in the [itex]\hat{\phi}[/itex]

    so [itex]\vec{K}=\frac{nI}{z'}\hat{\phi}[/itex] ? Since current is uniform.



    Where the limits of phi' is 0->2*pi and z' is 0 -> L (length of cylinder)
  2. jcsd
  3. Dec 1, 2013 #2
    Do you have an image of the particular set-up? Or could you reference to one in Griffiths?
  4. Dec 1, 2013 #3
    Hi Sandy, I just attached an image file its just turns of wire wrapped around a pvc. I looked up a few things I think I have to use elliptic integrals... My first aim is to write an expression for the current density and the position and source vectors r and r'.

    Attached Files:

  5. Dec 1, 2013 #4
    Are you neglecting fringing? If you use Biot-Savart, have you considered analyzing a single loop, and then applying superposition to n loops?
  6. Dec 1, 2013 #5
    I've thought about that since Jackson's has a solution to a single loop of wire. But I'm going to be inserting a ferromagntic material inside at some stage so I might need to take fringing fields into account?
  7. Dec 4, 2013 #6
    Well, I am not really in a position to help you with the fringing effects as I only have experience at the undergraduate level thus far.
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