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Homework Help: A question from my EMF exam

  1. Jul 15, 2010 #1
    1. The problem statement, all variables and given/known data

    An infinte cylinder (radius a) with a uniform volume charge density rho_v is given. The axis of the cylinder coincides with the z axis. The following magnetic field exists:

    B=B0cos(wt+a) for r<=a (i.e., inside the cylinder and on its walls)
    B=0 for r>a (i.e., outside the cylinder)

    One asks:

    1) What is the magnetic vector potential everywhere
    2) What is the electric field everywhere
    3) What can one learn from the magnetic field boundary conditions

    3. The attempt at a solution

    Unfortunately, I do not have any clue how to address this question. There is a static charge which generated a static electric field, and there is an induced electric field due to the alternating magnetic field. Is the overall electric field a superposition of the two electric fields or am I mistaken ? Do the boundary conditions imply that the cylinder behaves as an ideal solenoid ? Do I only need to find the rotor of the magnetic field to get the magnetic vector potential ?

    Thank you for the help !!!
    Last edited: Jul 15, 2010
  2. jcsd
  3. Jul 16, 2010 #2
    It's straightforth once you use Maxwell's equations (with vector potential).
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