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H and B field at the midpoint inside of a magnet

  1. Oct 25, 2008 #1
    1. The problem statement, all variables and given/known data
    For a magnet of length l = 16 cm, cross-section .25 cm^2, and magnetization M = 7.8x10^5 A/m, estimate H and B at the midpoint.

    2. Relevant equations
    Unsure if any of these equations are relevant, but these are the ones that I've tried.

    q_m = MA
    B = \mu_0 M
    \mu_0 H = \mu_0 M

    3. The attempt at a solution
    The answers given in the book are H = 485 A/m, B = .98T. By just randomly plugging stuff into equations, I figured out that B = \mu_0 M applies. However, I can't explain why (I need to justify all of our answers, I can't just throw around equations). The book isn't very clear as to what situations that this applies in.

    I have yet to figure out how they got H = 485 A/m. Does it have anything to do with the hysteresis loop of the magnet? If so, how would I figure out the hysteresis loop specific to this magnet?

    I've noticed that I have yet to take into account the length or cross-sectional area of the magnet. However, I can't find any equations where those would be useful. I tried calculating the B-field from the equation for a magnetic dipole and that was incorrect. I thought about taking q_m and -q_m to be distributed evenly across across the north and south poles and then using a triple integral to find the B and H fields, but there haven't been any integrals used in the chapter related to this kind of problem, and besides that I haven't even learned how to do triple integrals yet, so I figured that that would be a dead end.

    So, I'm at a loss of what to do now. I kind of wish that I had a textbook that explained things better. Are there any online physics 2 textbooks I could consult?

    Edit: Right after I made this post I figured out that B = \mu_0 (H + M) applies, but that still doesn't explain why B = \mu_0 M worked.

    Edit2: Another relation: B = 2 pi k_m M^2 A / q_m sort of works. It's the equation for lifting strength, but it's off by a factor of 2. How can I justify that the lifting strength of the center of the magnet is twice as strong in the center of the magnet as it is from one pole? Would saying that both sides of the magnet are being attracted to a soft magnet be correct?
    Last edited: Oct 25, 2008
  2. jcsd
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