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Homework Help: Meissner Effect

  1. Oct 2, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider a sphere of type 1 superconductor with critical field Hc. (a) Show that in the Meissner regime the effective magnetisation M ithin the sphere is given by [tex] -3B_a/2\mu_0[/tex] (where Ba is the uniform applied magnetic field).

    (b) Show that the magnetic field at the surface of the sphere in the equatorial plane is [tex] 3B_a/2[/tex]. (It follows that the applied field at which the Meissner effect starts to break down is [tex] 2H_c/3[/tex].

    Reminder: The demagnetisation field of a uniformly magnetised sphere is -M/3.

    2. Relevant equations

    [tex] H = H_a - H_d[/tex]

    [tex] H_a = B_a/ \mu_0 + M[/tex]

    [tex] m = MV [/tex] magnetic field of a magnetic dipole where V is the volume of the sphere

    3. The attempt at a solution

    The first part of this question is quite easy. I'm given the demagnetisation field for a uniformly magnetised sphere and I know that with the Meissner effect in superconductors, the field inside must be equal to 0. So I used the expression for the applied field (second equation) and substituted it into the first equation with Hd = -M/3. This was then set to 0 and I solved for M.

    The second part of the question is what I really need help on. I don't really understand how to do this at all. I know that the magnetic field outside of the sphere is the magnetic field of a magnetic dipole, but I don't really know the significance of this. It was just a hint that we were meant to use this.

    i.e. [tex] m = (4 \pi/3 )r^3M[/tex] r is the radius of the sphere

    I'd appreciate any ideas on how to approach this second part of the problem. I'm sorry that I don't have much of an attempt for this, but I just don't have an idea of how to start this second part. You obviously need to consider that you are in equatorial plane, but I just can't see how to do this.
    Last edited: Oct 2, 2007
  2. jcsd
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