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Homework Help: More Vector Potential

  1. May 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the vector potential and magnetic field everyehere of a cylinder of radius R and length L which carries a magnetization [itex] \vec{M} = ks^2 \hat{\phi} [/itex] where k is a constant and s is the distance from the axis of the cylinder.

    2. Relevant equations
    [tex] A(r) = \frac{\mu_{0}}{4\pi}\int \frac{J_{b}(s')}{s'} d\tau' +\frac{mu_{0}}{4\pi} \int\frac{K_{b}(s')}{s'} da'[/tex]

    [tex] B = \nabla \times A [/tex]
    3. The attempt at a solution
    Ok so lets consider the inside part
    the surface charge is zero inside the cylinder
    [tex] A(r) = \frac{\mu_{0}}{4\pi} \int\frac{J_{b}(s')}{s'} d\tau' [/tex]

    [tex] J_{b}(s) = \nabla \times M = 3ks \hat{z} [/tex]

    so [tex] A(r) = \frac{\mu_{0}}{4\pi} \int\frac{J_{b}(s')}{s'} d\tau' [/tex]

    [tex] A(r) = \frac{\mu_{0}}{4\pi} \hat{z}\int\frac{3ks'}{s'} s'ds'd\phi' dz' [/tex]

    is the setup right??

    thanks for your help and advice!!
  2. jcsd
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