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Surface current density

  1. Jun 24, 2015 #1
    Surface current density, K is defined as:
    K = σv
    where σ is surface charge density and v is velocity.

    Given a uniformly charged spherical shell with radius R, spinning at constant angular velocity ω, find the current.

    So, I start with this formula:
    dI = K dl
    dI = σ Rω dl
    and I placed the spherical shell at cartesian coordinate with its center at origin and try to solve the question in spherical coordinate.

    What path should I take to express dl? Professor explained, dl = R dθ. What I don't understand is, why do we have to take R? Why not R sin(θ)?
  2. jcsd
  3. Jun 24, 2015 #2


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    Science Advisor
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    What might "uniformly" charged mean in this case? Imagine you had 10 wires wrapped round the upper hemisphere. You could do that "uniformly" in two different ways.
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