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Angular momentum of the EM field of rotating sphere

  1. Apr 6, 2013 #1
    The angular momentum of the electromagnetic field is defined as,

    $$
    \vec{L_{em}} = \int \vec{l_{em}} d^3r.
    $$

    To solve this for a rotating sphere I must consider the cases where r < R and r > R.

    When I did this problem I thought that there would be two solutions, one for both cases; however, it turns out that there is one solution,

    $$
    \vec{L_{em}} = \int \vec{l_{em}}_{(r<R)} \, d^3r + \int \vec{l_{em}}_{(r>R)} \, d^3r.
    $$

    Can anyone tell me why that is? Conceptually I do not understand what is going here.
     
  2. jcsd
  3. Apr 8, 2013 #2
    Also for the integration, would I integrate the r < R case from [itex] \int_0^R = \int_0^r + \int_r^R [/itex] and the case of r > R, [itex] \int_R^{\infty} [/itex]?

    Or would I simply just integrate [itex] \int_0^R [/itex] for both cases, without splitting the integral.
     
    Last edited: Apr 8, 2013
  4. Apr 9, 2013 #3
    I suppose when calculating the field angular momentum, we do not need to split the r < R integral [itex] \int_0^R [/itex]. I also understand now that we are integrating over all space or over the entire field.
     
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