- #1
icelevistus
- 17
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Express the current density of a spherical shell of radius a, rotating with angular velocity omega, with surface charge density sigma
Delta function will be denoted d(x). Spherical coordinates will be used
I have concluded that for a given chunk (if we restrict to the 0<theta<pi/2 domain), the velocity will be given by v=a*Sin(theta)*(omega). It is clear that the current density will only have a phi component. I have concluded:
J_phi = (sigma)*a*Sin(theta)*(omega)*d(r'-a)
Where the delta function is used to restrict the current density to the sphere's surface.
Can anyone confirm that this reasoning is correct?
Delta function will be denoted d(x). Spherical coordinates will be used
I have concluded that for a given chunk (if we restrict to the 0<theta<pi/2 domain), the velocity will be given by v=a*Sin(theta)*(omega). It is clear that the current density will only have a phi component. I have concluded:
J_phi = (sigma)*a*Sin(theta)*(omega)*d(r'-a)
Where the delta function is used to restrict the current density to the sphere's surface.
Can anyone confirm that this reasoning is correct?