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Spinning Spherical Shell with Surface Charge: Vector Potential Calculation

Calculate the vector potential for a spinning spherical shell with uniform surface charge and angular velocity, assuming it lies in the y=0 plane.

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Spinning Spherical Shell with Surface Charge: Vector Potential Calculation

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  1. Example: a spherical shell, radius R, carrying a uniform surface charge s, is spinning at angular velocity w. Find the vector potential. We assume that w lies in the y=0 plane

  2. Note that inside the sphere the magnetic field is uniform:

  3. Example: vector potential of an infinite solenoid with n turns per unit length, radius R, and current I We cannot use previous expressions for the vector potential since the current extends to infinity. However, we note that for r<R for r>R

  4. Magnetostatic Boundary Conditions • The electric field suffers a discontinuity at a surface charge • The magnetic field suffers a discontinuity at a surface current Gaussian pillbox amperian loop

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