If you can help with even one part of this problem it would be a big help. Thanks
Two halves of a spherical metallic shell of radius R and infinite conductivity are separated by a very small, insulating gap. A potential is applied on the two halves of the sphere, such that the upper half is at potential +V, the lower half at potential -V.
1) Find the solutions for the potential in terms of the Legendre polynomials. What's the leading term outside teh sphere in the long wavelength limit?
2) Determine the electric dipole moment of the sphere as a function of V.
3) If the potential were alternating as +/- V cos wt, take the long wavelength limit. Find the radiation fields, angular distribution of radiated power, and total radiated power.
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If you can help with even one part of this problem it would be a big...
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