4) [25 points total Consider the radiation emitted by a thin circu...

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4) [25 points total Consider the radiation emitted by a thin circular wire loop of radius R, centered about the origin in the xy plane at Z = 0. The current flowing in the loop is given by I(y,t) = where 4 is the usual azimuthal angle in spherical coordinates (i.e. the angle in the xy plane). . The frequency W is such that Rw < C. a) [8 pts If n = 0, show that there is magnetic dipole radiation but no electric dipole radiation. b) [8 pts If n = 1, show that there is electric dipole radiation but no magnetic dipole radiation. c) [9 pts If n = 2, show that there is neither electric dipole nor magnetic dipole radiation. What happens in this case? You must do a calculation or give a convincing argument to support your answer, not just give a guess. Hint: For all parts, think about what the charge in the loop is doing. If you argue convinc- ingly, you don't need to do an involved calculation.

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