Problem 1 [40 points]
Consider a point charge q moving in a circular orbit of radius R, centered about the origin in the xy plane. The charge is orbiting counterclockwise with an angular velocity ω . Working within the electric dipole approximation:
a) Compute the radiated electric and magnetic fields, expressing your answer in terms of spherical coordinates. Make sure your answers are given as real valued functions!
b) What is the polarization of the outgoing radiation at a general spherical angle (θ,φ)? What is the polarization when θ=0? when θ=π/2?
Hint: The trick to doing this problem easily is to figure out how to write the oscillating dipole moment as p(t)=Re [pωe-iωt], with the correct amplitude pω.