Question

For a charge e rotating in the x-y plane at radius a and angular speed w, show that there is only a z component of radiated angular momentum with magnitude dLz/dt=e²k³a²/6πϵ₀. What about a charge oscillating along the z axis?

For a charge e rotating in the x-y plane at radius a and angular speed w, show that there is only a z component of radiated angular momentum with mag- nitude dLz/dt = e2kw6πε0, what about a charge oscillating along the z axis?

Answer 1

We know that the rate of radiation of electromagnetic angular momentum is, dL dt 12πε0 The time-dependent charge density ofa moving charge is, The dipole moment is On Substituting and Integrating, p=ea@cos ar + y sin or) = Real ea(^+ iv) e-lar If the harmonic behaviour is not considered, the complex dipole moment is, Therefore, dL eka dt 12πεο ek a 12 πε0 6 πε dL For a charge oscillating along z axis, p pz. For this case,--0 dt