Past exam of the optics and electrodynamics course of the University of Cambridge / 2019 / Section B / B4 / Linear oscillation

For the prescribed displacement along $z$, the source acceleration is $\mathbf{a}(t_r)=-a{\omega }^2\cos (\omega t_r)\hat{\mathbf{z}}$. If $\theta$ is the angle from the $z$ axis, $|\mathbf{a}{|}^2-(\mathbf{n}\cdot \mathbf{a}{)}^2=a^2{\omega }^4{\cos }^2(\omega t_r){\sin }^2\theta$. Averaging ${\cos }^2$ over one wave period givesThe angular distribution of electric dipole radiation has zero intensity on the oscillation axis and maximum intensity in the equatorial plane, with no azimuthal dependence. Its total power isThe condition $a\omega \ll c$ is the required nonrelativistic condition. The plotted radial coordinate below is angular power, rather than field wave amplitude.