Dipole Radiation in 3D

An oscillating dipole radiates with the angular pattern $\sin^2(\theta)$, the toroidal donut shown here as a rotating projected surface with the pulsing source and outgoing wavefronts. The time-averaged power is the Larmor form $P = \mu_0 p_0^2 \omega^4 / (12\pi c)$, scaling as $\omega^4$, and in the far zone $E$, $B$ and $\hat{r}$ are mutually orthogonal with $|E| = c|B|$. Nothing is radiated along the dipole axis and the emission peaks broadside; the steep $\omega^4$ dependence is why the sky is blue (Rayleigh scattering). Switch to a magnetic dipole (same pattern, swapped polarization) or a half-wave antenna (sharper lobes, higher directivity); the side panel shows the polar pattern with the radiated power and directivity.