Electric Dipole Radiation Pattern

Far-field radiation pattern, polarization, and total radiated power of an oscillating electric dipole
3D Pattern
Polar Plot
Wave Fronts
P = 1.00 (rel.)
Total radiated power ∝ ω⁴p₀²

Larmor Radiation Formula

An oscillating electric dipole p = p₀cos(ωt) ẑ radiates electromagnetic waves. The angular power distribution is:

dP/dΩ = (μ₀ω⁴p₀²)/(32π²c) · sin²θ

Maximum radiation is perpendicular to the dipole axis; zero radiation along the axis. Total power:

P = μ₀ω⁴p₀² / (12πc)

The sin²θ "donut" pattern is fundamental to antenna theory (half-wave dipole antenna), Rayleigh scattering (why sky is blue: ω⁴ → shorter wavelengths scatter more), and atomic spontaneous emission.