Electromagnetic Waves — Energy, Momentum & Spectrum (Medium)

Quick Recap — Energy, Momentum & the Spectrum

• Energy density: $u=\tfrac12\varepsilon_0 E^2+\dfrac{B^2}{2\mu_0}$ — the electric and magnetic parts are equal; averaged, $u_{avg}=\tfrac12\varepsilon_0 E_0^2$.
• Intensity: $I=u_{avg}\,c=\tfrac12\varepsilon_0 E_0^2 c$. Momentum: an EM wave carries momentum $p=\dfrac{U}{c}$; radiation pressure $=\dfrac{I}{c}$ (absorbed) or $\dfrac{2I}{c}$ (reflected).
• EM spectrum (increasing frequency / decreasing wavelength): radio $\to$ microwave $\to$ infrared $\to$ visible ($\approx400$–$700$ nm) $\to$ ultraviolet $\to$ X-ray $\to$ gamma.
• Photon energy $E=hf$: gamma rays are the most energetic, radio waves the least.

Worked mini-example. A wave with $E_0=100$ V/m has intensity $I=\tfrac12\varepsilon_0 E_0^2 c=\tfrac12(8.85\times10^{-12})(10^4)(3\times10^8)\approx13.3$ W/m$^2$.