• Tags: energy-density, Poynting, momentum
• Difficulty: Advanced

EM waves carry energy. Energy density: u = u_E + u_B = (1/2)epsilon_0E^2 + B^2/(2mu_0). At any instant, u_E = u_B (electric and magnetic energies are equal). Using E = cB: u = epsilon_0E^2 = B^2/mu_0. The Poynting vector S = (1/mu_0)(E x B) gives the energy flow rate per unit area (W/m^2). Its direction is the direction of wave propagation (E x B). Magnitude: S = EB/mu_0 = E^2/(mu_0c) = cB^2/mu_0. Average intensity: I = = E_0B_0/(2mu_0) = (1/2)cepsilon_0E_0^2 = c. EM waves also carry momentum: p = U/c for complete absorption and p = 2U/c for perfect reflection, where U is the energy incident on the surface. Radiation pressure: P = I/c (absorbing), P = 2I/c (reflecting). Though tiny for everyday light, radiation pressure is significant for comets (tail pushed away from Sun) and in stellar interiors.