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

EM waves carry energy. Energy density: u = $u_E$ + $u_B$ = $\frac{1}{2}$$epsilon_0$$E^2$ + B^$\frac{2}{2*mu_0}$. At any instant, $u_E$ = $u_B$ (electric and magnetic energies are equal). Using E = cB: u = $epsilon_0$$E^2$ = $B^2$/$mu_0$. The Poynting vector S = $\frac{1}{mu_0}$(E x B) gives the energy flow rate per unit area (W/$m^2$). Its direction is the direction of wave propagation (E x B). Magnitude: S = $\frac{EB}{mu_0}$ = E^$\frac{2}{mu_0*c}$ = $cB^2$/$mu_0$. Average intensity: I = = $E_0$$\frac{B_0}{2*mu_0}$ = $\frac{1}{2}$c$epsilon_0$$E_0^2$ = c*. EM waves also carry momentum: p = $\frac{U}{c}$ for complete absorption and p = 2U/c for perfect reflection, where U is the energy incident on the surface. Radiation pressure: P = $\frac{I}{c}$ (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.