Electromagnetic Waves — Advanced Multi-Step Practice (Hard)

Quick Recap — Advanced EM Waves (Multi-step)

• Field & energy links: $E_0=cB_0$; average energy density $u=\tfrac12\varepsilon_0 E_0^2$; intensity $I=uc=\tfrac12\varepsilon_0 c E_0^2$.
• Momentum & pressure: absorbed $p=\dfrac{U}{c}$, pressure $\dfrac{I}{c}$; reflected doubles both.
• Photon counting: number per second $=\dfrac{\text{power}}{hf}$; photon momentum $\dfrac{h}{\lambda}$.
• Medium: $v=\dfrac{c}{n}$, $\lambda_{med}=\dfrac{\lambda_{vac}}{n}$, frequency unchanged; $n=\sqrt{\varepsilon_r\mu_r}$.

Worked mini-example. A wave has $E_0=100$ V/m: $I=\tfrac12\varepsilon_0 c E_0^2=\tfrac12(8.85\times10^{-12})(3\times10^8)(10^4)\approx13.3$ W/m$^2$, and it presses on an absorber with $\dfrac{I}{c}\approx4.4\times10^{-8}$ Pa.