Electromagnetic Waves — Nature & Speed (Medium)

Quick Recap — Nature & Speed of EM Waves

• Maxwell: a changing electric field acts as a displacement current $I_d=\varepsilon_0\dfrac{d\Phi_E}{dt}$, completing Ampere's law and predicting EM waves.
• Structure: $\vec E\perp\vec B\perp$ direction of propagation (transverse); the fields oscillate in phase, and propagation is along $\vec E\times\vec B$.
• Speed: in vacuum $c=\dfrac{1}{\sqrt{\mu_0\varepsilon_0}}=3\times10^8$ m/s (the same for all frequencies); in a medium $v=\dfrac{1}{\sqrt{\mu\varepsilon}}=\dfrac{c}{n}$, with $n\approx\sqrt{\varepsilon_r}$.
• Amplitude relation: $\dfrac{E_0}{B_0}=c$, i.e. $E=cB$.

Worked mini-example. If $B_0=2\times10^{-8}$ T, then $E_0=cB_0=3\times10^8\times2\times10^{-8}=6$ V/m.