Speed of EM Waves in Vacuum

$c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^8 \text{ m/s} \quad [\text{L T}^{-1}]$

$\mu_0 = 4\pi \times 10^{-7}$ H/m; $\varepsilon_0 = 8.85 \times 10^{-12}$ $C^{2}$/(N·$m^{2}$)

Wave Relation

$c = f\lambda \quad [\text{L T}^{-1}] = [\text{T}^{-1}][\text{L}]$

Electric-Magnetic Field Amplitude Ratio

$\frac{E_0}{B_0} = c \quad \Rightarrow \quad B_0 = \frac{E_0}{c}$

Unit check: [V/m] ÷ [T] = [V/m] ÷ [V·s/$m^{2}$] = [m/s] ✓

Intensity of EM Wave

$I = \frac{1}{2}\varepsilon_0 c E_0^2 \quad [\text{M T}^{-3}] = \text{W m}^{-2}$

Proportionality: $I \propto E_0^2$. Doubling $E_{0}$ → intensity × 4.

Displacement Current

$I_d = \varepsilon_0 \frac{d\Phi_E}{dt} = \varepsilon_0 A \frac{dE}{dt} \quad [\text{A}]$

Radiation Momentum and Pressure

$p_{\text{abs}} = \frac{U}{c} \quad [\text{M L T}^{-1}] \qquad p_{\text{refl}} = \frac{2U}{c} \quad [\text{M L T}^{-1}]$

$\text{Pressure}_{\text{abs}} = \frac{I}{c} \quad [\text{M L}^{-1} \text{T}^{-2}] \qquad \text{Pressure}_{\text{refl}} = \frac{2I}{c}$

Ampere-Maxwell Law

$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0\left(I_c + \varepsilon_0 \frac{d\Phi_E}{dt}\right)$

Values to Memorise