Physics · Ch 8 — Electromagnetic Waves

Summary

Maxwell’s displacement current: The term $\varepsilon_0 \frac{d\phi_E}{dt}$ added to Ampere’s law, where $\phi_E$ is electric flux. It ensures continuity of current and predicts electromagnetic waves.
Electromagnetic wave generation: An accelerating charge produces oscillating electric ( $\vec{E}$ ) and magnetic ( $\vec{B}$ ) fields, perpendicular to each other and to the direction of propagation.
Transverse nature: $\vec{E}$ and $\vec{B}$ are perpendicular to the wave velocity $\vec{v}$ . For a wave along $x$ , $\vec{E}$ along $y$ , $\vec{B}$ along $z$ .
Speed in vacuum: $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^8 \, \text{m/s}$ .
Relation between fields: $E_0 = c B_0$ (peak values) and $E = cB$ (instantaneous magnitudes).
Energy density: Electric energy density $u_E = \frac{1}{2} \varepsilon_0 E^2$ , magnetic $u_B = \frac{1}{2} \frac{B^2}{\mu_0}$ ; in a wave, $u_E = u_B$ .
Poynting vector: $\vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B})$ gives energy flux (W/m²). Magnitude $S = c u$ , where $u$ is total energy density.
Intensity: Time-averaged power per unit area: $I = \frac{1}{2} c \varepsilon_0 E_0^2 = \frac{1}{2} \frac{c B_0^2}{\mu_0}$ .
Electromagnetic spectrum (increasing frequency): Radio waves → Microwaves → Infrared → Visible → Ultraviolet → X-rays → Gamma rays. All travel at $c$ in vacuum. …