Electromagnetic Waves - Quick Revision
Displacement current
- Maxwell found Ampere's law incomplete: a changing electric field also produces a magnetic field.
- Displacement current id = eps0 d(Phi_E)/dt; inside a charging capacitor id equals the conduction current i.
- Ampere-Maxwell law: integral of B.dl = mu0 ic + mu0 eps0 d(Phi_E)/dt.
Maxwell's equations (vacuum), in words
- Gauss for E (flux of E = Q/eps0); Gauss for B (flux of B = 0, no monopoles).
- Faraday (changing magnetic flux makes an E field); Ampere-Maxwell (conduction + displacement current make a B field).
Nature of em waves
- Produced by accelerated (oscillating) charges; an electric dipole is a basic source.
- E, B and the direction of propagation are mutually perpendicular (transverse wave).
- E = E0 sin(kz - wt), B = B0 sin(kz - wt); the fields oscillate in phase.
- Key relations: c = nu lambda, omega = c k, E0 = c B0.
- c = 1/sqrt(mu0 eps0) = 3 x 10^8 m/s in vacuum, same for all wavelengths; in a medium v = 1/sqrt(mu eps) < c.
- Energy density splits equally between E and B; average intensity I = (1/2) c eps0 E0^2.
Electromagnetic spectrum (increasing wavelength)
- gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves.
- Visible band ~ 400-700 nm (4 to 7 x 10^14 Hz). All travel at c in vacuum; they differ only in frequency/wavelength.
Common traps
- Inside a capacitor there is NO conduction current, only displacement current (and vice versa outside).
- c is the same for all wavelengths in vacuum; only the medium slows light.
- E0 = c B0 means B0 is numerically much smaller than E0, but the two carry equal energy.