Electromagnetic Waves
Electromagnetic waves are produced by accelerated charges and involve mutually perpendicular oscillating electric and magnetic fields. The exam tests Maxwell’s displacement current, wave properties and the electromagnetic spectrum.
Core rules and concepts
- Changing electric field produces displacement current I_d = ε0 dΦE/dt; this completes the circuit in a capacitor and lets Maxwell’s equations give electromagnetic waves.
- EM waves are transverse: E, B and the direction of propagation are mutually perpendicular. E and B oscillate in phase.
- Speed in vacuum c = 1/√(μ0ε0) = 3×10⁸ m s⁻¹; in a medium v = 1/√(με).
- Ratio E0/B0 = c. Energy density is shared equally between electric and magnetic fields; intensity I = ½ε0cE0².
- Spectrum in increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays. Visible runs from red to violet.
Worked example
An EM wave has E0 = 300 V m⁻¹ in vacuum. Find B0 and intensity. B0 = E0/c = 300/(3×10⁸) = 1×10⁻⁶ T. I = ½ε0cE0² = ½(8.85×10⁻¹²)(3×10⁸)(300)² ≈ 1.2×10² W m⁻².
Traps
- Displacement current is not a flow of charge; it is due to a changing electric field.
- EM waves need no medium and can travel through vacuum.
- E and B are in phase, not 90° out of phase.
- Intensity depends on E0², so doubling E0 quadruples intensity.
- Do not reverse the spectrum order; gamma rays have the shortest wavelength.