Electromagnetic Waves (EM Waves)

Topics covered: Maxwell’s equations, nature of electromagnetic waves, energy and momentum of EM waves, production of EM waves, electromagnetic spectrum (JEE Main focus).

1) Maxwell’s Equations (Integral Form)

Gauss’s Law (Electrostatics):

∮ E · dS = q / ε₀

Gauss’s Law (Magnetism):

∮ B · dS = 0

Faraday’s Law of Electromagnetic Induction:

∮ E · dl = − dΦ_B / dt

Ampere–Maxwell Law:

∮ B · dl = μ₀I + μ₀ε₀ dΦ_E / dt

2) Important Features of Electromagnetic Waves

• Electromagnetic waves are transverse waves.
• Electric field (E) and magnetic field (B) oscillate sinusoidally.
• E ⟂ B ⟂ direction of propagation.
• E and B have the same frequency and phase.
• EM waves can propagate through vacuum (non-mechanical waves).
• Direction of propagation is given by E × B.

Speed of EM wave in vacuum:

c = 1 / √(μ₀ε₀) = 3 × 10⁸ m s⁻¹

Relation between amplitudes:

E₀ = cB₀

3) Energy Density of Electromagnetic Wave

Average energy density due to electric field:

U_E = ½ ε₀ ⟨E²⟩ = ¼ ε₀E₀²

Average energy density due to magnetic field:

U_B = ⟨B²⟩ / (2μ₀) = B₀² / (4μ₀)

• In EM waves, U_E = U_B

4) Momentum of Electromagnetic Wave

Electromagnetic waves carry momentum.

Momentum carried by wave of energy U:

p = U / c

According to Planck:

p = h / λ

5) Production of Electromagnetic Waves

• When an electron jumps from a higher to a lower energy level in an atom.
• Accelerated charges (e.g. LC oscillator) produce EM waves.
• X-rays are produced when fast-moving electrons are suddenly stopped by a metal target.

6) Electromagnetic Spectrum

The electromagnetic spectrum arranged in increasing order of wavelength:

• Gamma rays: λ < 6 × 10⁻¹⁹ m
• X-rays: 6 × 10⁻¹⁹ m to 3 × 10⁻⁸ m
• Ultraviolet: 6 × 10⁻¹⁰ m to 4 × 10⁻⁷ m
• Visible light: 4 × 10⁻⁷ m to 8 × 10⁻⁷ m
• Infrared: 8 × 10⁻⁷ m to 3 × 10⁻⁵ m
• Heat radiation: 8 × 10⁻⁵ m to 10⁻¹ m
• Microwaves: 10⁻³ m to 0.03 m
• Ultra-high frequency waves: 10⁻¹ m to 1 m
• Very high frequency waves: 1 m to 10 m
• Radio waves: 10 m to 10⁴ m