Electromagnetic Waves

Electromagnetic waves are self-propagating transverse waves consisting of oscillating electric and magnetic fields that do not require a medium for propagation.

The whole range of frequencies/wavelengths of electromagnetic waves arranged in ascending or descending order is known as the electromagnetic spectrum.

• Produced by accelerated charges; neither stationary charges nor charges in uniform motion can produce EM waves
• An oscillating charge → oscillating electric field → oscillating magnetic field → the two fields continuously regenerate each other

Nature and Direction

• EM waves are transverse in nature
• The electric field (\[\vec{E}\]) and magnetic field (\[\vec{B}\]) are:
  Perpendicular to each other: \[\vec E\] ⊥ \[\vec B\]
  Both perpendicular to the direction of propagation: \[\vec E\] ⊥ \[\vec B\] ⊥ \[\vec k\]
• \[\vec E\] and \[\vec B\] oscillate sinusoidally and are in phase

Speed

• Speed of EM waves in free space (vacuum):
  c = \[\frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^8 \text{ m/s}\]
• This speed is independent of wavelength
• Speed in a material medium (permittivity ε, permeability μ):
  v = \[\frac{1}{\sqrt{\mu \varepsilon}\]
• All EM waves travel at the same speed (3 × 10⁸ m/s) in a vacuum

Amplitude Relationship

• The magnitudes of the electric and magnetic fields are related by:
  B₀ = \[\frac {E_0}{c}\]
• The ratio of amplitudes of E and B fields equals the velocity of the wave:
  \[\frac {E_0}{B_0}\] = c

Frequency and Wavelength

• The frequency of an EM wave equals the frequency of oscillation of the accelerating charge that produces it
• Obey the wave equation: c = fλ
• When an EM wave travels from one medium to another, frequency does not change — only speed and wavelength change

No Medium Required

• EM waves are non-mechanical waves — they do not require any material medium for propagation
• They can propagate through a vacuum (e.g., sunlight reaching Earth)

Other Wave Behaviours

• EM waves exhibit reflection and refraction without any change in frequency

Order of EM spectrum (increasing wavelength / decreasing frequency):

• EM waves are transverse
• E ⟂ B ⟂ direction of propagation
• E and B are in phase
• Speed:
  \[c=\frac{1}{\sqrt{\mu_0\varepsilon_0}}=3\times10^8\mathrm{m/s}\]
• Poynting Vector:
  \[\vec{S}=\frac{\vec{E}\times\vec{B}}{\mu_{0}}\]

• Intensity:
  \[I=\frac{1}{2}c\varepsilon_0E_0^2\]