Understand transverse nature, E ⊥ B relation, velocity of EM waves, E₀/B₀ = c, polarisation, energy density, Poynting vector, momentum, radiation pressure and advanced numerical applications.
Still Confused in Electromagnetic Waves?
If transverse nature, E ⊥ B relation, polarisation, radiation pressure, momentum, energy density or EM-wave numericals are not clear, students can contact Kumar Sir for one-to-one Physics guidance.
Electromagnetic waves are waves of oscillating electric and magnetic fields. Maxwell predicted that a changing electric field produces a magnetic field and a changing magnetic field produces an electric field. This self-sustaining mechanism allows EM waves to travel even through vacuum.
Mechanical waves Require a material medium. Sound waves need air, water or solid particles for propagation.
Electromagnetic waves Do not require a material medium. Light from the Sun reaches Earth through vacuum because EM waves are field waves.
Section 2: Transverse Nature of EM Waves
EM waves are transverse because both electric and magnetic fields oscillate perpendicular to the direction of propagation. A longitudinal EM wave in vacuum is impossible because Maxwell equations require the fields to be divergence-free away from charges and perpendicular to the direction of energy flow.
E ⊥ B
E ⊥ direction
B ⊥ direction
E ⊥ B ⊥ c
Concept Example 1 If propagation is +x and E is +y, then B must be +z.
Concept Example 2 If propagation is +z and E is +x, then B must be +y.
Concept Example 3 If E and B are parallel, E × B = 0, so there is no propagation direction.
Section 3: E ⊥ B ⊥ Direction of Propagation
For propagation along +x direction:
Ey = E0 sin(kx - ωt)Bz = B0 sin(kx - ωt)
Electric field is along y-axis, magnetic field is along z-axis and propagation is along x-axis. The right-hand rule gives E × B = direction of propagation.
Section 4: Velocity of Electromagnetic Waves
Vacuum
c = 1 / √(μ0ε0)
Substituting μ0 = 4π × 10-7 and ε0 = 8.854 × 10-12 gives c ≈ 3 × 108 m/s.
Medium
v = 1 / √(με)
In a medium, permeability μ and permittivity ε determine the wave speed, so v is generally less than c.
Physical significance: Maxwell's value matched the speed of light, proving that light is an electromagnetic wave. Radio waves, microwaves, visible light, X-rays and gamma rays all travel at c in vacuum.
Section 5: Relation E₀/B₀ = c
Amplitude Relation
E0 = cB0E0/B0 = c
Meaning: E0 is the electric field amplitude in V/m. B0 is the magnetic field amplitude in tesla. Their ratio is the speed of the wave in vacuum.
Unit analysis: (V/m)/T = (N/C)/(N/(A m)) = A m/C = m/s because A = C/s.
Section 6: Energy Density of EM Waves
ElectricUE = 1/2 ε0E²
MagneticUB = B²/(2μ0)
Equal sharingUE = UB
TotalU = UE + UB = ε0E²
Using E = cB and c² = 1/(μ0ε0), electric and magnetic energy densities become equal. This means energy is equally shared between electric and magnetic fields.
Section 7: Poynting Vector
S = (E × B)/μ0
The Poynting vector gives the rate of energy flow per unit area. Its direction is the direction of propagation and its SI unit is W/m².
Section 8: Polarisation
Polarisation is the restriction of vibrations of a transverse wave to one plane. Only transverse waves can be polarised, so polarisation is strong evidence that electromagnetic waves are transverse.
Polariser Allows only one component of the electric field to pass.
Proof of transverse nature Longitudinal waves cannot be polarised because their oscillations are along propagation.
Wrong photon relation For EM radiation, energy and momentum follow E = pc.
Mixing absorbing and reflecting force Use F = IA/c for absorption and F = 2IA/c for reflection.
Section 16: Final Revision Sheet
E ⊥ B ⊥ c
c = 1/√(μ₀ε₀)
v = 1/√(με)
E₀ = cB₀
E₀/B₀ = c
UE = 1/2 ε₀E²
UB = B²/2μ₀
UE = UB
U = ε₀E²
S = (E × B)/μ₀
E = pc
Pabs = I/c
Pref = 2I/c
Fabs = IA/c
Fref = 2IA/c
Still Confused in Electromagnetic Waves?
If transverse nature, E ⊥ B relation, polarisation, radiation pressure, momentum, energy density or EM-wave numericals are not clear, students can contact Kumar Sir for one-to-one Physics guidance.
