Transverse Nature of EM Waves: Proof and Explanation

An electromagnetic wave is transverse, which means its electric and magnetic fields vibrate at right angles to the direction in which the wave travels. If the wave moves along the x-axis, the electric field may vibrate along y and the magnetic field along z.

Proving the transverse nature matters because it explains polarisation. Longitudinal waves such as sound in air cannot be polarised in the same way, so polarisation experiments are a direct test of the transverse character of light.

Key Concepts

For a plane EM wave in vacuum, E ⊥ B ⊥ direction of propagation. The direction of propagation is given by the cross product E × B. Transverse means the displacement is perpendicular to travel, unlike a longitudinal wave where vibration is parallel to travel. In vacuum Maxwell equations require the divergence of E and B to be zero where there are no charges, which forces the fields of a plane wave to be perpendicular to the wave vector. Polarisation describes the plane in which E vibrates: linear, circular or elliptical.

How It Works

1. Start with a wave travelling along x with wave vector along x.
2. Apply the condition that the electric field has no component along the direction of travel in a source-free region, otherwise a varying longitudinal component would imply charge density oscillations in vacuum.
3. Repeat for the magnetic field, giving B also perpendicular to travel.
4. Use Faraday law to link a changing B to E, which places E and B at right angles to each other.
5. Test with a polariser: rotating a polarising filter changes the transmitted intensity of light, which only happens for transverse waves.

Worked Example

A wave travels in the +z direction with E along +x and amplitude 120 V/m. Find the direction and size of B. Step 1: Propagation is along E × B, so B must be along +y to give x cross y = z. Step 2: Use B = E / c = 120 / (3 × 10^8) = 4.0 × 10^-7 T. Step 3: Check transversality. E is along x, B along y, travel along z; all three are mutually perpendicular, so the wave is transverse. If E had a z component along travel, it would not satisfy the vacuum condition for a simple plane wave.

Common Misconceptions

• Students confuse the direction of E vibration with the direction of travel. The wave energy moves forward while fields vibrate sideways.
• Some think magnetic field vibrates parallel to electric field. In a vacuum plane wave they are perpendicular and in phase.
• Polarisation is sometimes thought to prove particle nature. Polarisation mainly proves transverse wave behaviour.

Real-World Applications

• Polarised sunglasses cut glare because reflected light is partly polarised.
• LCD screens, 3D cinema glasses and optical instruments control polarisation.
• Radio antennas are aligned with the electric field direction of the transmitted transverse wave.

The transverse nature means E and B vibrate sideways to the motion, mutually perpendicular in vacuum. Polarisation experiments confirm this and make many optical devices possible.