12.2.3 Electromagnetic waves

Electromagnetic (EM) Waves

Electromagnetic waves consist of alternating electric and magnetic fields that travel together in phase. These fields oscillate perpendicularly to each other and in the direction perpendicular to the wave's propagation. This transverse wave nature means that as the electric field oscillates up and down, the magnetic field oscillates side to side, and both are perpendicular to the direction of energy transfer. The wavelength (λ) is the distance between peaks of the electric or magnetic fields in the wave.

Maxwell's Prediction of EM Waves

James Clerk Maxwell proposed the existence of electromagnetic waves and derived an equation for their speed in a vacuum (c) even before they were experimentally observed. The speed of EM waves, including visible light, in a vacuum is given by:

$$c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$$

Where:

• $\mu_0$ is the permeability of free space (relating the magnetic field to current),
• $\varepsilon_0$ is the permittivity of free space (relating the electric field to charge). This relationship indicates that the speed of light in a vacuum is determined by the fundamental properties of electric and magnetic fields.

Hertz's Experimental Confirmation

Heinrich Hertz experimentally confirmed the existence of radio waves, a type of EM wave, through an apparatus involving a spark gap transmitter. High voltage sparks produced in the transmitter generated radio waves, which were detected using:

1. Dipole receiver - detected the electric field of the radio waves by placing parallel metal plates to form sparks.
2. Loop of wire with a gap - detected the magnetic field of the radio waves through induced current that created a visible spark in the gap.

Confirming Wave Properties

To confirm that radio waves were indeed electromagnetic, Hertz placed a metal sheet in front of the transmitter. This caused stationary waves (standing waves) to form as the radio waves reflected back. By observing nodes and antinodes (points of no movement and maximum movement respectively), he could measure the wavelength of the radio waves. Combining wavelength with frequency, Hertz calculated the speed of the waves, which matched Maxwell's prediction for EM waves. This showed that radio waves behaved similarly to visible light in speed and confirmed Maxwell's theory.

Polarisation of EM Waves

Hertz also demonstrated the polarisation of radio waves. When the receiver was rotated relative to the transmitter, the detected signal oscillated between a maximum and minimum at every 90° rotation:

• Maximum signal when the receiver was perpendicular to the oscillation direction of the electric field.
• Minimum signal when the receiver was parallel to the oscillation direction, as no signal was detected in this alignment. This behaviour confirmed that the radio waves were polarised, a characteristic of transverse waves.

Fizeau's Measurement of Light Speed

Armand Fizeau devised an experiment to measure the speed of light on Earth, providing further evidence for EM wave theory. His apparatus involved a toothed wheel and a distant mirror:

3. A pulsed light beam was sent through a gap in the rotating wheel toward the mirror.
4. As the wheel rotated faster, the light pulse could pass through successive gaps, eventually being blocked by teeth of the wheel when speed was high enough.

If the wheel's rotation was precisely synchronised, the light would pass through a gap on its return, allowing Fizeau to measure the time delay for light to travel a known distance, enabling calculation of its speed:

$$c = 4dnf$$

Where:

• $d$ is the distance to the mirror,
• $n$ is the number of gaps in the wheel,
• $f$ is the rotation frequency.