# Maxwell's Contribution to Electromagnetism

This is part of the HSC Physics course under the topic Electromagnetic Spectrum.

### HSC Physics Syllabus

• investigate Maxwell’s contribution to the classical theory of electromagnetism, including:

–unification of electricity and magnetism
–prediction of electromagnetic waves
–prediction of velocity (ACSPH113)

• describe the production and propagation of electromagnetic waves and relate these processes qualitatively to the predictions made by Maxwell’s electromagnetic theory (ACSPH112, ACSPH113)

### Unification of Electric and Magnetic Fields

In Module 6: Electromagnetism, we learnt about Faraday’s Law of Induction where an object experiencing change in magnetic flux experiences an induced emf. Faraday proposed that changing magnetic fields produced electric fields.

When the object is a closed conductor, the emf induces a current. The induction of current resembles an electric field as electrons are directed in a certain direction that is parallel to the orientation of the electric field.

Maxwell extended Faraday’s proposal by mathematically deriving that changing electric fields produced magnetic fields and in fact the two phenomena should be perceived as a single entity.

This means oscillating electric fields would produce magnetic fields. Oscillating magnetic fields would produce electric fields. A moving electric charge would thus produce a magnetic field due to the presence of its intrinsic electric field.

### Maxwell's Prediction of Electromagnetic Waves

Maxwell used his four equations to derive two new equations describing these oscillating magnetic and electric fields. The equation was characteristic of a wave, and also implied that the electric and magnetic fields were in phase and perpendicular to each other, oscillating in a direction perpendicular to the wave's propagation.

Maxwell's theory of electromagnetism also related electromagnetic waves to charges. He explained that an oscillating charge will produce a changing electric field, which in turn produces a changing magnetic field. These two changing fields will continue to mutually produce each other. When this oscillating charge is made to propagate, it results in a self-propagating electromagnetic wave.

### Maxwell's Prediction of the Velocity of Electromagnetic Waves

Maxwell also used his four equations to calculate the speed of these waves, arriving at:

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

This gave a value of 310,740,000 ms-1, which was close to the experimental values of the speed of light at the time. Maxwell did not think this was a coincidence as he commented:

"We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

Therefore, he predicted there was a non-coincidental link between speed of electromagnetic waves and light. In his comment, he alluded to the possibility that light may be associated with the same ‘medium’ in which electric and magnetic fields oscillate.

Maxwell’s contribution to electromagnetism allowed for more accurate methods to be used to calculate the speed of light.

In 1907, Rosa and Dorsey indirectly determined the speed of light through using the electric and magnetic permeability of air.

This positive finding verified the existence of electromagnetic waves and confirmed that light in fact does have electromagnetic properties.

The value attained from this experiment had to be later corrected because speed of electromagnetic waves was deduced to be independent of the medium they propagate in.

The German physicist Heinrich Hertz was the first to generate and detect certain types of electromagnetic waves in the laboratory. He performed a series of experiments that not only confirmed the existence of electromagnetic waves, but also verified that they travel at the speed of light.

Figure 2: Hertz's experimental set-up.

Hertz used an AC circuit that resonates at a known frequency and connected it to a loop of wire as shown in Figure 2. High voltages induced across the gap in the loop produced sparks that were visible evidence of the current in the circuit and that helped generate electromagnetic waves.
• Frequency of alternating current = frequency of oscillating electric field = frequency of oscillating magnetic field = frequency of electromagnetic wave produced.
Across the laboratory, Hertz had another loop attached to another circuit, which could be tuned (as the dial on a radio) to the same resonant frequency as the first and could, thus, be made to receive electromagnetic waves.
This loop also had a gap across which sparks were generated, giving solid evidence that electromagnetic waves had been received. Therefore, Hertz validated Maxwell's prediction of the existence of electromagnetic waves.

### Hertz's Calculation of the Speed of Radiowaves

Hertz also studied the reflection, refraction, and interference patterns of the electromagnetic waves he generated, verifying their wave character.

From determining the distances between nodes, he was able to determine wavelength from the interference patterns, and knowing their frequency, he could calculate the propagation speed using the equation:
$$v = f\lambda$$
Hertz was thus able to validate Maxwell's prediction of the velocity of electromagnetic waves.

Next Section: Speed of Light