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How did Maxwell unify electricity and magnetism into electromagnetic radiation?

Electromagnetic radiation as orthogonal oscillating electric and magnetic fields, the unification of electricity and magnetism by Maxwell, and the speed of light from the relationship c equals one over the square root of permittivity times permeability.

An SQA Advanced Higher Physics answer on electromagnetic radiation, covering radiation as orthogonal oscillating electric and magnetic fields, Maxwell's unification of electricity and magnetism, and how the speed of light follows from the permittivity and permeability of free space.

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  1. What this key area is asking
  2. The nature of an electromagnetic wave
  3. Maxwell's unification
  4. The speed of light
  5. Examples in context
  6. Try this

What this key area is asking

The SQA wants you to describe electromagnetic radiation as orthogonal oscillating electric and magnetic fields, explain how Maxwell unified electricity and magnetism, and use the relationship c=1ε0μ0c = \dfrac{1}{\sqrt{\varepsilon_0 \mu_0}} for the speed of light in free space.

The nature of an electromagnetic wave

The electric and magnetic fields oscillate in step, in planes at right angles, with the wave advancing perpendicular to both. Because the fields regenerate each other, the wave is self-sustaining and propagates through empty space, which is why light from distant stars reaches us. All electromagnetic radiation, from radio waves to gamma rays, has this same structure and differs only in frequency and wavelength.

Maxwell's unification

Before Maxwell, electricity and magnetism were studied separately, linked only by the observation that currents make magnetic fields and changing fields induce currents. Maxwell's equations tied them into one framework and predicted a remarkable consequence: a disturbance in the electromagnetic field would propagate as a wave. This was one of the great unifications in physics and set the stage for relativity.

The speed of light

The striking point is that this speed depends only on two electric and magnetic constants, with no reference to light. When Maxwell put in the measured values of ε0\varepsilon_0 and μ0\mu_0, he obtained 3×108 m s−13 \times 10^{8}\ \text{m s}^{-1}, exactly the measured speed of light. This agreement was overwhelming evidence that light is an electromagnetic wave, and that the same theory governs radio, infrared, visible light, X-rays and gamma rays.

Examples in context

Radio and television broadcasting generate electromagnetic waves by oscillating currents in an aerial, exactly the changing fields Maxwell described. Mobile phones and Wi-Fi transmit information on electromagnetic waves of different frequencies, all travelling at cc. Light from the Sun and stars crosses the vacuum of space because the wave needs no medium. The whole electromagnetic spectrum, used in medicine, communication and astronomy, is unified by Maxwell's single theory.

Try this

Q1. State the two fields that make up an electromagnetic wave and their relative orientation. [1 mark]

  • Cue. Oscillating electric and magnetic fields, at right angles to each other (and to the direction of travel).

Q2. Write the relationship for the speed of light in terms of the permittivity and permeability of free space. [1 mark]

  • Cue. c=1ε0μ0c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}}.

Q3. State what Maxwell's calculation of this speed revealed about the nature of light. [1 mark]

  • Cue. That light is an electromagnetic wave.

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA AH style4 marksCalculate the speed of electromagnetic radiation in a vacuum from the permittivity and permeability of free space. Take ε0=8.85×10−12 F m−1\varepsilon_0 = 8.85 \times 10^{-12}\ \text{F m}^{-1} and μ0=4π×10−7 H m−1\mu_0 = 4\pi \times 10^{-7}\ \text{H m}^{-1}.
Show worked answer →

The speed of light in free space is c=1ε0μ0c = \dfrac{1}{\sqrt{\varepsilon_0 \mu_0}}.

Compute the product: ε0μ0=8.85×10−12×4π×10−7=1.11×10−17\varepsilon_0 \mu_0 = 8.85 \times 10^{-12} \times 4\pi \times 10^{-7} = 1.11 \times 10^{-17}.

Square root: 1.11×10−17=3.34×10−9\sqrt{1.11 \times 10^{-17}} = 3.34 \times 10^{-9}.

So c=13.34×10−9=3.0×108 m s−1c = \dfrac{1}{3.34 \times 10^{-9}} = 3.0 \times 10^{8}\ \text{m s}^{-1}.

Markers reward the relationship, computing the product under the root, and the value matching the measured speed of light, which was Maxwell's key insight.

SQA AH style4 marksDescribe the nature of an electromagnetic wave and state how Maxwell's work unified electricity and magnetism.
Show worked answer →

An electromagnetic wave consists of an oscillating electric field and an oscillating magnetic field, at right angles to each other and to the direction of travel, so it is a transverse wave that needs no medium.

Maxwell showed that a changing electric field produces a magnetic field and a changing magnetic field produces an electric field, so the two are aspects of a single electromagnetic field.

His equations predicted that these self-sustaining waves travel at a speed set by the permittivity and permeability of free space, which equals the measured speed of light, showing light is an electromagnetic wave.

Markers reward describing the orthogonal oscillating fields, the mutual generation of one field by the other, and the conclusion that light is an electromagnetic wave.

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