Electromagnetic Waves: common doubts, answered
The questions students ask most often about Electromagnetic Waves, each with a short answer. For the full chapter, read the Electromagnetic Waves notes.
The charging capacitor puzzle
Read this section in the notes →Why was Ampere's circuital law found to be incomplete?
Because it gave two different answers for the same loop while a capacitor was charging. Take a circular loop round the wire leading to the capacitor. A flat surface on that loop is pierced by the current i, but a pot-shaped surface bulging between the plates is pierced by no conduction current at all. The law would give a magnetic field for one surface and zero for the other, which cannot both be true.
Displacement current
Read this section in the notes →What is displacement current?
It is the term ε₀ dΦE/dt, which acts like a current wherever the electric flux is changing, even when no charge moves. Between the plates of a charging capacitor the electric field grows, giving id = ε₀ dΦE/dt, exactly equal to the current in the leads. It produces a magnetic field just as an ordinary current does, so the field between the plates is not zero.
Is displacement current an actual flow of charge?
No, no charge crosses the gap of a capacitor. The name is historical: id = ε₀ dΦE/dt behaves like a current only in the sense that it produces a magnetic field. The sum of conduction current and displacement current is continuous all round the circuit, which is what repairs Ampere's law. In a steady DC circuit it is zero, because the electric flux is not changing.
Maxwell's equations
Read this section in the notes →What is the Ampere–Maxwell law?
It is Ampere's circuital law with Maxwell's extra term: ∮B·dl = μ₀ic + μ₀ε₀ dΦE/dt. It says magnetic fields are produced both by conduction currents and by changing electric fields. Combined with Faraday's law, in which changing magnetic fields produce electric fields, it allows each field to keep regenerating the other, so the pair can travel through space as an electromagnetic wave.
What are Maxwell's four equations in simple words?
They are Gauss's law for electricity, Gauss's law for magnetism, Faraday's law and the Ampere–Maxwell law. In words: charges produce electric flux, there are no magnetic charges, changing magnetic flux produces an electric field, and currents together with changing electric flux produce a magnetic field. With the Lorentz force law they describe all of classical electromagnetism and predict waves travelling at c = 1/√(μ₀ε₀).
Sources of electromagnetic waves
Read this section in the notes →Does a charge moving at constant velocity produce electromagnetic waves?
No, only accelerated charges radiate. A charge at rest has a steady electric field, and a charge moving at constant velocity, or a steady current, also has fields that do not vary in a way that sends out a wave. An oscillating charge accelerates all the time, so it produces changing electric and magnetic fields that travel outward at the frequency of its oscillation.
Who first produced and detected electromagnetic waves in a laboratory?
Heinrich Hertz did, some years after Maxwell had predicted them. The waves he made had wavelengths of a few metres, far longer than light, yet they behaved as Maxwell's theory said they should. His success turned the prediction into established physics, and Marconi and others soon used such waves for communication over long distances.
Nature of electromagnetic waves
Read this section in the notes →Are the electric and magnetic fields of an electromagnetic wave in phase?
Yes, in a travelling wave they reach their maxima and zeros together: Ex = E₀ sin(kz − ωt) and By = B₀ sin(kz − ωt). The two fields point at right angles to one another and also at right angles to the way the wave moves, so the wave is transverse. Do not confuse this with an LC circuit, where the electric and magnetic energies peak a quarter cycle apart.
Why is B₀ so much smaller than E₀ in an electromagnetic wave?
Because B₀ = E₀/c, and c is about 3 × 10⁸ m/s. An electric amplitude of 6.3 V/m comes with a magnetic amplitude of only about 2.1 × 10⁻⁸ T. This does not mean the magnetic part is unimportant; the small number partly reflects the units chosen for E and B. Remember B₀ = E₀/c, not B₀ = E₀, in every numerical question.
How do I find the direction in which an electromagnetic wave travels?
It travels along E × B, at right angles to both fields. For Ex = E₀ sin(kz − ωt) and By = B₀ sin(kz − ωt), the wave moves along +z, because the x direction crossed with the y direction gives z. So whenever two of the three directions are known, the cross product gives the third. Questions often test the transverse nature of the wave this way.
Do electromagnetic waves need a medium to travel?
No. They are self-sustaining oscillations in which a changing electric field produces a magnetic one and the reverse, so they can cross empty space; that is how sunlight reaches the Earth. Sound, by contrast, needs a material medium because it is a vibration of matter itself. Electromagnetic waves can also travel through many materials, but there they move more slowly than in vacuum.
Speed in vacuum and in media
Read this section in the notes →Do all electromagnetic waves travel at the same speed?
In vacuum, yes: every electromagnetic wave, from radio to gamma rays, travels at c = 1/√(μ₀ε₀), about 3 × 10⁸ m/s. Frequency and wavelength trade off through c = νλ, so a higher frequency means a shorter wavelength, not a faster wave. In a material the speed drops to v = 1/√(με), where ε and μ belong to the medium.
How did Maxwell conclude that light is an electromagnetic wave?
He worked out the speed of electromagnetic waves from two constants of electricity and magnetism, c = 1/√(μ₀ε₀), and found it matched the measured speed of light. Two measurements from completely different experiments agreeing so closely could hardly be chance. This tied optics to electricity and magnetism, showing light to be one band of electromagnetic waves.
The electromagnetic spectrum
Read this section in the notes →What is the order of the electromagnetic spectrum from longest to shortest wavelength?
Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Frequency and photon energy increase in the same order. The bands have no sharp edges; neighbouring regions overlap and are named mainly by how the radiation is produced or detected. Visible light is a narrow band, roughly 400 nm to 700 nm, between infrared and ultraviolet.
Radio waves and microwaves
Read this section in the notes →What are radio waves and microwaves each used for?
Radio waves, the longer of the two, carry AM and FM broadcasts, television and mobile phone signals; microwaves, with shorter wavelengths, suit radar and microwave ovens. Radio waves come from charges accelerating in conducting wires and antennas, while microwaves are produced in special vacuum tubes. Their short wavelength lets radar send narrow beams that reflect from distant objects such as aircraft.
How does a microwave oven heat food?
Its microwaves are tuned to a frequency that water molecules absorb readily. Energy passes efficiently from the waves into the motion of these molecules, and faster molecular motion means a higher temperature. Any food that contains water therefore heats up. The same short-wavelength band, roughly 0.1 m down to 1 mm, is also what radar uses.
Infrared and visible light
Read this section in the notes →Why is infrared radiation sometimes called heat waves?
Because it is readily absorbed by the water molecules present in most materials, which raises their temperature. Our skin and most objects warm up when infrared falls on them, and hot bodies give out strong infrared. Infrared also keeps the Earth warm through the greenhouse effect, and it is used in remote controls and in lamps for physical therapy.
Why can our eyes see only a narrow part of the electromagnetic spectrum?
Because the light-sensitive cells in our eyes respond only to wavelengths of roughly 400 nm to 700 nm, the band we call visible light. Other animals respond to somewhat different ranges: snakes can sense infrared, and many insects see well into the ultraviolet. Radiation outside our band can still reach our eyes, but it produces no sensation of sight.
Ultraviolet, X-rays and gamma rays
Read this section in the notes →Why don't we get sunburnt through a closed glass window?
Because ordinary glass absorbs most ultraviolet radiation, and UV is what causes tanning and sunburn. Visible light passes through glass easily, so the room is bright while the UV is largely held back. For the same reason welders wear goggles or face masks with glass windows, which protect their eyes from the strong UV given off by the welding arc.
Why is the ozone layer important for life on Earth?
It absorbs most of the Sun's ultraviolet radiation before it can reach the ground. Ultraviolet in large doses damages living cells, so this layer shields living things from harm. Its thinning, caused largely by chlorofluorocarbon gases released by people, has therefore been treated as a serious environmental problem across the world.
What is the difference between X-rays and gamma rays if their wavelengths overlap?
The difference lies in their source, not a sharp wavelength boundary. X-rays are usually produced when fast electrons strike a metal target, while gamma rays come from nuclear reactions and radioactive nuclei. Their wavelength ranges overlap, so the same wavelength could be called either depending on how it was produced. X-rays are used in medical imaging; gamma rays in medicine to destroy cancer cells.
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