Electromagnetic Waves: One Mark Questions, Book Back Answers and Notes

About Electromagnetic Waves

Medium ~120 min study

By Maxwell's time, Gauss's law, Faraday's law and Ampere's law were known, but they were not consistent with each other. Maxwell noticed that Ampere's circuital law did not work for a charging capacitor, and fixed it by adding a displacement current term. With that correction, his equations predicted waves of electric and magnetic fields travelling through empty space at \( 3 \times 10^{8} \) m s^-1, the measured speed of light. Light, it turned out, is an electromagnetic wave.

This unit ties together laws you already know. Faraday's law says a changing magnetic field produces an electric field. Displacement current says a changing electric field produces a magnetic field. Each keeps producing the other, and the disturbance moves forward as a wave. Radio, mobile phones and satellite communication all use such waves.

Book back questions here are mostly conceptual, with some short numericals. Be ready to state Maxwell's equations, list the properties of electromagnetic waves, arrange the spectrum in order of wavelength or frequency with one use of each region, and distinguish emission spectra from absorption spectra.

What you'll learn

• Define displacement current and explain why Maxwell added it to Ampere's circuital law.
• State Maxwell's four equations and what each one means physically.
• Explain how electromagnetic waves are produced and list their properties.
• Calculate the speed of electromagnetic waves from \( \mu \) and \( \varepsilon \) of a medium.
• Arrange the regions of the electromagnetic spectrum in order and give one use of each.
• Distinguish between continuous, line and band spectra, in emission and in absorption.

Before you start

• Gauss's law in electrostatics and the idea of magnetic flux.
• Faraday's law of electromagnetic induction.
• Frequency, wavelength and speed of a wave.

Electromagnetic Waves explained

What This Unit Covers

Displacement Current and Maxwell's Equations

When a capacitor is charging, conduction current flows in the wires but not across the gap between the plates. Ampere's law then gives different answers depending on which surface you choose. Maxwell resolved this by adding the displacement current, \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \), which arises from the changing electric flux between the plates. With this term included, the four Maxwell's equations are Gauss's law for electricity, Gauss's law for magnetism, Faraday's law and the Ampere-Maxwell law. Together they describe all of classical electromagnetism.

Production and Properties of Electromagnetic Waves

Electromagnetic waves are produced by accelerated charges, for example charges oscillating in an antenna. The electric and magnetic fields are perpendicular to each other and to the direction of propagation, so the waves are transverse. They need no material medium. In vacuum they travel at \( c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \), about \( 3 \times 10^{8} m s^{-1} \), and the ratio of the field amplitudes is \( \frac{E_0}{B_0} = c \). They carry energy and momentum, and they can be polarised.

The Electromagnetic Spectrum

In order of increasing frequency (decreasing wavelength), the spectrum runs through radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Each region has its own sources and uses. Radio waves are used for broadcasting and communication, microwaves in radar and microwave ovens, infrared in remote controls and night vision, ultraviolet in sterilising water, X-rays in medical imaging, and gamma rays in cancer treatment.

Emission and Absorption Spectra

A spectrum shows how intensity is spread over different wavelengths. An emission spectrum comes from a hot or excited source and may be continuous (a white-hot filament), a line spectrum (excited atoms, such as sodium vapour) or a band spectrum (excited molecules). An absorption spectrum is formed when white light passes through a cooler substance, which removes the same wavelengths it would emit. The dark Fraunhofer lines in the solar spectrum are an example. Because each element has its own set of lines, spectra are used to identify elements in the laboratory and in stars.

Common mistakes to avoid

• Thinking displacement current is a flow of charges. It comes from a changing electric flux, and exists even in the empty gap of a capacitor.
• Assuming electromagnetic waves need a medium. They travel through vacuum, which is how sunlight reaches the Earth.
• Getting the spectrum order wrong, especially swapping ultraviolet and infrared, or X-rays and gamma rays. Learn it once in order of increasing frequency.
• Drawing \( \vec{E} \) and \( \vec{B} \) in the same plane as the direction of travel. \( \vec{E} \), \( \vec{B} \) and the propagation direction are mutually perpendicular.

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

What exactly is displacement current?

It is the term \( \varepsilon_0 \frac{d\Phi_E}{dt} \) that Maxwell added to Ampere's law. It is not a movement of charges. It represents the fact that a changing electric field produces a magnetic field, just like a conduction current does.

How are electromagnetic waves produced?

By accelerated charges. A charge at rest produces only an electric field. A charge moving with constant velocity produces steady electric and magnetic fields that move along with it, but no radiation. Only an accelerated charge, such as one oscillating in an antenna, sends out electromagnetic waves.

Why are electromagnetic waves called transverse?

The electric and magnetic fields oscillate perpendicular to the direction in which the wave travels. Electromagnetic waves, including light, can be polarised, and only transverse waves can be polarised.

What is the electromagnetic spectrum?

It is the full range of electromagnetic radiation arranged by frequency or wavelength. It extends from long wavelength radio waves to very short wavelength gamma rays. Visible light is only a narrow band, roughly 400 nm to 700 nm.

What is the difference between emission and absorption spectra?

An emission spectrum comes directly from an excited source and shows bright lines or bands on a dark background. An absorption spectrum is seen when white light passes through a cooler substance; it shows dark lines on a bright continuous background at the wavelengths the substance absorbs.

How does a microwave oven heat food?

Water molecules in food are polar. The rapidly oscillating electric field of the microwaves makes them keep turning back and forth, and this energy spreads to neighbouring molecules as heat. Microwaves penetrate only a few centimetres, so thick food is not heated from the centre outwards; heat reaches the middle by conduction.