PhysicsISC Class 12 · Electromagnetic Waves

Properties of Electromagnetic Waves: Production, Transverse Nature and Speed

Updated 15 October 2026 · Fact-checked

Electromagnetic waves are produced by accelerated charges. They consist of electric and magnetic fields oscillating in phase, at right angles to each other and to the direction of travel, so they are transverse. They need no medium, travel in vacuum at $c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} = 3 \times 10^8$ m/s, and carry energy and momentum.

Understand Properties of Electromagnetic Waves

How they are produced. A charge at rest has only an electric field. A charge moving at steady velocity also has a magnetic field, but neither field radiates away. A charge that accelerates, for example one oscillating to and fro in an antenna, sets up a changing electric field; this produces a changing magnetic field (Ampère-Maxwell law), which in turn produces a changing electric field (Faraday's law), and so on. The disturbance travels outwards as an electromagnetic wave whose frequency equals the frequency of oscillation of the charge. An LC circuit oscillating at $f_{0} = \frac{1}{2 π L C}$ connected to an antenna radiates at $f_{0}$ .

Transverse nature (qualitative). For a wave travelling along +x:

E oscillates along one perpendicular direction (say y) and B along the other (z).
E, B and the direction of travel are mutually perpendicular; the direction of travel is that of $E \times B$ .
E and B reach their maxima and zeros together: they are in phase.
For example, $E_{y} = E_{0} sin (k x - ω t)$ and $B_{z} = B_{0} sin (k x - ω t)$ , with $k = \frac{2 π}{λ}$ and $ω = 2 π f$ .

Speed. Maxwell's equations give the speed in vacuum as
$c = \frac{1}{μ _{0} ε _{0}} = \frac{1}{4 π \times 1 0 ^{- 7} \times 8.854 \times 1 0 ^{- 12}} \approx 3 \times 1 0^{8} m/s,$
exactly the measured speed of light. This showed that light is an electromagnetic wave. In a medium of permittivity ε and permeability μ, $v = \frac{1}{μ ε}$ ; for a non-magnetic medium of relative permittivity $ε_{r}$ , $v = \frac{c}{ε _{r}}$ and the refractive index is $n = \frac{c}{v}$ .

Field amplitudes. In vacuum the peak fields are linked by $\frac{E _{0}}{B _{0}} = c$ , so B is tiny in tesla when E is moderate in V/m. Also $c = \frac{ω}{k} = f λ$ .

List of properties to quote.
1. Produced by accelerated (oscillating) charges.
2. Transverse: E ⊥ B ⊥ direction of travel; E and B in phase.
3. Need no material medium; travel through vacuum.
4. Speed in vacuum $c = \frac{1}{μ _{0} ε _{0}}$ , the same for all wavelengths.
5. Not deflected by electric or magnetic fields (they carry no charge).
6. Carry energy and momentum (and so exert a small pressure on surfaces they strike).
7. Show reflection, refraction, interference, diffraction and polarisation; polarisation itself is evidence of transverse nature.
8. When a wave passes from one medium into another its frequency stays the same; its speed and wavelength change.

Properties of Electromagnetic Waves: formulas and key facts

Speed in vacuum: $c = \frac{1}{μ _{0} ε _{0}} \approx 3 \times 1 0^{8} m/s$; Same for all regions.
Speed in a medium: $v = \frac{1}{μ ε} = \frac{c}{μ _{r} ε _{r}}$; n = c/v.
Field ratio: $\frac{E _{0}}{B _{0}} = c$; E in V/m, B in T.
Wave relations: $c = f λ = \frac{ω}{k}, k = \frac{2 π}{λ}$; From the wave equation.
Direction of travel: $\overset{v}{^} ∥ E \times B$; Right-hand rule.
Frequency of radiation from an LC circuit: $f_{0} = \frac{1}{2 π L C}$; Equals the oscillation frequency.

How to solve Properties of Electromagnetic Waves questions

Most questions are short: a direction, a field ratio, a speed or reading a wave equation.

1Direction questions: use $E \times B$ along the direction of travel (x̂ × ŷ = ẑ, ŷ × ẑ = x̂, ẑ × x̂ = ŷ).
2Field amplitude: $B_{0} = \frac{E _{0}}{c}$ or $E_{0} = c B_{0}$ (vacuum).
3Wave equation $sin (k x - ω t)$ : read k and ω; then $λ = \frac{2 π}{k}$ , $f = \frac{ω}{2 π}$ , and check $\frac{ω}{k} = c$ .
4Medium: $v = \frac{c}{ε _{r}}$ (non-magnetic), $n = \frac{c}{v}$ ; frequency unchanged, $λ_{m e d i u m} = \frac{λ}{n}$ .
5Explain-type questions: quote the numbered properties in short lines.

Properties of Electromagnetic Waves in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

No medium needed

Suppose an astronaut on the Moon radios the Earth, 3.84 × 10⁸ m away, and also bangs a hammer on a metal plate.

How long does the radio message take, and why does the bang never reach Earth?

Try it first, then show the solutionSolution

$t = \frac{3.84 \times 1 0 ^{8}}{3 \times 1 0 ^{8}} = 1.28$ s.
Radio waves are electromagnetic and cross vacuum; sound is a mechanical wave and needs a medium.

Answer: About 1.28 s; sound cannot travel through the vacuum of space.

Memory hook: Light needs no road; sound needs a road.

Antennas line up with E

Imagine a radio station using a vertical transmitting mast, and a listener holding a portable radio with its telescopic aerial horizontal and getting poor reception.

Explain using the transverse nature of the wave.

Try it first, then show the solutionSolution

The vertical mast makes the electric field of the wave oscillate vertically.
A receiving aerial works by the field pushing electrons along it; a horizontal aerial is perpendicular to E and picks up little signal.
Turning the aerial vertical lines it up with E and improves reception.

Answer: Turn the aerial parallel to the electric field (vertical).

Memory hook: Aerial follows E.

Tricks to remember Properties of Electromagnetic Waves

Short memory aids. Say each one aloud once, then use it on a question the same day.

E cross B gives the way
Point fingers along E, curl towards B; the thumb shows where the wave goes.
Use it when: Direction questions.
E is c times B
$E_{0} = c B_{0}$ : big E, tiny B.
Use it when: Field amplitudes.
Frequency is faithful
Changing medium changes speed and wavelength, never frequency.
Use it when: Refraction questions.
Accelerate to radiate
Rest: E only; steady speed: E and B; acceleration: waves.
Use it when: Production questions.

Properties of Electromagnetic Waves: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Direction of B · 1 mark · MCQBoard level

An electromagnetic wave travels along +z and its electric field oscillates along x. Its magnetic field oscillates along:
(a) x
(b) y
(c) z
(d) any direction

Try it first, then show the solutionSolution

B must be perpendicular to E and to the direction of travel, and $\overset{x}{^} \times \overset{y}{^} = \overset{z}{^}$ . So B is along y.

Answer: (b).

Example 2: Electric field from magnetic field · 1 mark · Short answerBoard level

The peak magnetic field of an electromagnetic wave in vacuum is $2 \times 1 0^{- 8}$ T. Find the peak electric field.

Try it first, then show the solutionSolution

$E_{0} = c B_{0} = 3 \times 1 0^{8} \times 2 \times 1 0^{- 8} = 6$ V/m. (1)

Answer: 6 V/m.

Example 3: Speed in vacuum and in a medium · 3 marks · Short answerHarder board level

(a) Using $μ_{0} = 4 π \times 1 0^{- 7}$ T m/A and $ε_{0} = 8.854 \times 1 0^{- 12}$ C² N⁻¹ m⁻², show that $\frac{1}{μ _{0} ε _{0}}$ is about $3 \times 1 0^{8}$ m/s. (b) Find the speed of an electromagnetic wave in a non-magnetic medium of relative permittivity 4, and the refractive index.

Try it first, then show the solutionSolution

(a) $μ_{0} ε_{0} = 4 π \times 1 0^{- 7} \times 8.854 \times 1 0^{- 12} \approx 1.113 \times 1 0^{- 17}$ ; its square root is $\approx 3.34 \times 1 0^{- 9}$ , so the speed $\approx 3.0 \times 1 0^{8}$ m/s. (1)
(b) $v = \frac{c}{ε _{r}} = \frac{3 \times 1 0 ^{8}}{2} = 1.5 \times 1 0^{8}$ m/s. (1)
$n = \frac{c}{v} = 2$ . (1)

Answer: (a) ≈ $3 \times 1 0^{8}$ m/s; (b) $1.5 \times 1 0^{8}$ m/s, n = 2.

Example 4: Reading a wave equation · 4 marks · Long answerHarder board level

The electric field of a wave in vacuum is $E_{y} = 30 sin (1.0 \times 1 0^{3} x - ω t)$ V/m (x in metres). Find the wavelength, ω, the frequency, the region, and the amplitude and direction of B.

Try it first, then show the solutionSolution

$k = 1 0^{3}$ rad/m, so $λ = \frac{2 π}{k} \approx 6.28 \times 1 0^{- 3}$ m = 6.28 mm. (1)
$ω = c k = 3 \times 1 0^{11}$ rad/s; $f = \frac{ω}{2 π} \approx 4.77 \times 1 0^{10}$ Hz. (1)
6.28 mm lies between 1 mm and 0.1 m: microwaves. (1)
$B_{0} = \frac{30}{3 \times 1 0 ^{8}} = 1 0^{- 7}$ T; travel along +x and E along y, so B is along z ( $\overset{y}{^} \times \overset{z}{^} = \overset{x}{^}$ ). (1)

Answer: λ ≈ 6.28 mm; ω = $3 \times 1 0^{11}$ rad/s; f ≈ $4.77 \times 1 0^{10}$ Hz; microwaves; $B_{0} = 1 0^{- 7}$ T along z.

Example 5: Wave from an LC circuit · 3 marks · Short answerHOTS / competency

An LC circuit with L = 2 µH and C = 50 pF is coupled to an antenna. Find the frequency and wavelength of the radiation and name the region. Why does the circuit radiate at all?

Try it first, then show the solutionSolution

$L C = 2 \times 1 0^{- 6} \times 50 \times 1 0^{- 12} = 1 0^{- 16}$ ; $f = \frac{1}{2 π \times 1 0 ^{- 8}} \approx 1.59 \times 1 0^{7}$ Hz = 15.9 MHz. (1)
$λ = \frac{c}{f} \approx 18.8$ m: radio waves. (1)
The charges in the antenna oscillate, that is they accelerate, and accelerated charges radiate electromagnetic waves at their oscillation frequency. (1)

Answer: ≈ 15.9 MHz; ≈ 18.8 m; radio waves.

Example 6: Laser light in water · 4 marks · Case-basedHOTS / competency

Suppose a red laser of wavelength 650 nm in air shines into water of refractive index 1.33. The peak electric field of the beam in air is 100 V/m.
(i) Find the frequency of the light. (1 mark)
(ii) Find its speed in water. (1 mark)
(iii) Find its wavelength in water. (1 mark)
(iv) Find the peak magnetic field in air. (1 mark)

Try it first, then show the solutionSolution

(i) $f = \frac{3 \times 1 0 ^{8}}{650 \times 1 0 ^{- 9}} \approx 4.62 \times 1 0^{14}$ Hz (unchanged in water).
(ii) $v = \frac{c}{n} = \frac{3 \times 1 0 ^{8}}{1.33} \approx 2.26 \times 1 0^{8}$ m/s.
(iii) $λ_{w} = \frac{650}{1.33} \approx 489$ nm.
(iv) $B_{0} = \frac{100}{3 \times 1 0 ^{8}} \approx 3.33 \times 1 0^{- 7}$ T.

Answer: (i) ≈ $4.62 \times 1 0^{14}$ Hz; (ii) ≈ $2.26 \times 1 0^{8}$ m/s; (iii) ≈ 489 nm; (iv) ≈ $3.33 \times 1 0^{- 7}$ T.

Where students lose marks in Properties of Electromagnetic Waves

The slips examiners see most often, and what to write instead.

Mistake: Saying the wave needs a medium
Students carry over ideas from sound waves.
Do this: Electromagnetic waves are field oscillations; they cross vacuum.
Usually costs: 1 mark.
Mistake: E and B shown 90° out of phase
Students mix up the space angle (90°) with the phase.
Do this: E and B are perpendicular in space but in phase in time.
Usually costs: 1 mark in a diagram.
Mistake: Taking $B_{0} = c E_{0}$
The ratio is turned upside down, giving huge B.
Wrong working
$B_{0} = 3 \times 1 0^{8} \times 30$ T.
Right working
$B_{0} = \frac{30}{3 \times 1 0 ^{8}} = 1 0^{- 7}$ T.
Do this: E is the big one: $E_{0} = c B_{0}$ .
Usually costs: 1 mark.
Mistake: Changing frequency on entering a medium
Speed falls, so students lower f too.
Do this: f is fixed by the source; λ falls as $\frac{λ}{n}$ .
Usually costs: 1 mark.

Exam tips

Draw E and B as two sine waves in perpendicular planes, in phase, with the direction of travel marked.
When asked for "characteristics", write short numbered points.
Keep units: V/m for E, T for B, m/s for speed.
Show $\frac{ω}{k} = c$ as a check whenever a wave equation is given.

Practice questions on Properties of Electromagnetic Waves

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Electromagnetic waves are produced by:
(a) charges at rest
(b) charges moving with constant velocity
(c) accelerated charges
(d) neutral particles
Hint
Changing fields need changing motion.
Answer
(c).
Q2 · 1 mark · Short answerBoard level
The peak electric field of a wave in vacuum is 120 V/m. Find the peak magnetic field.
Hint
$B_{0} = \frac{E _{0}}{c}$ .
Answer
$4 \times 1 0^{- 7}$ T.
Q3 · 1 mark · Assertion-reasonHarder board level
Assertion (A): Electromagnetic waves can travel through vacuum.
Reason (R): They are oscillations of electric and magnetic fields, which need no material medium.
(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.
Hint
Light from the Sun.
Answer
(a).
Q4 · 2 marks · Short answerHarder board level
Find the speed of an electromagnetic wave in a non-magnetic medium of relative permittivity 2.25, and the refractive index.
Hint
$2.25 = 1.5$ .
Answer
$2 \times 1 0^{8}$ m/s; n = 1.5.
Q5 · 1 mark · Short answerHarder board level
At a point, the electric field of a wave is along +y and the magnetic field along −x. In which direction is the wave travelling?
Hint
$\overset{y}{^} \times (- \overset{x}{^})$ .
Answer
Along +z.
Q6 · 3 marks · Short answerHarder board level
State four properties of electromagnetic waves and one piece of evidence that they are transverse.
Hint
Use the numbered list.
Answer
Any four: produced by accelerated charges; E ⊥ B ⊥ direction of travel; travel in vacuum at $c = \frac{1}{μ _{0} ε _{0}}$ ; not deflected by fields; carry energy and momentum. Evidence: they can be polarised.
Q7 · 2 marks · Short answerHOTS / competency
An LC circuit with L = 0.5 µH and C = 2 pF drives an antenna. Find the frequency and wavelength radiated.
Hint
$L C = 1 0^{- 18}$ .
Answer
≈ 159 MHz; ≈ 1.88 m.
Q8 · 4 marks · Case-basedHOTS / competency
Case study: Suppose the magnetic field of a radio wave in vacuum is $B_{z} = 4 \times 1 0^{- 9} sin (2.0 x - 6.0 \times 1 0^{8} t)$ T.
(i) Find the wavelength. (1 mark)
(ii) Find the frequency and name a use for waves of this frequency. (1 mark)
(iii) Check that the speed is c. (1 mark)
(iv) Find the amplitude and direction of the electric field. (1 mark)
Hint
k = 2 rad/m, ω = 6 × 10⁸ rad/s.
Answer
(i) $λ = \frac{2 π}{2} \approx 3.14$ m. (ii) $f \approx 95.5$ MHz: FM radio broadcasting. (iii) $\frac{ω}{k} = 3 \times 1 0^{8}$ m/s. (iv) $E_{0} = c B_{0} = 1.2$ V/m along y (so that $\overset{y}{^} \times \overset{z}{^} = \overset{x}{^}$ , the direction of travel).

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What produces electromagnetic waves?Show answer
Accelerated charges.
2.Speed in vacuum in terms of μ₀ and ε₀?Show answer
$c = \frac{1}{μ _{0} ε _{0}}$ .
3.Are E and B in phase?Show answer
Yes.
4.B₀ = 10⁻⁶ T: E₀ in vacuum?Show answer
300 V/m.
5.Which quantity stays the same when a wave enters glass?Show answer
Frequency.

Properties of Electromagnetic Waves: frequently asked questions

Why are electromagnetic waves called transverse?

Because both the electric and magnetic fields oscillate at right angles to the direction in which the wave travels.

Why does a charge moving at constant speed not radiate?

Its fields move along with it without changing shape; only an accelerating charge creates the changing fields that break away as a wave.

Why are electromagnetic waves not deflected by magnetic fields?

They carry no electric charge, so no force acts on them.

What does the ISC 2027 syllabus need here?

A qualitative account of electromagnetic waves and their characteristics, including transverse nature (E and B perpendicular to c), and the common features of all regions of the spectrum.

Is $E_0 = cB_0$ needed for ISC?

The syllabus treats transverse nature qualitatively, but the relation is a one-line result used in short questions and helps you check directions and magnitudes.