PhysicsISC Class 12 · Chapter 8

Electromagnetic Waves ISC Class 12: Notes, Spectrum and Questions

Q: Is this chapter examined with numericals?

Mostly qualitative ('qualitative ideas only' in the syllabus), but simple calculations with c = f\lambda, E_0 = cB_0 or the displacement current can appear in short answers.

Q: How many marks is Electromagnetic Waves worth?

2 of the 70 theory marks, as a separate unit in the 2027 weightage table.

Q: Do I need exact wavelength ranges?

The syllabus asks for the approximate range of λ or f, or at least the proper order of increasing f or λ. Learn order-of-magnitude values for each region.

Q: Do I need Maxwell's equations?

No. Only the basic idea of displacement current and the qualitative features of EM waves are required.

Q: Why does the frequency of light not change when it enters glass?

Frequency is set by the source. In glass the speed falls, so the wavelength falls in proportion (\lambda = v/f).

Q: Are communication systems in the 2027 syllabus?

No. The Communication Systems unit was removed in the 2027 revision; this chapter covers only the spectrum and its uses.

Updated 14 October 2026 · Fact-checked

Electromagnetic Waves is Chapter 8 of ISC Class 12 Physics, treated qualitatively. It covers the basic idea of displacement current, how accelerated charges produce electromagnetic waves, their transverse nature and common properties, and the complete spectrum from radio waves to gamma rays, with sources, detection, uses and the approximate wavelength or frequency of each region.

What Electromagnetic Waves is about

This short chapter (2 of the 70 theory marks) ties electricity and magnetism to light. Maxwell noticed that Ampère's law fails for a charging capacitor: current flows in the wires but not across the gap between the plates. He added a displacement current, $I_{d} = ε_{0} \frac{d ϕ _{E}}{d t}$ , produced by the changing electric field in the gap, so that a changing electric field produces a magnetic field just as a changing magnetic field produces an electric field (Faraday). The syllabus asks only for the basic idea.

Together these two effects let electric and magnetic fields sustain each other and travel as an electromagnetic wave. Such waves are produced by accelerated (for example oscillating) charges. They are transverse: $E$ and $B$ oscillate in phase, perpendicular to each other and to the direction of travel. All of them travel through vacuum at $c = \frac{1}{μ _{0} ε _{0}} = 3 \times 1 0^{8} m s^{- 1}$ , need no medium, obey $c = f λ$ and $E_{0} / B_{0} = c$ , and carry energy and momentum.

The electromagnetic spectrum, in order of increasing frequency (decreasing wavelength), is: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. For each you need the source, detection, properties, uses and the approximate range of λ or f, or at least the correct order. Questions are short: name the radiation for a given frequency or use, convert λ to f, or arrange the regions in order.

Weightage: Electromagnetic Waves is part of the unit Electromagnetic Waves, which carries 2 of the 70 marks in the ISC Physics Paper 1 (Theory). Questions on it can appear in any section of the paper.Source: CISCE ISC Physics syllabus, examination year 2027, distribution of marks

Key concepts

Displacement current (basic idea): While a capacitor charges, a conduction current I flows in the wires, but no charge crosses the gap. Ampère's law $\oint B \cdot d l = μ_{0} I$ then gives different answers for two surfaces bounded by the same loop: one cut by the wire, one passing through the gap. Maxwell resolved this by noting that the electric field (and so the flux $ϕ_{E}$ ) between the plates is changing, and that this acts like a current: the displacement current $I_{d} = ε_{0} \frac{d ϕ _{E}}{d t}$ . In the gap $I_{d}$ equals the conduction current in the wires, so current is continuous round the circuit. The modified law is $\oint B \cdot d l = μ_{0} (I + I_{d})$ . The key idea: a changing electric field produces a magnetic field.; Worked example
The plates of a capacitor have area $0.01 m^{2}$ . While it charges, the field between them grows at $1 0^{12} V m^{- 1} s^{- 1}$ . Find the displacement current, and the conduction current in the connecting wires at that moment.
Try it first, then show the solutionSolution
$I_{d} = ε_{0} \frac{d ϕ _{E}}{d t} = ε_{0} A \frac{d E}{d t} = 8.85 \times 1 0^{- 12} \times 0.01 \times 1 0^{12}$
$I_{d} = 0.0885 A$
Current is continuous: the conduction current in the wires is also 0.0885 A.
Answer: About 0.089 A in the gap and in the wires
Production and transverse nature of electromagnetic waves: A charge at rest has only an electric field; a charge moving at constant velocity also has a steady magnetic field; but an accelerated charge sends out a disturbance in both fields that travels away as a wave. An oscillating charge (for example in an antenna driven by an LC circuit) radiates waves at its own frequency. In the wave, the changing $E$ produces $B$ and the changing $B$ produces $E$ . $E$ and $B$ are in phase, perpendicular to each other and both perpendicular to the direction of propagation ( $E \times B$ points along the direction of travel), so the waves are transverse. For a wave along x: $E_{y} = E_{0} sin (k x - ω t)$ , $B_{z} = B_{0} sin (k x - ω t)$ .; Worked example
An electromagnetic wave travels along +x with its electric field along y. Along which axis does its magnetic field oscillate? Why can it not be along x?
Try it first, then show the solutionSolution
$E \times B$ must point along +x. With $E$ along y, $\hat{j} \times \hat{k} = \hat{i}$ , so $B$ is along z.
B along x would be along the direction of travel, but both fields in an electromagnetic wave are perpendicular to it (transverse).
Answer: Along z; the wave is transverse, so neither field has a component along x
Common properties of all electromagnetic waves: (1) They need no medium and travel through vacuum. (2) All travel in vacuum at the same speed $c = \frac{1}{μ _{0} ε _{0}} \approx 3 \times 1 0^{8} m s^{- 1}$ ; in a medium they travel at $v = \frac{1}{μ ε}$ , which is less. (3) They are transverse ( $E ⊥ B$ , both ⊥ direction). (4) The amplitudes are related by $E_{0} = c B_{0}$ . (5) They obey $c = f λ$ ; frequency is set by the source and does not change from one medium to another. (6) They carry energy and momentum (so they exert radiation pressure). (7) They show reflection, refraction, interference, diffraction and polarisation, and are not deflected by electric or magnetic fields (they carry no charge).; Worked example
In a light wave in vacuum, the peak electric field is $30 V m^{- 1}$ . Find the peak magnetic field. Show that $\frac{1}{μ _{0} ε _{0}}$ gives the speed of light.
Try it first, then show the solutionSolution
$B_{0} = \frac{E _{0}}{c} = \frac{30}{3 \times 1 0 ^{8}} = 1 \times 1 0^{- 7} T$
$\frac{1}{4 π \times 1 0 ^{- 7} \times 8.854 \times 1 0 ^{- 12}} = \frac{1}{1.113 \times 1 0 ^{- 17}} = 3.0 \times 1 0^{8} m s^{- 1}$
Answer: $B_{0} = 1 0^{- 7} T$ ; $c \approx 3.0 \times 1 0^{8} m s^{- 1}$
The electromagnetic spectrum: order and approximate ranges: In order of increasing frequency (decreasing wavelength), with approximate wavelengths: radio waves (above about 0.1 m; frequencies below about 1 GHz), microwaves (about 1 mm to 0.1 m; roughly 1 GHz to 300 GHz), infrared (about 700 nm to 1 mm), visible light (400 nm violet to 700 nm red), ultraviolet (about 1 nm to 400 nm), X-rays (about $1 0^{- 3}$ nm to 10 nm), gamma rays (below about $1 0^{- 3}$ nm, i.e. less than about $1 0^{- 12}$ m). The boundaries overlap; the regions are distinguished as much by how they are produced as by wavelength. Photon energy rises with frequency, so the high-frequency end (UV, X-rays, gamma rays) is ionising and harmful in large doses.; Worked example
Name the region and find the frequency of radiation of wavelength 3 nm.
Try it first, then show the solutionSolution
$f = \frac{c}{λ} = \frac{3 \times 1 0 ^{8}}{3 \times 1 0 ^{- 9}} = 1 \times 1 0^{17} H z$
3 nm lies in the soft X-ray region (between about $1 0^{- 3}$ nm and 10 nm), at the boundary with extreme ultraviolet.
Answer: $1 0^{17}$ Hz; X-rays (soft)
Sources and detection of each region: Radio: produced by oscillating currents in antennas (LC circuits); detected by aerials and receivers. Microwaves: produced by special vacuum tubes (klystron, magnetron, Gunn diode); detected by point-contact diodes and receiving horns. Infrared: given out by hot bodies and by vibrating molecules; detected by thermopiles, bolometers, IR-sensitive film and our skin (warmth). Visible: emitted when electrons in atoms move from higher to lower energy levels (Sun, lamps); detected by the eye, photocells, film. Ultraviolet: from the Sun, arc lamps and very hot bodies; detected by photocells and photographic film. X-rays: produced when high-energy electrons strike a metal target; detected by photographic film, Geiger tubes, ionisation chambers. Gamma rays: emitted by radioactive nuclei and in nuclear reactions; detected by Geiger tubes, ionisation chambers and scintillation counters.; Worked example
State the source and a detector for (a) microwaves and (b) gamma rays.
Try it first, then show the solutionSolution
(a) Microwaves: produced by a magnetron or klystron tube (or Gunn diode); detected by a point-contact diode.
(b) Gamma rays: emitted by radioactive nuclei (nuclear decay or reactions); detected by a Geiger tube or ionisation chamber.
Answer: (a) magnetron / klystron; point-contact diode (b) radioactive nuclei; Geiger tube
Uses of each region: Radio waves: radio and TV broadcasting, mobile communication (lower bands). Microwaves: radar, satellite and mobile communication, microwave ovens (polar water molecules are set rotating by the oscillating field, producing heat). Signals between a satellite and a dish antenna are microwaves. Infrared: TV remote controls, night-vision cameras, physiotherapy (heating), weather forecasting; it keeps the Earth warm through the greenhouse effect. Visible: vision, photography, optical fibres. Ultraviolet: sterilising water and surgical instruments, detecting forged notes, LASIK eye surgery; most solar UV is absorbed by the ozone layer. X-rays: medical imaging (bones), detecting cracks in metals, studying crystal structure. Gamma rays: treating cancer (radiotherapy), sterilising medical equipment and food.; Worked example
A microwave oven works at 2.45 GHz. Find the wavelength of the microwaves and explain how they heat food.
Try it first, then show the solutionSolution
$λ = \frac{c}{f} = \frac{3 \times 1 0 ^{8}}{2.45 \times 1 0 ^{9}} = 0.122 m = 12.2 c m$
The oscillating electric field makes polar water molecules in the food rotate back and forth; this molecular motion becomes heat.
Answer: About 12 cm; by setting water molecules rotating

Physics in real life: Electromagnetic Waves

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.

Microwaves for satellite communication

Suppose your home has a dish antenna receiving TV signals from a satellite broadcasting at 12 GHz.

Which region of the spectrum is this, and what is the wavelength? Why is a dish a few tens of centimetres across suitable?

Try it first, then show the solutionSolution

$λ = \frac{3 \times 1 0 ^{8}}{12 \times 1 0 ^{9}} = 0.025 m = 2.5 c m$ : microwaves.
The dish is many wavelengths across, so it can focus the parallel beam onto the receiver at its focus.

Answer: Microwaves, wavelength 2.5 cm; a dish many wavelengths wide reflects them to a focus.

Memory hook: Satellite to dish: microwaves, centimetres long.

Radio wavelengths

Imagine comparing an FM station on 100 MHz with an AM station on 1 MHz.

Find the wavelength of each.

Try it first, then show the solutionSolution

FM: $λ = \frac{3 \times 1 0 ^{8}}{1 0 ^{8}} = 3 m$
AM: $λ = \frac{3 \times 1 0 ^{8}}{1 0 ^{6}} = 300 m$

Answer: 3 m and 300 m: both radio waves, AM a hundred times longer.

Memory hook: c = fλ: higher station number, shorter wave.

X-rays in medical imaging

Suppose a hospital X-ray machine produces radiation of frequency $3 \times 1 0^{18} H z$ .

Find its wavelength and explain why it can pass through flesh but is stopped more by bone.

Try it first, then show the solutionSolution

$λ = \frac{3 \times 1 0 ^{8}}{3 \times 1 0 ^{18}} = 1 0^{- 10} m = 0.1 nm$
Such short-wavelength, high-energy photons pass easily through soft tissue but are absorbed more by bone, which contains heavier atoms (calcium), so bones cast shadows on the detector.

Answer: 0.1 nm; bone absorbs X-rays more strongly than flesh.

Memory hook: Tiny wavelength, big energy, sees through skin, not bone.

Topics in this chapter

Electromagnetic Waves formula sheet

Displacement current: $I_{d} = ε_{0} \frac{d ϕ _{E}}{d t}$; Equals the conduction current in the wires of a charging capacitor.
Ampère-Maxwell law: $\oint B \cdot d l = μ_{0} (I + I_{d})$; Basic idea only.
Speed of EM waves in vacuum: $c = \frac{1}{μ _{0} ε _{0}} = 3 \times 1 0^{8} m s^{- 1}$; In a medium $v = 1/ μ ε$ .
Wave relation: $c = f λ$; Convert nm to m: $1 nm = 1 0^{- 9} m$ .
Field amplitudes: $E_{0} = c B_{0}$; E in V m⁻¹, B in T.
Wave equations: $E_{y} = E_{0} sin (k x - ω t), B_{z} = B_{0} sin (k x - ω t)$; E, B and the direction of travel are mutually perpendicular.

Electromagnetic Waves: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

An electromagnetic wave

'Show the transverse nature of an electromagnetic wave with a labelled sketch'.

Draw

Draw three perpendicular axes x, y, z; x is the direction of travel.
Draw a sine wave in the x-y plane for $E$ and a sine wave in the x-z plane for $B$ , in phase (crests at the same x).
Mark one wavelength λ and the direction of propagation.

Label

$E$ (along y)
$B$ (along z)
direction of propagation (x)
λ

Watch out: Peaks of E and B must line up; drawing them a quarter-wave apart is wrong for a travelling wave.

Charging capacitor and displacement current

Explaining the need for displacement current.

Draw

A parallel-plate capacitor connected to a battery through wires carrying current I.
Show field lines between the plates growing (label 'E increasing').
Draw a circular loop round the wire; show one flat surface cut by the wire and one 'pot-shaped' surface passing between the plates.

Label

I (conduction current)
$I_{d}$ in the gap
E increasing
surfaces $S_{1}$ and $S_{2}$

Watch out: Write: 'no conduction current crosses $S_{2}$ , but $ε_{0} d ϕ_{E} / d t$ does'.

The spectrum as a labelled strip

Arranging the seven regions in order; useful for every one-mark spectrum item.

Draw

A long horizontal strip divided into seven parts: radio, microwave, infrared, visible, UV, X-ray, gamma.
Arrow above it: frequency increasing to the right; arrow below: wavelength increasing to the left.
Write a typical wavelength under each band (1 m, 1 cm, 10 µm, 500 nm, 100 nm, 0.1 nm, 1 pm).

Label

region names
f increasing →
← λ increasing
typical λ values

Watch out: Put the visible band narrow, with violet next to UV and red next to IR.

How the board asks Electromagnetic Waves

The question patterns to expect, and the method that works for each.

Question type	How it is asked	Method
Name the radiation	From a frequency or wavelength (e.g. $1 0^{11}$ Hz), a use (remote control, satellite link, sterilisation) or a source.	Convert to wavelength if needed, then place it on the spectrum strip.
Arrange in order	'Arrange the seven types in increasing order of frequency' or wavelength.	Radio, micro, IR, visible, UV, X, gamma for increasing frequency; reverse for wavelength.
Short calculations	f from λ (with nm conversion), $B_{0}$ from $E_{0}$ , c from $μ_{0}$ and $ε_{0}$ .	SI units throughout; give the unit Hz or T.
Displacement current	Why it is needed; its expression; its value in a charging capacitor.	Changing E between plates; $I_{d} = ε_{0} d ϕ_{E} / d t$ equals the conduction current.
Properties and transverse nature	State two properties; show directions of E and B; why EM waves are not deflected by fields.	List no medium, same speed c, transverse, $E_{0} = c B_{0}$ , carry energy and momentum.

Tricks to remember Electromagnetic Waves

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

Raging Martians Invaded Venus Using X-ray Guns
Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma: increasing frequency.
Use it when: Arranging the spectrum in order.
E, B, travel: a right-handed trio
Point fingers along E, curl towards B: the thumb shows the direction of travel ( $E \times B$ ).
Use it when: Finding the third direction from two.
E is c times B
$E_{0} = c B_{0}$ : the electric amplitude is 300 million times the magnetic one in SI units.
Use it when: Field-amplitude questions.
Changing E makes B
Faraday: changing B makes E. Maxwell: changing E makes B (displacement current). Together they make light.
Use it when: Explaining why EM waves are self-sustaining.
Satellite = microwave, remote = infrared
Dish on the roof talks in microwaves; the TV remote talks in infrared.
Use it when: Uses-based identification items.

Electromagnetic Waves: board-level solved questions

Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.

Example 1: Order of frequencies · 1 mark · MCQBoard level

Which list is in order of increasing frequency?
(a) X-rays, ultraviolet, visible, infrared
(b) microwaves, infrared, ultraviolet, gamma rays
(c) gamma rays, X-rays, radio waves, microwaves
(d) infrared, visible, radio waves, X-rays

Try it first, then show the solutionSolution

Frequency increases from radio through microwaves, IR, visible, UV, X-rays to gamma; only (b) follows that order.

Answer: (b)

Example 2: Transverse nature · 1 mark · Assertion-reasonBoard level

Assertion: Electromagnetic waves are transverse.
Reason: In an electromagnetic wave, the electric and magnetic fields oscillate perpendicular to each other and to the direction of propagation.
(a) Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
(b) Both Assertion and Reason are true, but Reason is not the correct explanation for Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Try it first, then show the solutionSolution

Transverse means oscillation perpendicular to the direction of travel, which is exactly what the reason states.

Answer: (a)

Example 3: Frequency from wavelength · 2 marks · Short answerHarder board level

Radiation has a wavelength of 3 nm in vacuum. Find its frequency and name the region of the spectrum. [2]

Try it first, then show the solutionSolution

Convert: $3 nm = 3 \times 1 0^{- 9} m$ ; $f = \frac{c}{λ} = \frac{3 \times 1 0 ^{8}}{3 \times 1 0 ^{- 9}} = 1 0^{17} H z$
This lies in the X-ray region (soft X-rays).

Answer: $1 0^{17}$ Hz; X-rays

Example 4: Why displacement current is needed · 3 marks · Short answerHarder board level

Explain, using a charging capacitor, why Maxwell introduced displacement current, and write its expression. If the charging current is 0.5 A and the plate area is $0.01 m^{2}$ , find the rate at which the field between the plates is increasing. [3]

Try it first, then show the solutionSolution

Ampère's law applied to a loop round the wire gives $μ_{0} I$ for a surface cut by the wire but zero for a surface passing between the plates, where no charge flows: a contradiction.
Between the plates the electric flux is changing; Maxwell's displacement current $I_{d} = ε_{0} \frac{d ϕ _{E}}{d t}$ fills the gap and equals I, making current continuous.
$\frac{d E}{d t} = \frac{I _{d}}{ε _{0} A} = \frac{0.5}{8.85 \times 1 0 ^{- 12} \times 0.01} = 5.65 \times 1 0^{12} V m^{- 1} s^{- 1}$

Answer: $I_{d} = ε_{0} d ϕ_{E} / d t$ ; $d E / d t \approx 5.6 \times 1 0^{12} V m^{- 1} s^{- 1}$

Example 5: Fields in a light wave · 3 marks · Short answerHarder board level

The electric field of a plane electromagnetic wave in vacuum has amplitude $600 V m^{- 1}$ and frequency $5 \times 1 0^{14} H z$ . Find (a) the amplitude of its magnetic field, (b) its wavelength and the region it belongs to. [3]

Try it first, then show the solutionSolution

(a) $B_{0} = \frac{E _{0}}{c} = \frac{600}{3 \times 1 0 ^{8}} = 2 \times 1 0^{- 6} T$
(b) $λ = \frac{c}{f} = \frac{3 \times 1 0 ^{8}}{5 \times 1 0 ^{14}} = 6 \times 1 0^{- 7} m = 600 nm$
600 nm lies between 400 and 700 nm: visible light (orange).

Answer: (a) $2 \times 1 0^{- 6} T$ (b) 600 nm, visible

Example 6: Spectrum: sources, detection and uses · 5 marks · Long answerHarder board level

(a) State any two properties common to all electromagnetic waves. [1]
(b) For microwaves, infrared, ultraviolet and X-rays, give one source and one use of each. [3]
(c) Find the wavelength of the microwaves used by a 2.45 GHz oven. [1]

Try it first, then show the solutionSolution

(a) They travel through vacuum at $3 \times 1 0^{8} m s^{- 1}$ and are transverse (also: carry energy, need no medium).
(b) Microwaves: magnetron/klystron; radar, ovens, satellite links. Infrared: hot bodies; remote controls, night vision, physiotherapy.
Ultraviolet: Sun, arc lamps; sterilising water, detecting forged notes. X-rays: high-energy electrons hitting a metal target; imaging bones, crystal structure.
(c) $λ = \frac{3 \times 1 0 ^{8}}{2.45 \times 1 0 ^{9}} = 0.122 m$

Answer: (c) about 12.2 cm

Example 7: Which radiation, and why? · 3 marks · Short answerHOTS / competency

Name the electromagnetic radiation involved in each case and give a reason: (a) the ozone layer protects living things from it; (b) it is trapped by greenhouse gases and keeps the Earth warm; (c) it is used by air-traffic radar. [3]

Try it first, then show the solutionSolution

(a) Ultraviolet: ozone absorbs most solar UV, which would otherwise damage skin cells and DNA.
(b) Infrared: the warm Earth re-radiates IR, which greenhouse gases absorb and re-emit, reducing heat loss.
(c) Microwaves: short enough wavelength to give sharp beams and reflect well from aircraft, yet pass through clouds.

Answer: (a) UV (b) IR (c) microwaves

Example 8: Why accelerated charges radiate · 2 marks · Short answerHOTS / competency

A charge moving with constant velocity does not emit electromagnetic waves, but the same charge oscillating up and down an antenna does. Explain. [2]

Try it first, then show the solutionSolution

A charge at constant velocity carries steady electric and magnetic fields along with it; nothing changes with time in its own frame, so no wave is sent out.
An oscillating charge is accelerated: its electric field changes, which produces a changing magnetic field and so on; this self-sustaining disturbance travels outward as an EM wave at the charge's frequency.

Answer: Only accelerated charges produce changing fields that propagate as waves

Case-study practice (Section D style)

Read the situation, then answer every part. In the board paper this is a 5-mark question split into 2 + 1 + 1 + 1 marks.

Radiation in a hospital

Suppose a hospital uses four kinds of electromagnetic radiation: P to photograph broken bones, Q to sterilise surgical instruments in a sealed pack, R in a heat lamp for physiotherapy, and S in a lamp that kills germs on work surfaces. One of them is emitted by a radioactive cobalt source.

(i) · 2 marks
Identify P, Q, R and S.
Answer
Answer: P: X-rays; Q: gamma rays; R: infrared; S: ultraviolet.
Bones absorb X-rays; gamma rays from radioactive cobalt penetrate sealed packs; IR heats tissue; UV kills germs on surfaces.
(ii) · 1 mark
Arrange P, Q, R and S in increasing order of wavelength.
Answer
Answer: Q, P, S, R
Gamma < X-rays < UV < IR in wavelength.
(iii) · 1 mark
P has frequency $3 \times 1 0^{18} H z$ . Find its wavelength.
Answer
Answer: 0.1 nm
$λ = c / f = 1 0^{- 10} m$
(iv) · 1 mark
Why are P and Q more dangerous to staff than R?
Answer
Answer: They are ionising.
Their photons have far higher energy (higher frequency), so they ionise atoms and damage cells and DNA; IR only warms tissue.

Current that crosses a gap

Suppose a capacitor with plates of area $0.01 m^{2}$ is being charged by a steady current of 0.5 A in the connecting wires. A student asks how the current 'gets across' the gap between the plates.

(i) · 1 mark
What is the displacement current between the plates?
Answer
Answer: 0.5 A
Displacement current in the gap equals the conduction current in the wires, so current is continuous.
(ii) · 1 mark
Find the rate of change of electric field between the plates.
Answer
Answer: $5.65 \times 1 0^{12} V m^{- 1} s^{- 1}$
$\frac{d E}{d t} = \frac{I}{ε _{0} A} = \frac{0.5}{8.85 \times 1 0 ^{- 14}}$
(iii) · 2 marks
Is there a magnetic field in the gap between the plates? Explain.
Answer
Answer: Yes.
The changing electric field acts as a current ( $I_{d}$ ), and by the Ampère-Maxwell law it produces a magnetic field circling the axis between the plates, just as a real current would.
(iv) · 1 mark
What happens to the displacement current once the capacitor is fully charged?
Answer
Answer: It becomes zero.
The field stops changing, so $d ϕ_{E} / d t = 0$ , and the conduction current has also stopped.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Electromagnetic radiation has wavelength 3 nm. Find its frequency and name it. (2 marks)

Step	Marks
$f = c / λ = 3 \times 1 0^{8} / (3 \times 1 0^{- 9}) = 1 0^{17} H z$ , with nm converted to m and unit Hz	1
X-rays	1

What is displacement current? Why was it needed? Write its expression. (3 marks)

Step	Marks
Current due to a changing electric field (changing electric flux)	1
Needed to make Ampère's law consistent for a charging capacitor (current continuity across the gap)	1
$I_{d} = ε_{0} \frac{d ϕ _{E}}{d t}$	1

Arrange the seven regions of the electromagnetic spectrum in increasing order of frequency and give one use each of microwaves, infrared and gamma rays. (5 marks)

Step	Marks
Radio, microwaves, infrared (correct first three)	1
Visible, ultraviolet, X-rays, gamma rays (correct last four)	1
Microwaves: radar / satellite communication / ovens	1
Infrared: remote controls / night vision / physiotherapy	1
Gamma rays: cancer treatment / sterilisation	1

Where students lose marks in Electromagnetic Waves

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

Mistake: Confusing microwaves with radio waves
CISCE examiners' comments, 2024 and 2025: asked to name radiation of frequency $1 0^{11}$ Hz, or the wave from a satellite to a dish antenna, candidates wrote radio waves, ultraviolet or infrared.
Wrong working
$1 0^{11}$ Hz is a radio wave.
Right working
$λ = 3 \times 1 0^{8} /1 0^{11} = 3 mm$ : microwaves. Satellite links also use microwaves.
Do this: Convert to wavelength and compare with the ranges: microwaves about 1 mm to 0.1 m.
Usually costs: 1 mark.
Mistake: Not converting nanometres
CISCE examiners' comments, 2025: finding the frequency for a wavelength in nm, candidates did not convert nm to metres, used the wrong formula, or gave the wrong unit.
Wrong working
$f = 3 \times 1 0^{8} /6 = 5 \times 1 0^{7} H z$
Right working
$f = 3 \times 1 0^{8} / (6 \times 1 0^{- 9}) = 5 \times 1 0^{16} H z$
Do this: Write the SI conversion as the first line.
Usually costs: 1 mark.
Mistake: Giving the speed of sound or omitting the unit
CISCE examiners' comments, 2024: asked for the speed of radio waves in vacuum, some candidates gave the speed of sound in air or omitted the unit.
Wrong working
330 m/s
Right working
$3 \times 1 0^{8} m s^{- 1}$ , the same for all electromagnetic waves in vacuum.
Do this: All EM waves: same speed c in vacuum.
Usually costs: 1 mark.
Mistake: Drawing E and B out of phase
A frequent diagram error: the E and B waves are drawn a quarter-wavelength apart or in the same plane.
Wrong working
E maximum where B is zero.
Right working
E and B reach their maxima together, in perpendicular planes.
Do this: Line up the crests of both waves.
Usually costs: 1 mark.

Practice questions on 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
The speed of radio waves in vacuum is:
(a) 330 m s⁻¹
(b) $3 \times 1 0^{6} m s^{- 1}$
(c) $3 \times 1 0^{8} m s^{- 1}$
(d) less than that of light
Hint
All EM waves travel at the same speed in vacuum.
Answer
(c)
Q2 · 1 mark · MCQBoard level
Which of these has the longest wavelength?
(a) X-rays
(b) infrared
(c) radio waves
(d) ultraviolet
Hint
Lowest frequency.
Answer
(c) radio waves
Q3 · 1 mark · MCQBoard level
X-rays are produced when:
(a) radioactive nuclei decay
(b) high-energy electrons strike a metal target
(c) charges oscillate in an antenna
(d) hot bodies cool
Hint
Think of an X-ray tube.
Answer
(b)
Q4 · 1 mark · Very short answerBoard level
Name the electromagnetic radiation used in a TV remote control.
Hint
Invisible, just beyond red.
Answer
Infrared.
Q5 · 2 marks · Short answerBoard level
Give one source and one use of gamma rays.
Hint
Nuclear origin.
Answer
Source: radioactive nuclei (nuclear decay or reactions). Use: treating cancer (radiotherapy) or sterilising medical equipment.
Q6 · 2 marks · Short answerHarder board level
Find the wavelengths of an FM signal at 100 MHz and an AM signal at 1 MHz.
Hint
λ = c/f.
Answer
3 m and 300 m.
Q7 · 2 marks · Short answerHarder board level
Calculate $\frac{1}{μ _{0} ε _{0}}$ using $μ_{0} = 4 π \times 1 0^{- 7} T m A^{- 1}$ and $ε_{0} = 8.854 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$ . What does the result tell you?
Hint
Multiply, take the square root, invert.
Answer
$μ_{0} ε_{0} = 1.113 \times 1 0^{- 17}$ , so the result is $3.0 \times 1 0^{8} m s^{- 1}$ : the speed of light, showing light is an electromagnetic wave.
Q8 · 2 marks · Short answerHOTS / competency
Why are electromagnetic waves not deflected by electric or magnetic fields, while a beam of electrons is?
Hint
What does each carry?
Answer
An electron beam carries charge, so fields exert qE and qvB on it. EM waves are oscillating fields carrying no charge, so no such force acts on them.
Q9 · 3 marks · Short answerHarder board level
A capacitor is charged by a current of 2 A. (a) What is the displacement current between its plates? (b) Write the Ampère-Maxwell law. (c) What produces a magnetic field in the gap?
Hint
Current continuity.
Answer
(a) 2 A (b) $\oint B \cdot d l = μ_{0} (I + I_{d})$ (c) the changing electric field (displacement current) between the plates.
Q10 · 3 marks · Short answerHarder board level
Arrange the seven regions of the electromagnetic spectrum in decreasing order of wavelength and give one detector each for infrared, ultraviolet and gamma rays.
Hint
Longest first.
Answer
Radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma. Detectors: IR: thermopile or bolometer; UV: photocell or photographic film; gamma: Geiger tube or ionisation chamber.
Q11 · 3 marks · Short answerHarder board level
An EM wave in vacuum has $E_{0} = 600 V m^{- 1}$ and $f = 5 \times 1 0^{14} H z$ . Find $B_{0}$ and λ, and name the region. In which direction does B point if E is along y and the wave travels along +x?
Hint
$E_{0} = c B_{0}$ , $E \times B$ along travel.
Answer
$B_{0} = 2 \times 1 0^{- 6} T$ ; λ = 600 nm, visible; B along +z (since $\hat{j} \times \hat{k} = \hat{i}$ ).
Q12 · 5 marks · Long answerHarder board level
(a) State four properties of electromagnetic waves. [2]
(b) Describe how microwaves and X-rays are produced and give one use of each. [2]
(c) A satellite transmits at 12 GHz. Find the wavelength. [1]
Hint
Speed, transverse nature, no medium, E0 = cB0.
Answer
(a) Travel in vacuum at c; transverse with E ⊥ B ⊥ direction; need no medium; $E_{0} = c B_{0}$ (also carry energy and momentum). (b) Microwaves: magnetron or klystron tubes; radar or ovens. X-rays: fast electrons striking a metal target; imaging bones. (c) λ = 2.5 cm.
Q13 · 2 marks · Short answerHarder board level
Name the wave travelling from a satellite to a dish antenna. Find its wavelength if its frequency is 12 GHz.
Hint
GHz frequencies.
Answer
Microwaves; $λ = 3 \times 1 0^{8} /1.2 \times 1 0^{10} = 0.025 m$ .

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 is displacement current?Show answer
The 'current' $I_{d} = ε_{0} d ϕ_{E} / d t$ associated with a changing electric field.
2.What produces electromagnetic waves?Show answer
Accelerated (e.g. oscillating) charges.
3.Why are EM waves called transverse?Show answer
E and B oscillate perpendicular to the direction of propagation (and to each other).
4.Relation between $E_{0}$ and $B_{0}$ ?Show answer
$E_{0} = c B_{0}$ .
5.Order of the spectrum by increasing frequency?Show answer
Radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays.
6.Wavelength range of visible light?Show answer
About 400 nm (violet) to 700 nm (red).
7.Which radiation is used in radar and satellite links?Show answer
Microwaves.
8.Which radiation is used to sterilise water?Show answer
Ultraviolet.

Best order to study it

Understand why Ampère's law needs the displacement current; learn $I_{d} = ε_{0} d ϕ_{E} / d t$ .
Learn how accelerated charges produce EM waves and draw the transverse wave.
List the common properties, including $c = 1/ μ_{0} ε_{0}$ and $E_{0} = c B_{0}$ .
Memorise the spectrum order with approximate wavelengths.
Make a table of source, detector and uses for each region.
Practise λ-f conversions with nm, µm and GHz.

Quick revision checklist

The night before the exam: can you do each of these without looking?

Can you explain why displacement current is needed and write its formula?
Can you draw an EM wave with E, B and the direction of travel?
Can you list four properties common to all EM waves?
Can you arrange all seven regions by frequency and by wavelength?
Can you give one source, one detector and one use for each region?
Can you convert nm or GHz to SI and use c = fλ?
Can you name the radiation for a satellite link, a remote control, sterilisation and bone imaging?

Electromagnetic Waves: frequently asked questions

Is this chapter examined with numericals?

Mostly qualitative ('qualitative ideas only' in the syllabus), but simple calculations with c = f\lambda, E_0 = cB_0 or the displacement current can appear in short answers.

How many marks is Electromagnetic Waves worth?

2 of the 70 theory marks, as a separate unit in the 2027 weightage table.

Do I need exact wavelength ranges?

The syllabus asks for the approximate range of λ or f, or at least the proper order of increasing f or λ. Learn order-of-magnitude values for each region.

Do I need Maxwell's equations?

No. Only the basic idea of displacement current and the qualitative features of EM waves are required.

Why does the frequency of light not change when it enters glass?

Frequency is set by the source. In glass the speed falls, so the wavelength falls in proportion (\lambda = v/f).

Are communication systems in the 2027 syllabus?

No. The Communication Systems unit was removed in the 2027 revision; this chapter covers only the spectrum and its uses.

Based on: CISCE ISC 2027 Physics syllabus (revised, uploaded February 2026); CISCE ISC 2027 Physics specimen Paper 1 (Theory) question paper and answer key; CISCE Analysis of Pupil Performance, ISC Physics, 2025; CISCE Analysis of Pupil Performance, ISC Physics, 2024