Previous year questions: Electromagnetic Waves

The questions below come from official CBSE board papers and official Sample Question Papers. The year label in each heading is printed on the source, and the marks are the marks printed for that question or part. Try the question before reading the answer.

Q1 (CBSE Board 2024, 1 mark)

The electric field in four regions is described as: Region I, Ex = E0 sin (kz minus omega t); Region II, Ex = E0; Region III, Ex = E0 sin kz; Region IV, Ex = E0 cos kz. The displacement current will exist in the region (A) I (B) IV (C) II (D) III

Answer: Option (A), region I. The displacement current comes from epsilon0 multiplied by the time derivative of the electric flux, so it appears only where the field varies with time. In region I the field depends on time through sin (kz minus omega t), so its derivative is nonzero. In regions II, III and IV the field does not change with time, so the displacement current is zero there.

Q2 (CBSE Board 2025, 1 mark)

The amplitude of the electric field in an electromagnetic wave in free space is 1000 V per metre. The amplitude of the magnetic field in this wave is

Answer: In free space E0/B0 = c, so B0 = E0/c = 1000 divided by 3 x 10 to the power 8 = 3.33 x 10 to the power minus 6 T, that is about 3.3 microtesla. The two fields oscillate in phase, so the magnetic amplitude is reached at the same instant as the electric amplitude, and the corresponding option is the one giving 3.3 x 10 to the power minus 6 T.

Q3 (CBSE Board 2025, 3 marks)

(a) State any three characteristics of electromagnetic waves. (b) Briefly explain how and where the displacement current exists during the charging of a capacitor.

Answer: (a) Electromagnetic waves are produced by accelerated charges; the electric and magnetic fields oscillate in phase, perpendicular to each other and perpendicular to the direction of propagation, so the waves are transverse; they travel in vacuum at c = 1 divided by the square root of mu0 epsilon0, which is 3 x 10 to the power 8 m per second, and need no medium. Their field amplitudes satisfy E0/B0 = c, and they carry energy and momentum. (b) During charging, the electric field between the plates grows as charge accumulates. The changing electric flux gives a displacement current I_d = epsilon0 d(phi_E)/dt, and this current exists in the space between the plates, where there is no conduction current. Its value equals the charging current in the wires, so the circuit behaves as if it were continuous.

Q4 (CBSE Board 2026, 1 mark)

An electromagnetic wave passes from vacuum into a dielectric medium with relative electrical permittivity 3/2 and relative magnetic permeability 8/3. Then its speed becomes

Answer: The speed in a medium is v = c divided by the square root of (mu_r epsilon_r). The product of the relative permittivity and permeability is (3/2) times (8/3) = 4, so the square root is 2 and the speed becomes c/2. The frequency of the wave does not change when it enters the medium, so the wavelength also becomes half of its vacuum value.

Q5 (CBSE Board 2026, 1 mark)

Electromagnetic waves used in a diagnostic tool in medicine have a wavelength range (A) 1 nm to 10 to the power minus 3 nm (B) 1 m to 10 to the power minus 3 m (C) 1 mm to 10 to the power minus 3 mm (D) 1 cm to 10 to the power minus 3 cm

Answer: Option (A), 1 nm to 10 to the power minus 3 nm. The diagnostic tool is the X-ray machine, and X-rays lie between ultraviolet and gamma rays in the spectrum, with wavelengths of the order of a nanometre down to a picometre. The other ranges belong to radio and microwaves, and none of them can image bone the way X-rays do.

Q6 (CBSE Board 2023, 2 marks)

Consider an induced magnetic field due to a changing electric field and an induced electric field due to a changing magnetic field. Which one is more easily observed? Justify your answer.

Answer: The induced electric field due to a changing magnetic field is more easily observed. When a magnetic flux through a coil changes, the induced electric field drives the free electrons along the wire, and the resulting current can be large and is easy to detect, which is the everyday observation of electromagnetic induction. The induced magnetic field due to a changing electric field is much weaker because it is produced by the displacement current, which is a changing electric flux rather than a flow of charge, so the field is small and needs sensitive experiments to detect.

Q7 (CBSE Board 2022, 3 marks)

(a) Depict a plane electromagnetic wave propagating along the x-axis. Write the expressions for its oscillating electric and magnetic fields. (b) Write three characteristics of electromagnetic waves.

Answer: (a) The propagation direction is the x-axis, the electric field oscillates along y and the magnetic field along z, so each field is perpendicular to the other and to the direction of motion. For a wave moving along positive x, the fields are written as Ey = E0 sin (kx minus omega t) and Bz = B0 sin (kx minus omega t), with E0/B0 = c. (b) The waves are transverse with E and B in phase; they travel in vacuum at the speed of light given by 1 divided by the square root of mu0 epsilon0 and need no medium; they carry energy and momentum and show reflection, refraction, interference, diffraction and polarisation.

Q8 (CBSE SQP 2024-25, 1 mark)

A capacitor consists of two parallel plates with an area of cross-section of 0.001 square metre, separated by a distance of 0.0001 m. If the voltage across the plates varies at the rate of 10 to the power 8 V per second, the value of the displacement current through the capacitor is (A) 8.85 x 10 to the power minus 3 A (B) 8.85 x 10 to the power minus 4 A (C) 7.85 x 10 to the power minus 3 A (D) 9.85 x 10 to the power minus 3 A

Answer: Option (A), 8.85 x 10 to the power minus 3 A. The electric field is the voltage divided by the separation, so it rises at 10 to the power 8 divided by 10 to the power minus 4 = 10 to the power 12 V per metre per second. The displacement current is epsilon0 times the area times this rate, which is 8.85 x 10^-12 x 0.001 x 10^12 = 8.85 x 10^-3 A. This equals the conduction current in the connecting wires.

Q9 (CBSE SQP 2023-24, 3 marks)

Identify the part of the electromagnetic spectrum which (a) produces a heating effect, (b) is absorbed by the ozone layer in the atmosphere, (c) is used for studying crystal structure. Write any one method of production of each of the above radiations.

Answer: (a) Infrared produces the heating effect; it is produced by hot bodies and by the vibrations of atoms and molecules. (b) Ultraviolet is absorbed by the ozone layer; it is produced by very hot bodies such as the Sun, and by special lamps such as mercury vapour lamps. (c) X-rays are used for studying crystal structures; they are produced by high energy electron transitions in atoms or by bombarding a metal target with energetic electrons. The three bands differ in wavelength and frequency but all travel at c in vacuum.

Q10 (CBSE SQP 2023-24, 1 mark)

An electromagnetic wave has its electric field oscillating along the positive y direction and its magnetic field oscillating along the positive z direction. State the direction in which the wave propagates.

Answer: The wave propagates along the positive x direction. The direction of travel is the direction of the vector E cross B, and with E along y and B along z the cross product y cross z gives x. So the wave moves perpendicular to both fields, along the positive x axis, which is the transverse character of electromagnetic waves expressed with vectors.