The amplitude of the magnetic field of a plane electromagnetic wave propagating along positive X axis in vacuum is 510\ nT k and its angular frequency is 60×10^6 rad/sec. Write the expression for the electric field (E).

PhysicsCBSE Class 12 · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2025-26: question 17

From the official CBSE sample question paper for 2025-26, section B, question 17, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q17 · 2 marks · Very short answerElectromagnetic Waves

The amplitude of the magnetic field of a plane electromagnetic wave propagating along positive X axis in vacuum is $510 nT \hat{k}$ and its angular frequency is $60 \times 1 0^{6}$ rad/sec. Write the expression for the electric field $(E)$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

How are the amplitudes of E and B related in vacuum?

Hint 2

Find the wave number from $k = ω / c$ .

Hint 3

E must be perpendicular to both B ( $\hat{k}$ ) and the direction of travel ( $\hat{i}$ ); use $E \times B$ along $\hat{i}$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

For an EM wave, $E$ , $B$ and the direction of propagation are mutually perpendicular, with $E \times B$ along the direction of travel. Here $B$ is along $\hat{k}$ and the wave travels along $+ \hat{i}$ . Since $\hat{j} \times \hat{k} = \hat{i}$ , $E$ must be along $\hat{j}$ .
$E_{0} = c B_{0} = 3 \times 1 0^{8} \times 510 \times 1 0^{- 9} = 153 N/C$ and $k = \frac{ω}{c} = \frac{60 \times 1 0 ^{6}}{3 \times 1 0 ^{8}} = 0.2 rad/m$ .
1 mark
$E = 153 sin (60 \times 1 0^{6} t - 0.2 x) \hat{j} N/C$
1 mark

Answer: $E = 153 sin (6 \times 1 0^{7} t - 0.2 x) \hat{j}$ N/C

Where the marks are

Calculates $E_{0} = c B_{0} = 153$ N/C and $k = ω / c = 0.2$ rad/m (1 mark)
Writes the correct expression $E = 153 sin (60 \times 1 0^{6} t - 0.2 x)$ N/C along $\hat{j}$ (1 mark)

Revise the chapter

Chapter: Electromagnetic Waves (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Electromagnetic Waves, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Physics sample paper 2025-26: question 17

Hints

Step-by-step solution

Revise the chapter

More questions from Electromagnetic Waves