The electric field associated with an electromagnetic wave travelling in vacuum is given by $E_{0} \sin (3 y+4 z+\omega t) \hat{i}$, where $\omega$ is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are: [Given: speed of light in vacuum $c=3 \times 10^{8} \mathrm{~ms}^{-1}$.]

(A) The wave is travelling in $-\frac{1}{5}(3 \hat{j}+4 \hat{k})$ direction.; (C) The value of $\omega$ is $1.5 \times 10^{9} \mathrm{rad} \mathrm{s}^{-1}$.

(B) The magnitude of the wave vector is $0.5 \mathrm{~m}^{-1}$.

(D) The magnetic field associated with this wave is given by $\frac{E_{0}}{c} \sin (3 y+4 z+\omega t)(4 \hat{j}-3 \hat{k})$

EM Waves — JEE Advanced · 2026 · 17 May 2026 · Paper 1 Question with Solution

The electric field associated with an electromagnetic wave travelling in vacuum is given by

E_{0} sin (3 y + 4 z + ω t) \hat{i}

, where

ω

is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are:
[Given: speed of light in vacuum

c = 3 \times 1 0^{8} ms^{- 1}

(A)The wave is travelling in $- \frac{1}{5} (3 \hat{j} + 4 \hat{k})$ direction.✓ Correct
(B)The magnitude of the wave vector is $0.5 m^{- 1}$ .
(C)The value of $ω$ is $1.5 \times 1 0^{9} rad s^{- 1}$ .✓ Correct
(D)The magnetic field associated with this wave is given by $\frac{E _{0}}{c} sin (3 y + 4 z + ω t) (4 \hat{j} - 3 \hat{k})$

Answer: (A), (C)

Solution

The wave can be written as

E = E_{0} sin (ω t + 5 (\frac{3 j ^}{5} + \frac{4 k ^}{5}) \cdot r) \hat{i}

.

(A) Wave propagates opposite to the wave vector direction:

\overset{v}{^} = - (\frac{3 j ^}{5} + \frac{4 k ^}{5}) = - \frac{1}{5} (3 \hat{j} + 4 \hat{k})

✓

(B) Wave vector magnitude:

∣ k ∣ = 3^{2} + 4^{2} = 5

^{- 1}

, not 0.5 ✗

(C)

ω = ck = 3 \times 1 0^{8} \times 5 = 1.5 \times 1 0^{9}

rad/s ✓

(D)

\hat{B} = \overset{v}{^} \times \hat{E} = - (\frac{3 j ^}{5} + \frac{4 k ^}{5}) \times \hat{i} = \frac{3 k ^}{5} - \frac{4 j ^}{5}

, so

B = \frac{E _{0}}{5 c} sin (3 y + 4 z + ω t) (3 \hat{k} - 4 \hat{j})

✗

JEE Advanced · 2026 · 17 May 2026 · Paper 1 · One or more correct options

JEE Advanced · 2026 · 17 May 2026 · Paper 1 · EM Waves

Solution

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