The electric field a plane electromagnetic wave is given by : E y =69 sin [0.6 × 10 3 x -1.8 × 10 11 t ] V / m . The expression for magnetic field associated with this electromagnetic wave is \ \ \ \ T.

B z =2.3 × 10 -7 sin [0.6 × 10 3 x -1.8 × 10 11 t ]

B z =2.3 × 10 -7 sin [0.6 × 10 3 x +1.8 × 10 11 t ]

B y =69 sin [0.6 × 10 3 x +1.8 × 10 11 t ]

B y =2.3 × 10 -7 sin [0.6 × 10 3 x -1.8 × 10 11 t ]

Physics · Electromagnetic Waves

JEE Main 2026 — 21 January, Morning Shift — Question 34

The electric field a plane electromagnetic wave is given by : $\mathrm{E}_{\mathrm{y}}=69 \sin \left[0.6 \times 10^{3} \mathrm{x}-1.8 \times 10^{11} \mathrm{t}\right] \mathrm{V} / \mathrm{m}$ . The expression for magnetic field associated with this electromagnetic wave is $\_\_\_\_$ T.

Option A:
$\mathrm{B}_{\mathrm{z}}=2.3 \times 10^{-7} \sin \left[0.6 \times 10^{3} \mathrm{x}-1.8 \times 10^{11} \mathrm{t}\right]$
Correct
Option B:
$\mathrm{B}_{\mathrm{z}}=2.3 \times 10^{-7} \sin \left[0.6 \times 10^{3} \mathrm{x}+1.8 \times 10^{11} \mathrm{t}\right]$
Option C:
$\mathrm{B}_{\mathrm{y}}=69 \sin \left[0.6 \times 10^{3} \mathrm{x}+1.8 \times 10^{11} \mathrm{t}\right]$
Option D:
$\mathrm{B}_{\mathrm{y}}=2.3 \times 10^{-7} \sin \left[0.6 \times 10^{3} \mathrm{x}-1.8 \times 10^{11} \mathrm{t}\right]$

Answer: A

Step-by-step solution

$\hat{B}=\hat{c} \times \hat{E}$ $\Rightarrow \quad \hat{\mathrm{c}}=\hat{\mathrm{i}}$ because phase of electric field is function of x .

\begin{aligned} \Rightarrow \quad & \hat{\mathrm{E}}=\hat{\mathrm{j}} \text { (given) } \Rightarrow \quad & \hat{\mathrm{B}}=\hat{\mathrm{i}} \times \hat{\mathrm{j}}=\hat{\mathrm{k}} & |\mathrm{~B}|=\frac{|\mathrm{E}|}{\mathrm{c}}=\frac{69 \times 0.6 \times 10^{3}}{1.8 \times 10^{11}}=\frac{69}{3 \times 10^{8}} & |\mathrm{~B}|=2.9 \times 10^{-7} & \overrightarrow{\mathrm{~B}}_{2}=2.9 \times 10^{-7} \sin \left(0.6 \times 10^{3} \mathrm{x}-1.8 \times 10^{11} \mathrm{t}\right) \end{aligned}

(phase is same as that of electric field)

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 21 January, Morning Shift
Subject: Physics
Chapter: Electromagnetic Waves
Topic: Displacement Current and Equation of EM Waves