A magnetic field vector in an electromagnetic wave is represented by, $\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \sin \left(2 \pi \mathrm{vt}-\frac{2 \pi \mathrm{x}}{\lambda}\right) \hat{\mathrm{j}}$. Its associated electric field vector is ______ .

(A) $\overrightarrow{\mathrm{E}}=-\mathrm{v} \lambda \mathrm{B}_{0} \sin \left(2 \pi \mathrm{vt}-\frac{2 \pi \mathrm{x}}{\lambda}\right) \hat{\mathrm{k}}$

(B) $\overrightarrow{\mathrm{E}}=-v \lambda \mathrm{~B}_{0} \sin \left(2 \pi v \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right) \hat{\mathrm{i}}$

(C) $\overrightarrow{\mathrm{E}}=v \lambda \mathrm{~B}_{0} \sin \left(2 \pi v \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right) \hat{\mathrm{k}}$

(D) $\overrightarrow{\mathrm{E}}=v \lambda \mathrm{~B}_{0} \sin \left(2 \pi v \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right) \hat{\mathrm{i}}$

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · EM Waves

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A magnetic field vector in an electromagnetic wave is represented by,

B = B_{0} sin (2 π vt - \frac{2 π x}{λ}) \hat{j}

. Its associated electric field vector is ______ .

(A) $E = - v λ B_{0} sin (2 π vt - \frac{2 π x}{λ}) \hat{k}$ ✓ Correct
(B) $E = - v λ B_{0} sin (2 π v t - \frac{2 π x}{λ}) \hat{i}$
(C) $E = v λ B_{0} sin (2 π v t - \frac{2 π x}{λ}) \hat{k}$
(D) $E = v λ B_{0} sin (2 π v t - \frac{2 π x}{λ}) \hat{i}$

Answer: (A)

Solution

From the phase

2 π ν t - \frac{2 π x}{λ}

the wave travels along

+ \overset{x}{^}

, and

B

points along

\hat{j}

. The three directions satisfy

\hat{E} \times \hat{B} = \overset{c}{^}

with

\overset{c}{^} = \hat{i}

, so

\hat{E} \times \hat{j} = \hat{i}

, which requires

\hat{E} = - \hat{k}

. The amplitudes are related by

E_{0} = c B_{0} = ν λ B_{0}

. Therefore

E = - ν λ B_{0} sin (2 π ν t - \frac{2 π x}{λ}) \hat{k}

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 04 Apr 2026 · Shift 2 · EM Waves

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