For an electromagnetic wave propagating through vacuum, $\overrightarrow{k}$, $\overrightarrow{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by:

(B) $\frac{\overrightarrow{k} \times \overrightarrow{E}}{\omega}$

(A) $\frac{\overrightarrow{E} \times \overrightarrow{k}}{\omega}$

(C) $\omega(\overrightarrow{E} \times \overrightarrow{k})$

(D) $\omega(\overrightarrow{k} \times \overrightarrow{E})$

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · EM Waves

For an electromagnetic wave propagating through vacuum,

k

E

and

ω

represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by:

(A) $\frac{E \times k}{ω}$
(B) $\frac{k \times E}{ω}$ ✓ Correct
(C) $ω (E \times k)$
(D) $ω (k \times E)$

Answer: (B)

Solution

In an electromagnetic wave

E

B

and the propagation direction are mutually perpendicular, with

B = \frac{1}{c} (\hat{k} \times E)

. Writing

k = k \hat{k}

and

c = \frac{ω}{k}

gives

B = \frac{k}{ω} (\hat{k} \times E) = \frac{k \times E}{ω}

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Single correct option

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