In \overrightarrow E and \overrightarrow K represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : ( \omega - angular frequency) :

1 \over \omega ( \overline K \times \overline E )

\omega ( \overline K \times \overline E )

\omega ( \overline E \times \overline K )

Electromagnetic Waves PYQ — JEE Main 2023 · 24 Jan · Shift 1 · Q62 with Solution

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Correct answer: A

For an electromagnetic plane wave in vacuum,

\vec E,\; \vec B,\; \vec K

are mutually perpendicular, and the wave propagates along the wave vector $\vec K$ .

Also, from Maxwell's equations for a plane wave,

\vec B = \frac{1}{\omega}(\vec K \times \vec E).

For a plane wave,

\vec E = \vec E_0 e^{i(\vec K\cdot \vec r - \omega t)}

and using Faraday's law,

\nabla \times \vec E = -\frac{\partial \vec B}{\partial t}.

For the above form,

\nabla \times \vec E = i(\vec K \times \vec E),

and

-\frac{\partial \vec B}{\partial t} = i\omega \vec B.

Therefore,

i(\vec K \times \vec E)= i\omega \vec B

which gives

\vec B = \frac{1}{\omega}(\vec K \times \vec E).

A: $\frac{1}{\omega}(\vec K \times \vec E)$ ✔️
B: $\vec K \times \vec E$ ✖️ missing factor $\frac{1}{\omega}$
C: $\omega(\vec K \times \vec E)$ ✖️ wrong factor
D: $\omega(\vec E \times \vec K)$ ✖️ wrong factor and opposite cross-product order

The correct magnetic field vector is

\boxed{\vec B = \frac{1}{\omega}(\vec K \times \vec E)}.

So the correct option is A.