A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, \overrightarrow B = 2.0 \times 10^ - 8\widehat kT . (where, \widehat k is unit vector along z-direction) What is \overrightarrow E at this point?

Electromagnetic Waves PYQ — JEE Main 2021 · 18 Mar · Shift 1 · Q49 with Solution

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Correct answer: C

For a plane electromagnetic wave in vacuum,

\vec E \perp \vec B \perp \text{direction of propagation}

and

\vec E \times \vec B

points in the direction of propagation.

Here, the wave is travelling along the $+x$ -direction, and

\vec B = 2.0 \times 10^{-8} \hat k\, \text{T}

So we need $\vec E$ such that

\vec E \times \hat k = \hat i

Now,

\hat j \times \hat k = \hat i

Hence, $\vec E$ must be along $\hat j$ .

For electromagnetic waves in vacuum,

E = cB

where

c = 3 \times 10^8\, \text{m/s}

and

B = 2.0 \times 10^{-8}\, \text{T}

Thus,

E = (3 \times 10^8)(2.0 \times 10^{-8}) = 6.0\, \text{V/m}

Since magnitude is $6.0\,\text{V/m}$ and direction is $\hat j$ ,

\vec E = 6.0\, \hat j\, \text{V/m}

Therefore, the correct option is C.