A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 V m–1 along y-direction. Its corresponding magnetic field component, B would be :

2 × 10–8 T along z-direction

2 × 10–8 T along y-direction

6 × 10–8 T along z-direction

6 × 10–8 T along x-direction

Electromagnetic Waves PYQ — JEE Main 2019 · 8 Apr · Shift 1 · Q54 with Solution

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Correct answer: C

Use the relation between $E$ and $B$ for an electromagnetic wave in free space

For a plane electromagnetic wave in free space, $E = cB$ where $c = 3 \times 10^8\ \text{m s}^{-1}$ .
Compute the magnitude of $B$

Given, $E = 6\ \text{V m}^{-1}$

So, $B = \frac{E}{c} = \frac{6}{3 \times 10^8} = 2 \times 10^{-8}\ \text{T}$
Find the direction of $B$

The wave travels along the $x$ -direction, so the direction of propagation is along $\vec{E} \times \vec{B}$

Given $\vec{E}$ is along the $y$ -direction. We need $\vec{E} \times \vec{B}$ to be along $+x$ .

Using unit vectors, $\hat{j} \times \hat{k} = \hat{i}$

Therefore, if $\vec{E}$ is along $y$ and propagation is along $x$ , then $\vec{B}$ must be along the $z$ -direction.
Match with the options
- Magnitude: $2 \times 10^{-8}\ \text{T}$
- Direction: along $z$
Hence the correct option is: $\boxed{\text{C}}$