SATHEE: electromagnetic-waves Question 16

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Question: Q. 6. A plane electromagnetic wave of frequency 25 MHz travels in free space along the $x$ -direction. At $a$ particular point in space and time, $E =$

$6.3 \hat{j} V / m$ . What is $B$ at this point?

U] [SQP II 2017]

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Solution:

Ans. The magnitude of $B$ is

$\begin{aligned} B & = \frac{E}{c} & = \frac{6.3 V / m}{3 \times 10^{8} m / s} & = 2.1 \times 10^{- 8} T \end{aligned}$

To find the direction, we note that $E$ is along $y$ -direction and the wave propagates along $x$ -axis. Therefore, $B$ should be in a direction perpendicular to both $x$ and $y$ -axes. Using vector algebra, $E \times B$ should be along $x$ -direction.

Since, $(+ \hat{j}) \times (+ \hat{k}) = \hat{i}$ so, $B$ is along $z$ -direction and is $2.1 \times 10^{- 8} T$ .

[CBSE Marking Scheme 2017]

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