First slide

Electromagnetic waves and its nature

Question

A plane electromagnetic wave of frequency 25MHz travels in free space along the x-direction . At a particular point in the space and time, if the intensity of electric field $\vec{E} = 6.3 \hat{j} V / m$ , the magnetic induction $\vec{B}$ at this point is

Moderate

A

$2.1 \times 10^{- 4} \hat{k} T$
B

$2.1 \times 10^{- 6} \hat{k} T$
C

$2.1 \times 10^{- 8} \hat{k} T$
D

$2.1 \times 10^{- 3} \hat{k} T$

Solution

1. Given
Wave Frequency $= 25 MHz$
Intensity of Electric Field $\bar{E} = 6.3 \hat{j} V / m$
The magnitude of the magnetic field is given by
$B = \frac{E}{c} = \frac{6.3}{3 \times 10^{8}} = 2.1 \times 10^{- 8} T .$
2. The vector $\vec{E} \times \vec{B}$ should be along x-direction, and so
$\hat{j} \times (\hat{A}) = \hat{i},$ indicates that $\hat{A} = \hat{k}$ .
Thus, $\vec{B} = 2.1 \times 10^{- 8} \hat{k} T .$
Therefore, the correct answer is (C).

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