First slide

Introduction-Electromagnetic waves

Question

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

Moderate

A

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

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

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

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

Solution

Given
Frequency of electro magnetic wave= $25 MHz = 25 \times 10^{6} Hz$
Electric field $\vec{E} = 6.3 \hat{j} V / m$
$c = \frac{E}{B} \Rightarrow B = \frac{E}{c} = \frac{6.3}{3 \times 10^{8}} = 2.1 \times 10^{- 8} T$
Also velocity of EMW is along $\vec{E} \times \vec{B}$ , so direction of magnetic field is given by $\vec{v} \times \vec{E} = (\hat{i} \times \hat{j}) = \hat{k}$

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