# A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction.

Question:

A plane electromagnetic wave of frequency $25 \mathrm{GHz}$ is propagating in vacuum along the $z$-direction. At a particular point in space and time, the magnetic field is given by $\vec{B}=5 \times 10^{-8} \hat{j} T$. The corresponding electric field $\vec{E}$ is

(speed of light $c=3 \times 10^{8} \mathrm{~ms}^{-1}$ )

1. (1) $1.66 \times 10^{-16} \hat{i} \mathrm{~V} / \mathrm{m}$

2. (2) $-1.66 \times 10^{-16} \hat{i} \mathrm{~V} / \mathrm{m}$

3. (3) $-15 \hat{i} \mathrm{~V} / \mathrm{m}$

4. (4) $15 \hat{i} \mathrm{~V} / \mathrm{m}$

Correct Option: , 4

Solution:

(4) Amplitude of electric field $(E)$ and Magnetic field $(B)$ of an electromagnetic wave are related by the relation

$\Rightarrow E=B c$

$\Rightarrow E=5 \times 10^{-8} \times 3 \times 10^{8}=15 \mathrm{~N} / \mathrm{C}$

$\Rightarrow \vec{E}=15 \hat{i} \mathrm{~V} / \mathrm{m}$

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