Electromagnetic Waves Ques 23

23. In an electromagnetic wave in free space the root mean square value of the electric field is $E _{rms}=6 $ $V / m$. The peak value of the magnetic field is :-

[2017]

(a) $2.83 \times 10^{-8} T$

(b) $0.70 \times 10^{-8} T$

(c) $4.23 \times 10^{-8} T$

(d) $1.41 \times 10^{-8} T$

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Answer:

Correct Answer: 23.(a)

Solution:

  1. (a) Given, $E _{rms}=6$ $ V / m$

$\frac{E _{rms}}{B _{rms}}=c$

$\Rightarrow B _{rms}=\frac{E _{rms}}{c}$ $\quad$ …….(i)

$B _{rms}=\frac{B_0}{\sqrt{2}} \Rightarrow B_0=\sqrt{2} B _{rms}$

$B_0=\sqrt{2} \times \frac{E _{rms}}{c}\quad $ From equation (i)

$=\frac{\sqrt{2} \times 6}{3 \times 10^{8}}=2.83 \times 10^{-8} T$