Question

In an electromagnetic wave in free space the root mean square value of the electric field is $E_{rms}=6\text{V/m}.$ The peak value of the magnetic field is

• A. $1.41\times {10}^{-8}\text{T}$
• B. $2.83\times {10}^{-8}\text{T}$
• C. $0.70\times {10}^{-8}\text{T}$
• D. $4.23\times {10}^{-8}\text{T}$

Answer 1

The correct option is B $2.83\times {10}^{-8}\text{T}$

We know that for an electromagnetic wave

$\frac{E_{rms}}{B_{rms}}=c$

$B_{rms}=\frac{E_{rms}}{c}=\frac{6}{3\times {10}^8}$

$\therefore B_{rms}=2\times {10}^{-8}\text{T}$

Also, $B_{rms}=\frac{B_0}{\sqrt{2}}$

$\Rightarrow B_0=\sqrt{2}\times B_{rms}$

$=\sqrt{2}\times 2\times {10}^{-8}$

$\therefore B_0=2.83\times {10}^{-8}\text{T}$

Hence, option $\left(\text{B}\right)$ is correct.