Question

A plane electromagnetic wave of frequency $20MHz$ travels through space along the $X-$direction. If the electric field vector at a certain point in space is$6V{m}^{-1}$, what is the magnetic field vector at that point?

• A. $2x{10}^{-8}T$
• B. $\left(\frac{1}{2}\right)x{10}^{-8}T$
• C. $2T$
• D. $\left(\frac{1}{2}\right)T$

Answer 1

The correct option is A

$2x{10}^{-8}T$

Explanation for the correct answer is,

Step 1. Given Data:

Frequency electromagnetic wave $=20MHz$

Velocity of EM wave, $v=3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Electric field vector, $E=6\raisebox{1ex}{$V$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$

Step 2. The magnetic field:

We know that,

Magnitude of Electric Field $E=$ Magnetic Field $B\times$Speed of light $C$

$$\begin{gathered} E=B\times C \\ \Rightarrow B=\frac{E}{C} \end{gathered}$$

$$\begin{gathered} \Rightarrow B=\frac{6}{(3x{10}^8)} \\ \Rightarrow B=2x{10}^{-8}T \end{gathered}$$

Hence, the correct option is (A).