Question

A plane electromagnetic wave of frequency $50\, MHz$ travels in free space along the positive $x$-direction. At a particular point in space and time, $\vec{E} = 6.3 \hat{j} V/m$ . The corresponding magnetic field $\vec{B}$ , at that point will be:

• A. $18.9 \times 10^{-8} \hat{k} T$
• B. $6.3 \times 10^{-8} \hat{k} T$
• C. $2.1 \times 10^{-8} \hat{k} T$
• D. $18.9 \times 10^{8} \hat{k} T$

Answer 1

Answer: (C)

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

Answer 2

$\left|B\right| = \frac{\left|E\right|}{C} = \frac{6.3}{3 \times10^{8}} =2.1 \times10^{-8} T$
and $\hat{E} \times\hat{B} = \hat{C}$
$\hat{j} \times\hat{B} =\hat{i}$
$\hat{B} = \hat{k}$
$\vec{B} = \left| B\right|\hat{B} = 2.1 \times10^{8} \hat{k} T$