Question

A plane electromagnetic wave of frequency $25MHz$ travels in free space along the x-direction. At a particular point in space and time, $\overrightarrow{E}=6.3\hat{j}V/m$. What is $\overrightarrow{B}$ at this point?

Answer 1

The magnitude of B is

B = $\frac{E}{C}$

= $\frac{6.3}{3\times {10}^8}$

= $2.1\times {10}^{-8}T$

To find the direction, we note that E is along y - direction and the wave propagates along x - axis.

Therefore, B should be in a direction perpendicular to both x - and y - axes.

Using vector algebra, E $\times$ B should be along x - direction.

since, ( + j ) $\times (+k)=i$,

so, B is along + k

or the z - direction

so $\overrightarrow{B}=2.1\times {10}^{-8}k$