# The electric field in a region is given by

Question:

A plane electromagnetic wave of frequency $100 \mathrm{MHz}$ is travelling in

vacuum along the $\mathrm{x}$ - direction. At a particular point in space and time,

$\overrightarrow{\mathrm{B}}=2.0 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T} \cdot($ where,$\hat{\mathrm{k}}$ is unit vector along z-direction) What is $\overrightarrow{\mathrm{E}}$

at this point?

1. (1) $0.6 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$

2. (2) $6.0 \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}$

3. (3) $6.0 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$

4. (4) $0.6 \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}$

Correct Option: , 3

Solution:

(3)

$\mathrm{E}=\mathrm{BC}=6$

(Dir. of wave) $\|(\overrightarrow{\mathrm{E}} \times \overrightarrow{\mathbf{B}})$

$\hat{\mathrm{i}}=\hat{\mathrm{j}} \times \hat{\mathrm{k}}$

$\overrightarrow{\mathrm{E}}=6 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$