A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction.
Question:

A plane electromagnetic wave of frequency $500 \mathrm{MHz}$ is travelling in vacuum along $\mathrm{y}$-direction. At a particular point in space and time, $\overrightarrow{\mathrm{B}}=8.0 \times 10^{-8} \hat{\mathrm{z}} \mathrm{T}$. The value of electric field at this point is :

$\left(\right.$ speed of light $=3 \times 10^{8} \mathrm{~ms}^{-1}$ )

$\hat{\mathrm{x}}, \hat{\mathrm{y}}, \hat{\mathrm{z}}$ are unit vectors along $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ direction.

1. $-24 \hat{\mathrm{x}} \mathrm{V} / \mathrm{m}$

2. $2.6 \hat{\mathrm{x}} \mathrm{V} / \mathrm{m}$

3. $24 \hat{\mathrm{x}} \mathrm{V} / \mathrm{m}$

4. $-2.6 \hat{\mathrm{y}} \mathrm{V} / \mathrm{m}$

Correct Option: 1,

Solution:

$f=5 \times 10^{8} \mathrm{~Hz}$

EM wave is travelling towards $+\hat{\mathrm{j}}$

$\overrightarrow{\mathrm{B}}=8.0 \times 10^{-8} \hat{\mathrm{z}} \mathrm{T}$

$\overrightarrow{\mathrm{E}}=\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}}=\left(8 \times 10^{-8} \hat{\mathrm{z}}\right) \times\left(3 \times 10^{8} \hat{\mathrm{y}}\right)$

$=-24 \hat{\mathrm{x}} \mathrm{V} / \mathrm{m}$