Question

A $27\text{mW}$ laser beam has a cross-sectional area of $10{\text{mm}}^2$. The magnitude of the maximum electric field in this EM wave is given by $[$Given permittivity of space ${\epsilon }_0=9\times {10}^{-12}\text{F/m}$, speed of light $c=3\times {10}^8\text{m/s}]$

• A. $2\text{kV/m}$
• B. $0.7\text{kV/m}$
• C. $1\text{kV/m}$
• D. $1.4\text{kV/m}$

Answer 1

The correct option is D $1.4\text{kV/m}$

Given:
$P=27\text{mW},$ $A=10{\text{mm}}^2$

${\epsilon }_0=9\times {10}^{-12}\text{F/m},$ $c=3\times {10}^8\text{m/s}$

The intensity of the electromagnetic wave is given by,

$I=\frac{P}{A}=\frac{1}{2}{\epsilon }_0{E}^{2}c$

$\Rightarrow E=\sqrt{\frac{2P}{A{E}_{\circ }c}}$

Substituting the values,

$E=\sqrt{\frac{2\times 27\times {10}^{-3}}{10\times {10}^{-6}\times 9\times {10}^{-12}\times 3\times {10}^8}}$

$\Rightarrow E=\sqrt{2\times {10}^6}=1.4\times {10}^3\text{V/m}$

$\Rightarrow E=1.4\text{kV/m}$

Hence, option $\left(D\right)$ is correct correct answer.