Question

Amplitude of electric field in a laser beam of power 4.4 mW with cross-sectional area of $2m{m}^2$ is

• A. $\sqrt{\frac{2}{3}}kV/m$
• B. $\sqrt{\frac{5}{3}}kV/m$
• C. $2kV/m$
• D. $\frac{23}{2}kV/m$

Answer 1

The correct option is B $\sqrt{\frac{5}{3}}kV/m$

Intensity $I=\frac{Power}{Area}=\frac{4.4\times {10}^{-3}}{2\times {10}^{-6}}=\frac{4.4}{2}\times {10}^{3}W/m^2$
$I=\frac{1}{2}{\epsilon }_{0}C{E}_0^2\Rightarrow \frac{4.4}{2}\times {10}^3=\frac{1}{2}\times 8.8\times {10}^{-12}\times 3\times {10}^8{E}_0^2$

$E_0^2=\frac{4.4\times {10}^7}{8.8\times 3}=\frac{10}{6}\times {10}^6\Rightarrow E_0=\sqrt{\frac{5}{3}}\times {10}^{3}V/m$