# The electric field in a plane electromagnetic wave is given by

Question:

The electric field in a plane electromagnetic wave is given by

$\overrightarrow{\mathrm{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{\mathrm{~m}}\right) \mathrm{x}-\left(1.5 \times 10^{11} \frac{\mathrm{rad}}{\mathrm{s}} \times \mathrm{t}\right)\right] \frac{\mathrm{V}}{\mathrm{m}} \hat{\mathrm{j}}$

If this wave falls normally on a perfectly reflecting surface having an area of $100 \mathrm{~cm}^{2}$. If the radiation pressure exerted by the E.M. wave on the surface

during a 10 minute exposure is $\frac{\mathrm{x}}{10^{9}} \frac{\mathrm{N}}{\mathrm{m}^{2}}$. Find the value of $x$.

Solution:

$\mathrm{E}_{0}=200$

$\mathrm{I}=\frac{1}{2} \varepsilon_{0} \mathrm{E}_{0}^{2} \cdot \mathrm{C}$

$P=\frac{2 I}{C}$

$=\left(\frac{2}{\mathrm{C}}\right)\left(\frac{1}{2} \varepsilon_{0} \mathrm{E}_{0}^{2} \mathrm{C}\right)$

$=\varepsilon_{0} \mathrm{E}_{0}^{2}$

$=8.85 \times 10^{-12} \times 200^{2}$

$=8.85 \times 10^{-8} \times 4$

$=\frac{354}{10^{9}}$

Ans. $354.0$