The electric field in a plane electromagnetic wave is given by $\vec{E} = 200\cos\left[(0.5\times10^3\ \text{m}^{-1})x - (1.5\times10^{11}\ \text{rad s}^{-1})t\right]\ \text{V m}^{-1}\ \hat{j}$. If this wave falls normally on a perfectly reflecting surface having an area of $100$ cm$^2$. If the radiation pressure exerted by the E.M. wave on the surface during a $10$ min exposure is $\frac{k}{10^9}$ N m$^{-2}$. Find the value of $k$
Numerical value type. Enter your answer.
Answer: 354
Intensity:
$$I = \frac{1}{2}c\varepsilon_0E_0^2 = \frac{1}{2}\times3\times10^8\times8.85\times10^{-12}\times(200)^2 = 53.1\ \text{W m}^{-2}$$
For a perfect reflector:
$$P = \frac{2I}{c} = \frac{106.2}{3\times10^8} = 3.54\times10^{-7}\ \text{N m}^{-2} = \frac{354}{10^9}\ \text{N m}^{-2}$$
So $k = 354$ (the area and time do not affect the pressure).
Solution by Sreeraj P, M.Sc Physics