Question

A plane electromagnetic wave is incident on a plane surface area A normaly ,and is perfectly reflected . if energy E strikes the surface in time t then average pressure exerted on the surface is

Answer 1

Electromagnetic wave strikes the surface at normal incidence and transports a total energy E to the surface in a time t,
If the surface reflects all the incident energy, the total momentum transported to the surface has a magnitude,
p=2E/c
Then,
The pressure exerted on the surface by an electromagnetic wave is given by
P=F/A
=1/A (dp/dt)
=1/A d/dt(2E/c)
$$\begin{gathered} =\frac{1}{\mathrm{c}}\frac{(\mathrm{dE}/\mathrm{dt})}{\mathrm{A}} \\ \mathrm{Here}, \\ \frac{(\mathrm{dE}/\mathrm{dt})}{\mathrm{A}}=\mathrm{Rate}\mathrm{at}\mathrm{which}\mathrm{energy}\mathrm{is}\mathrm{arriving}\mathrm{at}\mathrm{the}\mathrm{surface}\mathrm{per}\mathrm{unit}\mathrm{area},\mathrm{which}\mathrm{is}\mathrm{the}\mathrm{magnitude}\mathrm{of}\mathrm{the}\mathrm{poynting}\mathrm{vector}. \\ \mathrm{Thus},\mathrm{the}\mathrm{pressure}\mathrm{exerted}\mathrm{on}\mathrm{the}\mathrm{surface}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{P}=\frac{1}{\mathrm{c}}\frac{(\mathrm{dE}/\mathrm{dt})}{\mathrm{A}} \end{gathered}$$