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  • The electric field in a plane electromagnetic wave is given by <img alt="\vec{E}= 200\cos \left [ \left ( \frac{0\cdot 5\times 10^{3}}{m} \right )x-\left ( 1\cdot 5\times 10^{11}\frac{rad}{s}\times t \right ) \right ]\frac{v}{m}\hat{j}" src="https:

The electric field in a plane electromagnetic wave is given by
\vec{E}= 200\cos \left [ \left ( \frac{0\cdot 5\times 10^{3}}{m} \right )x-\left ( 1\cdot 5\times 10^{11}\frac{rad}{s}\times t \right ) \right ]\frac{v}{m}\hat{j}
If this wave falls normally on a perfectly reflecting surface having an area of 100 cm2 . if the radiation pressure exerted by the E.M.wave on the surface during a 10 minute exposure is \frac{x}{10^{9}}\: \frac{N}{m^{2}}. Find the value of x.
 

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best_answer

\bar{E}= 200\left [ \cos \left ( 0\cdot 5\times 10^{3}x-1\cdot 5\times 10 ^{\frac{1}{t}} \right ) \right ]\frac{V}{m}
A= 100 \, cm^{2}= 10^{-2}\, m^{2}
Radiation\; \; pressure \rightarrow \frac{2I}{C}= 2\left ( \frac{1}{2}\varepsilon _{0}E_{0}^{2} \right )= 2\left ( \frac{1}{2}\times \frac{1}{4\pi \times 9\times 10^{9}}\times \left ( 200 \right ) ^{2}\right )
                                                        = 2\left ( \frac{4\times 10^{4}}{8\times 9\pi \times 10^{9}} \right )= 2\left ( \frac{10000}{18\pi \times 10^{9}} \right )
Radiation\; \; pressure = \frac{354}{10^{9}}\; \; \; \therefore x= 354
 

Posted by

vishal kumar

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