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The electric field in a plane electromagnetic wave is given by
$\overrightarrow{{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{{m}}\right) {x}-\left(1.5 \times 10^{11} \frac{{rad}}{{s}} \times {t}\right)\right] \frac{{V}}{{m}} \hat{{j}}$
If this wave falls normally on a perfectly reflecting surface having an area of $100 \;{cm}^{2}$. 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 ${x}$.
$254$
$354$
$154$
$54$
Solution
${E}_{0}=200$
${I}=\frac{1}{2} \varepsilon_{0} {E}_{0}^{2} \cdot {C}$
Radiation pressure
$P=\frac{2 I}{C}$
$=\left(\frac{2}{C}\right)\left(\frac{1}{2} \varepsilon_{0} E_{0}^{2} C\right)$
$=\varepsilon_{0} E_{0}^{2}$
$=8.85 \times 10^{-12} \times 200^{2}$
$=8.85 \times 10^{-8} \times 4$
$=\frac{354}{10^{9}}$
Ans. $354.0$
