The electric field in a plane electromagnetic wave is given by $\vec E = 200\cos\left[\left(\frac{0.5\times10^3}{m}\right)x - \left(1.5\times10^{11}\,\mathrm{rad/s}\right)t\right]\,\frac{V}{m}\,\hat{j}$ If this wave falls normally on a perfectly reflecting surface having an area of 100 c

Question

The electric field in a plane electromagnetic wave is given by $\vec E = 200\cos\left[\left(\frac{0.5\times10^3}{m}\right)x - \left(1.5\times10^{11}\,\mathrm{rad/s}\right)t\right]\,\frac{V}{m}\,\hat{j}$ 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 the value of x. Find the value of x.

Accepted Answer

x N / 10^5 m^2. The radiation pressure exerted by an electromagnetic wave on a perfectly reflecting surface is given by the formula P = 2I/c, where I is the intensity of the wave and c is the speed of light. Given the electric field, we can calculate the intensity and subsequently the radiation pressure, which leads to the correct unit of x being N / 10^5 m^2.

Solution

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