Question

A ball of radius R=50 cm is located in a non-magnetic medium with permitivity k = 4.0. In that medium a plane electromagnetic wave propagates, the strength amplitude of whose electric component is equal to $E_m=200V/m$. The amount of energy that reaches the ball during a time interval of $t=1.0\min$ is (in kJ) ?

Answer 1

For the Poyinting vector we can derive as in

$<S>=\frac{1}{2}\sqrt{\frac{k{\epsilon }_0}{{\mu }_0}}{E}_m^2$
along the direction of propagation.

Hence in time $t$ (which is much longer than the time period $T$ of the wave), the energy
reaching the ball is
$$\pi R^2\times \frac{1}{2}\sqrt{\frac{k{\epsilon }_0}{{\mu }_0}}{E}_m^2\times t=5kJ$$