Answer
$9.07\times10^{-7}J$.
Work Step by Step
The energy per unit area per unit time is the magnitude of the average intensity, equation 22–8. The area and time are given, so we find the intensity and solve for the energy transported in that time.
$$\overline{I}==\frac{1}{2}\epsilon_ocE_o^2=\frac{1}{2}\epsilon_oc(\sqrt{2}E_{rms})^2=\epsilon_ocE_{rms}^2=\frac{\Delta U}{A\Delta t}$$
The area and time are given, so we find the intensity and solve for the energy transported in that time.
$$\Delta U =\epsilon_ocE_{rms}^2A\Delta t$$
$$=(8.85\times10^{-12})(3.00\times10^8m/s)(0.0308V/m)^2(1.00\times10^{-4}m^2)(3600s)$$
$$=9.07\times10^{-7}J$$
