Answer
a. $1.2\times10^{-10}J$.
b. $8.7\times10^{-6}V/m$, $2.9\times10^{-14}T$.
Work Step by Step
a. Intensity is energy per unit time per unit area. Find the energy by multiplying the intensity, the area of the antenna, and the elapsed time.
$$\Delta U=IA\Delta t$$
$$=(1.0\times10^{-13}W/m^2)(\pi(0.165m)^2)(4.0h)(3600s/h)=1.2\times10^{-10}J$$
b. The energy per unit area per unit time is the magnitude of the average intensity, equation 22–8. Find the amplitude of the electric field.
$$\overline{I}=\frac{1}{2}\epsilon_ocE_o^2$$
$$E_o=\sqrt{\frac{2\overline{I}}{\epsilon_oc }}$$
$$E_o=\sqrt{\frac{2(1.0\times10^{-13}W/m^2)}{( (8.85\times10^{-12} C^2/(N\cdot m^2))(3.00\times10^8m/s) }}$$
$$\approx 8.7\times10^{-6}V/m$$
Now find the amplitude of the magnetic field.
$$B_o=\frac{E_o}{c}=\frac{8.679\times10^{-6}V/m }{3.00\times10^8m/s }=2.9\times10^{-14}T$$
