Question

A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area of 0.700 m2 . At the window, the electric field of the wave has an rms value 0.0400 V/m .
Part A
How much energy does this wave carry through the window during a 30.0-s commercial?
Express your answer with the appropriate units

Answer 1

Answer

given,

Area = 0.7 m²

electric field of wave = 0.0400 V/m

time = t =30 s

intensity of electromagnetic wave

$I = \dfrac{E_0^2}{2\mu_0c}$

$E_0^2 = 2 E_{rms}^2$

c is speed of light

$I = \dfrac{2E_{rms}^2}{2\mu_0c}$

$I = \dfrac{E_{rms}^2}{\mu_0c}$

$I = \dfrac{0.04^2}{4\pi \times 10^{-7}\times 3 \times 10^8}$

I = 4.24 x 10⁻⁶ W/m²

the amount of energy required

E = I A t

E = 4.24 x 10⁻⁶ x 0.7 x 30

E = 8.9 x 10⁻⁵ J