Question

How much energy is transported across a 1.25 cm2 area per hour by an EM wave whose E field has an rms strength of 38.5 mV/m

Answer 1

Answer:

The energy transported per hour is 4.92 x 10⁻¹⁰ J.

Explanation:

Given;

root mean square strength of the field, $E_{rms}$ = 38.5 mV/m

area per hour, A = 1.25 cm²/hr = 1.25 x 10⁻⁴ m²/hr

The peak strength of the field is given by;

E₀ = $E_{rms}$√2

E₀ = (38.5 mV)√2

E₀ = 54.45 mV

the average intensity is given by;

$I_{avg} = \frac{c\epsilon E_o^2}{2}\\\\ I_{avg} = \frac{(3*10^8)(8.85*10^{-12})(54.45*10^{-3})^2}{2}\\\\I_{avg} = 3.936*10^{-6} \ W/m^2$

Energy transported per hour is given by;

$E = \frac{P}{t} = \frac{I*A}{t} = (\frac{A}{t})(I)\\\\E = (1.25*10^{-4} \ \frac{m^2}{hr} )(3.936*10^{-6} \ \frac{W}{m^2} )\\\\E = 4.92*10^{-10} \ J$

Therefore, the energy transported per hour is 4.92 x 10⁻¹⁰ J.