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

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

Step-by-step 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) = (c\epsilon E_o^2)/(2)\\\\ I_(avg) = ((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 = (P)/(t) = (I*A)/(t) = ((A)/(t))(I)\\\\E = (1.25*10^(-4) \ (m^2)/(hr) )(3.936*10^(-6) \ (W)/(m^2) )\\\\E = 4.92*10^(-10) \ J`

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