Question 5: EM energy (16 points total) The Solar constant is the radiant flux d

Question

Question 5: EM energy (16 points total) The Solar constant is the radiant flux density (irradiance) from the sun at the surface of earth's atmosphere and is about 0.135 W/cm2. Assume an average wavelength of 700 nm for the sun's radiation that reaches the earth a) b) c) (6p) Find the amplitude of the E- and B- fields (4p) Find the number of photons that arrive each second each square meter of a solar panel (6p) Assuming that all photons are absorbed, what is the radiation pressure on 1 m2 solar panel? Hint: use the momentum of a photon

Explanation / Answer

Given,

I = 0.135 W/cm^2 = 1350 W/m^2 ; lambda = 700 nm

a)We know that

u = I/c = 1350/3 x 10^8 = 4.5 x 10^-6 J/m^3

E = sqrt(u/2e0)

E = sqrt(4.5 x 10^-6/(2 x 8.85 x 10^-12)) = 504.22 N/C

B = sqrt (u x u0/2)

B = sqrt (4.5 x 10^-6 x 4 x 3.14 x 10^-7/2) = 1.68 x 10^-6 T

Hence, E = 504.22 N/C ; B = 1.68 x 10^-6 T

b)we know that, energy of a simple photon is:

e = h c/lambda

e = 6.626 x 10^-34 x 3 x 10^8/(700 x 10^-9) = 2.84 x 10^-19 J

I = P/A = (E/t)/A = 1350 J/m^2 s

n = 1350/(2.84 x 10^-19) = 4.75 x 10^21

Hence, n = 4.75 x 10^21 photons

c)we know that

k = 2 pi/lambda

k = 2 x 3.14 /(700 x 10^-9) = 8.97 x 10^6 rad/m

Hence, k = 8.97 x 10^6 rad/m

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