At one location on the Earth, the rms value of the magnetic field caused by sola

Question

At one location on the Earth, the rms value of the magnetic field caused by solar radiation is 1.70 muT. (a) Calculate the rms electric field due to solar radiation. V/m (b) Calculate the average energy density of the solar component of electromagnetic radiation at this location. mu J/m^3 (c) Calculate the average magnitude of the Poynting vector for the Sun's radiation. w/m^2 (d) Assuming that the average magnitude of the Poynting vector for solar radiation at the surface of the Earth is S_av = 1000 W/m^2, compare your result in part (c) with this value. %

Explanation / Answer

(A) B =1.70uT = 1.70 x 10^-6 T

and E = c B

E = (3 x 10^9)(1.70 x 10^-6 ) = 510 V/m

(B) Average energy density = B^2 / u0

= (1.70 x 10^-6)^2 / (4pi x 10^-7) = 2.30 x 10^-6 J/m^3

= 2.30 uJ/m^3

(c) S = Erms^2 / (c u0)

S = (510)^2 / (3 x 10^8 x 4pi x 10^-7) = 690 W/m^2

(D) = (690/1000) x 100 = 69% of Sw

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