8. Sunlight strikes the surface of the earth with an intensity of 1.4 kW/m2. Not

Question

8. Sunlight strikes the surface of the earth with an intensity of 1.4 kW/m2. Note: eo = 8.85x10-12 F/m, Ho = 44x10-7 T·m/A. (a) Treating the sun as a point source and assuming that the radiation from the sun is spread uniformly in all directions, find the power output of the sun. The earth is at a distance 1.5x 1011 m from the sun. (b) Find the maximal magnitudes of the electric field and the magnetic field on the surface of the earth respectively by considering the sunlight on the surface of the earth as a plane wave. (c) Find the force on a plate of area, 2 m2. Assume that the plate absorbs all the energy of the sunlight and the sunlight shines on the plate perpendicularly.

Explanation / Answer

a)

I=P/A

I=P/4r2

P=4Ir2

P=4*1.4*10^3*3.14*(1.5*10^11)^2

P=3.96*10^26 W

b)

I=1/2*0*c*Emax2

Emax = sqrt[2I/(c 0)]

Plugging values,

Emax = sqrt[(2*1.4*10^3)/(3*10^8*8.85*10^-12)] = 1026.94 N/C

I=c Bmax2/(2µ0)

B0 = sqrt[2Iµ0/c]

Plugging values,

Bmax = sqrt[(2*1.4*10^3*4*10^-7)/(3*10^8) = 3.4*10^-6 T

c)

Pressure = P = Emax/c = (1026.94)/(3*10^8) = 3.42*10^-6 N/m^2

F=PA=3.42*10^-6*2.0 = 6.84*10^6 N

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