The energy flow to the earth from sunlight is about

zgribestika 2021-12-15 Answered
The energy flow to the earth from sunlight is about 1.4{kWm}2.
(a) Find the maximum values of the electric and magnetic fields for a sinusoidal wave of this intensity.
(b) The distance from the earth to the sun is about 1.5×1011m Find the total power radiated by the sun.
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Expert Answer

Vivian Soares
Answered 2021-12-16 Author has 36 answers
(a) The given value represents the intensity I=1.4kWm2 of the light. The intenity of a sinusoidal electromagnetic wave in vacuum is related to the electric-field amplitude Emax and the amplitude of magnetic field Bmax and is given by the equation:
I=12ϵ0cEmax2, where ϵ0 is a electric constant, c is speed of light.
Now, solve the equation for Emax
Emax=2Iϵ0c
Plug the values for I,ϵ,c into equation
Emax=2Iϵ0c
=2(1400Wm2)(8.85×1012C2N×m2)(3×108ms)
The maximum electric field is related to the maximum magnetic field in form:
Bmax=Emaxc
Now, plug the values into the equation
Bmax=Emaxc=1026Vm3×108ms=3.42×106T
(b) The intensity is propotional to Emax2 and represents the incident power P per area A
P=IA
The distance between the Earth and the Sun represents the radius of the path of the Earth around the Sun and it is considered to be sphere. So, the area is calculated:
A=4πr2=4π(1.5×1011m)2=2.82×1023m2
Now, plug in the values:
P=IA=(1400Wm2)(2.82×1023m2)=3.95×1026W
The answer is: (a) 3.42×106T, (b) 3.95×1026W
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