Question

At the upper surface of the earth's atmosphere, the time-averaged magnitude of the Poynting vector is referred to as the solar constant and is given by </S/>=1.35×103W⋅m−2 .

(a) If you assume that the sun's electromagnetic radiation is a plane sinusoidal wave, what is the magnitude of the electric field in V/m?

(b)What is the magnitude of the magnetic field in T?

(c) What is the time-averaged power (in Watt) radiated by the sun? The mean sun-earth distance is res=1.50×1011m

Answer 1

(a) The time-averaged Poynting vector is
<S> =cε₀E₀²/2.
The amplitude of electric field is
E=sqrt{2<S>/ cε₀} =
=sqrt{2•1.35•10³/3•10⁸•8.85•10⁻¹²} = 1.01•10³ V/m.
(b) The magnetic field is
B₀=E₀/c =1.01•10³/3•10⁸ =3.4•10⁻⁶ T.
(c) The time-averaged power radiated by the Sun at distance R is
<P> =<S>A = <S>4πR² =
=1.35•10³•4π•(1.5•10¹¹)²=3.8•10²⁶W

Answer 2

thnx Elena :)