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 .
plz help....!
To find the answers to these questions, we need to use the formula that relates the magnitude of the Poynting vector to the magnitudes of the electric field (E) and magnetic field (B):
<S> = (1/2) * ε_0 * c * |E|^2
where ε_0 is the vacuum permittivity and c is the speed of light in a vacuum.
(a) To find the magnitude of the electric field (E), we can rearrange the formula:
|E| = sqrt((2 * <S>) / (ε_0 * c))
Given the value of the solar constant, <S> = 1.35 × 10^3 W⋅m^-2, and the known values for ε_0 (8.85 × 10^-12 F⋅m^-1) and c (3 × 10^8 m/s), we can substitute them into the formula:
|E| = sqrt((2 * 1.35 × 10^3) / (8.85 × 10^-12 * 3 × 10^8))
Simplifying the expression gives:
|E| ≈ 109.30 V/m
Therefore, the magnitude of the electric field is approximately 109.30 V/m.
(b) To find the magnitude of the magnetic field (B), we can use the relationship between the electric field and magnetic field in electromagnetic waves:
B = |E| / c
Substituting the value of |E| and c:
B = 109.30 / 3 × 10^8
Simplifying the expression gives:
B ≈ 3.64 × 10^-7 T
Therefore, the magnitude of the magnetic field is approximately 3.64 × 10^-7 T.
(c) To calculate the time-averaged power radiated by the sun, we can use the formula:
Power = <S> * surface area
The surface area is determined by the sphere centered at the sun with a radius equal to the mean sun-earth distance (res = 1.50 × 10^11 m). The surface area of a sphere is given by:
4πr^2
Plugging in the values into the formula, we get:
Power = 1.35 × 10^3 * 4π * (1.50 × 10^11)^2
Simplifying the expression gives:
Power ≈ 3.85 × 10^26 W
Therefore, the time-averaged power radiated by the sun is approximately 3.85 × 10^26 Watt.