Chapter 41: Problem 20

Question: Sunlight strikes the earth, just outside its atmosphere, with an intensity of $I=1.38~{\rm kW/m^2}$. Calculate (a) E_m and (b) B_m for sunlight, assuming it to be a plane wave.

Solution: The relation between the average intensity and the maximum value of the electric field is found from the magnitude of the Poynting vector

$$\vert\overline{\bf S}\vert~=~{1\over 2\mu_0}\vert{\bf E}_m\vert\vert{\bf B}_m\vert \ \ \ .,$$ (8)

for an electromagnetic plane wave of the form

$$\vert\vert{\bf E}\vert~=~\vert{\bf E}_m\vert\sin\left(k x- \omega t\right) \ \ \ ,$$ (9)

traveling in the x direction. This gives $~\vert{\bf E}_m\vert=1019.7~{\rm V/m}$. We can easily find the magnetic field from the relation $\vert{\bf B}_m\vert~=~\vert{\bf E}_m\vert/c~=~3.4\times 10^{-6}~{\rm T}$.