Question

The intensity of the sunlight reaching Earth is 1380 W m⁻². Assume this light to be a plane, monochromatic wave. Find the amplitudes of electric and magnetic fields in this wave.

Answer 1

Given:
$$\begin{gathered} \mathit{}I=1380\mathrm{W}/{\mathrm{m}}^2 \\ I=\frac{1}{2}{\in }_0{E_0}^{2}c \\ \Rightarrow E_0=\sqrt{\frac{2I}{{\in }_{0}c}} \\ \Rightarrow E_0=\sqrt{\frac{2\times 1380}{8.83\times {10}^{-12}\times 3\times {10}^8}} \\ \Rightarrow E_0=103.95\times {10}^4 \\ \Rightarrow E_0=10.195\times {10}^2 \\ \Rightarrow E_0=1.02\times {10}^3\mathrm{N}/\mathrm{C} \\ \mathrm{Since}{E}_0=B_{\mathit{0}}c, \\ {B}_0=\frac{E_0}{c}=\frac{1.02\times {10}^2}{3\times {10}^{28}} \\ \Rightarrow B_0=3.398\times {10}^{-6} \\ \Rightarrow B_0=3.4\times {10}^{-6}\mathrm{T} \end{gathered}$$