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 : 

${\displaystyle I=1380 {\text{W/m}}^2}$

${\displaystyle I=\frac{1}{2}{\in }_0{E}_0^{2}c}$

⇒ ${\displaystyle E_0=\sqrt{\frac{2I}{{\in }_{0}c}}}$

⇒ ${\displaystyle E_0=\sqrt{\frac{2\times 1380}{8.83\times {10}^{-12}\times 3\times {10}^8}}}$

⇒ ${\displaystyle E_0=103.95\times {10}^4}$

⇒ ${\displaystyle E_0=10.195\times {10}^2}$

⇒ ${\displaystyle E_0=1.02\times {10}^3 \text{N/C}}$

Since ${\displaystyle E_0=B_{0}c}$ , 

${\displaystyle B_0=\frac{E_0}{c}=\frac{1.02\times {10}^2}{3\times {10}^{28}}}$

⇒ ${\displaystyle B_0=3.398\times {10}^{-6}}$

⇒ ${\displaystyle B_0=3.4\times {10}^{-6} \text{T}}$