If the radiant energy from the sun comes in as a plane EM wave of intensity 1340 W/m², calculate the peak values of E and B.

Question

Quizplus · Accepted Answer

The peak values of electric field and magnetic field are related to the intensity of the wave by the formula:

$$I = \frac{1}{2}\epsilon_0 c E_{max}^2$$
where $\epsilon_0$ is the vacuum permittivity and c is the speed of light in vacuum, and 
$$I = \frac{1}{2}\frac{1}{\mu_0} c B_{max}^2$$
where $\mu_0$ is the vacuum permeability.

Solving for $E_{max}$ and $B_{max}$, we get:

$$E_{max} = \sqrt{\frac{2I}{\epsilon_0 c}}$$

$$B_{max} = \sqrt{\frac{2I}{c \mu_0}}$$

Plugging in the given values, we get:

$$E_{max} = \sqrt{\frac{2(1340)}{(8.85	imes10^{-12})(3	imes10^8)}} \approx 1,000 	ext{ V/m}$$

$$B_{max} = \sqrt{\frac{2(1340)}{(3	imes10^8)(4\pi	imes10^{-7})}} \approx 3.35 	imes 10^{-16} 	ext{ T}$$

Therefore, the best choice is B, with peak values of 1,000 V/m and 3.35 × 10−16 T.

If the Radiant Energy from the Sun Comes in as a Plane