Question

A red LED emits light at 0.1 watts uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is

• A. 2.45 V/m
• B. 5.48 V/m
• C. 7.75 V/m
• D. 1.73 V/m

Answer 1

The correct option is A 2.45 V/m

We know intensity at a distance r for a light source of power P is given by

$I=\frac{P}{4\pi r^2}\to$ (1)
Intensity of electromagnetic wave is given by
$I=\frac{1}{2}C{ϵ}_0{E}_0^2\to$ (2)
From equation (1) and (2) we get
$\frac{1}{2}C{ϵ}_0{E}_0^2=\frac{p}{4\pi r^2}or{E}_0=\sqrt{\frac{p}{4\pi r^2}\times \frac{2}{C{ϵ}_0}}$
Given: P = 0.1 W, r = 1 m, $\frac{1}{4\pi {ϵ}_0}=9\times {10}^9$
$E_0=\sqrt{\frac{0.1}{1}\times \frac{2\times 9\times {10}^9}{3\times {10}^8}}$ $=\sqrt{6}=2.449$ V/m