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Q.

A red LED emits light at $0.1 watt$ uniformly around it. The amplitude of the electric field of the light at a distance of $1 m$ from the diode is ________ $V m^{- 1}$ .

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a

$1.45$

b

$2.15$

c

$2.45$

d

$3.45$

answer is D.

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Detailed Solution

Intensity of light, $I = u_{av} c$

Also, $I = \frac{P}{4 {πr}^{2}}$ and $u_{av} = \frac{1}{2} ε_{0} {E_{0}}^{2}$

$∴ \frac{P}{4 {πr}^{2}} = \frac{1}{2} ε_{0} {E_{0}}^{2} c$

$\Rightarrow E_{0} = \sqrt{\frac{2 P}{4 {πε}_{0} r^{2} c}}$

$∴ E_{0} = \sqrt{\frac{2 \times 0.1 \times 9 \times 10^{9}}{1^{2} \times 3 \times 10^{8}}} = \sqrt{6} = 2.45 V m^{- 1}$

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