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Electromagnetic waves and its nature

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Question

Find amplitude of electric field in parallel beam of light of intensity $\frac{6}{10 π} W / m^{2}$ . and take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} / C^{2}$

Moderate

Solution

Given
Intensity of light $I = 2.0 W / m^{2}$
We know intensity of light $I = \frac{1}{2} ε_{0} E_{0}^{2} C$
Where $ε_{0} =$ Permitivity= $8.85 \times 10^{- 12} F / m$
$C =$ Speed of light= $3 \times 10^{8} m$
$∴ I = \frac{1}{2} \times 8.85 \times 10^{- 12} \times E_{0}^{2} \times 3 \times 10^{8}$
$\Rightarrow \frac{6}{10 π} = \frac{1}{2} \times 8.85 \times 10^{- 12} \times E_{0}^{2} \times 3 \times 10^{8}$
$\Rightarrow E_{0}^{2} = 144$
$\Rightarrow E_{0} = 12 V / m$

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