A laser beam of power 27mW has a cross-sectional area of 10 mm ^ 2...

A laser beam of power $27mW$ has a cross-sectional area of $10{mm}^{2}$ . The magnitude of the maximum electric field in this electromagnetic wave is given by

$[Given permittivity of space$ {ε}_{0} \approx 9 \times {10}^{- 12}C^{2}N^{- 1}m^{- 2}$, speed of light \leftc = 3 \times {10}^{8}ms^{- 1}]

Options

A $1kVm^{- 1}$
B $1. 4kVm^{- 1}$
C $0.7kVm^{- 1}$
D $2kVm^{- 1}$

Correct answer

B. $1. 4kVm^{- 1}$

Step-by-step solution

$I = \dfrac{P}{A} = \dfrac{1}{2}{ε}_{0}{E}_{0}^{2}c$

$∴ {E}_{0} = \sqrt{\dfrac{2P}{{ε}_{0}CA}} = \sqrt{\dfrac{2 \times 27 \times {10}^{- 3} \times 36\pi \times {10}^{9}}{3 \times {10}^{8} \times 10 \times {10}^{- 6}}}$

${E}_{0} = 1. 4kVm^{- 1}$

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