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  4. A laser beam of power 27 mW has a cross-sectional area of 10 mm2 . The magnitude of the maximum electric field in this electromagnetic wave is given by [Given permittivity of space ε0 ≈ 9 × 10-12 C 2 N -1 m -2, speed of light c =3 × 108 m s -1 ]

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Q. A laser beam of power $27 \, mW$ 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 $\varepsilon_{0} \approx 9 \times 10^{-12} \quad C ^{2} \quad N ^{-1} \quad m ^{-2}$, speed of light $c =3 \times 10^{8} \quad m s ^{-1}$ ]

NTA AbhyasNTA Abhyas 2022

Solution:

$I=\frac{P}{A}=\frac{1}{2}\epsilon _{0}E_{0}^{2}c$
$\therefore E_{0}=\sqrt{\frac{2 P}{\epsilon _{0} cA}}=\sqrt{\frac{2 \times 27 \times 10^{- 3}}{9 \times 10^{- 12} \times 3 \times 10^{8} \times 10 \times 10^{- 6}}}$
$E_{0}\approx1.4kVm^{- 1}$