1. Given data

• Power of laser beam:
  $P = 27\,\text{mW} = 27 \times 10^{-3}\,\text{W}$
• Cross-sectional area:
  $A = 10\,\text{mm}^2 = 10 \times 10^{-6}\,\text{m}^2 = 10^{-5}\,\text{m}^2$
• Permittivity of free space:
  $\varepsilon_0 = 9 \times 10^{-12}\,\text{SI}$
• Speed of light:
  $c = 3 \times 10^8\,\text{m/s}$

2. Find intensity of the laser beam

Intensity is power per unit area: $I = \frac{P}{A}$

Substitute values: $I = \frac{27 \times 10^{-3}}{10^{-5}}$ $I = 27 \times 10^2 = 2700\,\text{W/m}^2$

3. Use relation between intensity and maximum electric field

For an electromagnetic wave, $I = \frac{1}{2} \varepsilon_0 c E_0^2$

So, $E_0 = \sqrt{\frac{2I}{\varepsilon_0 c}}$

4. Substitute the values

First compute $\varepsilon_0 c$: $\varepsilon_0 c = 9 \times 10^{-12} \times 3 \times 10^8 = 27 \times 10^{-4} = 2.7 \times 10^{-3}$

Now, $E_0 = \sqrt{\frac{2 \times 2700}{2.7 \times 10^{-3}}}$

$E_0 = \sqrt{\frac{5400}{2.7 \times 10^{-3}}}$

$\frac{5400}{2.7 \times 10^{-3}} = 2 \times 10^6$

Thus, $E_0 = \sqrt{2 \times 10^6} = \sqrt{2} \times 10^3 \approx 1.4 \times 10^3\,\text{V/m}$

$E_0 \approx 1.4\,\text{kV/m}$

5. Check options

• A: $2\,\text{kV/m}$ — incorrect
• B: $1\,\text{kV/m}$ — incorrect
• C: $1.4\,\text{kV/m}$ — correct
• D: $0.7\,\text{kV/m}$ — incorrect

Therefore, the correct option is C.