# A 27 mW laser beam has a cross-sectional area

Question:

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

[Given permittivity of space $\epsilon_{0}=9 \times 10^{-12}$ SI units, Speed of light $\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ ]

1. (1) $2 \mathrm{kV} / \mathrm{m}$

2. (2) $0.7 \mathrm{kV} / \mathrm{m}$

3. (3) $1 \mathrm{kV} / \mathrm{m}$

4. (4) $1.4 \mathrm{kV} / \mathrm{m}$

Correct Option: , 4

Solution:

(4) EM wave intensity

$\Rightarrow \mathrm{I}=\frac{\text { Power }}{\text { Area }}=\frac{1}{2} \varepsilon_{0} \mathrm{E}_{0}^{2} \mathrm{c}$

[where $\mathrm{E}_{0}=$ maximum electric field]

$\Rightarrow \frac{27 \times 10^{-3}}{10 \times 10^{-6}}=\frac{1}{2} \times 9 \times 10^{-12} \times \mathrm{E}_{0}^{2} \times 3 \times 10^{8}$

$\Rightarrow \mathrm{E}_{0}=\sqrt{2} \times 10^{3} \mathrm{kV} / \mathrm{m}=1.4 \mathrm{kV} / \mathrm{m}$