An 8.0-mW laser beam emits a cylindrical beam of single-wavelength sinusoidal light $0.90 \mathrm {~mm}$ in diameter. What is the rms value of the electric field in this laser beam? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \right.$. $\left. \mathrm { m } ^ { 2 } , \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } , c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$
A) $1100 \mathrm {~N} / \mathrm { C }$
B) $2000 \mathrm {~N} / \mathrm { C }$
C) $2200 \mathrm {~N} / \mathrm { C }$
D) $1000 \mathrm {~N} / \mathrm { C }$
E) $4100 \mathrm {~N} / \mathrm { C }$

Question

Quizplus · Accepted Answer

The intensity of the laser beam is given by:$$I = \frac{P}{A} = \frac{8.0 	imes 10^{-3} \mathrm{~W}}{\pi (0.90 	imes 10^{-3} \mathrm{~m})^2} = 3.0 	imes 10^6 \mathrm{~W/m^2}$$The rms value of the electric field is given by:$$E_{rms} = \sqrt{\frac{2I}{\varepsilon_0 c}} = \sqrt{\frac{2(3.0 	imes 10^6 \mathrm{~W/m^2})}{8.85 	imes 10^{-12} \mathrm{~C^2/Nm^2} (3.0 	imes 10^8 \mathrm{~m/s})}} = 2200 \mathrm{~N/C}$$

An 80-MW Laser Beam Emits a Cylindrical Beam of Single-Wavelength Sinusoidal