An 8.0-mW laser beam emits a cylindrical beam of single-wavelength sinusoidal light 0.90 mm in diameter.What is the rms value of the electric field in this laser beam? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²,μ₀ = 4π × 10^-7 T ∙ m/A,c = 3.0 × 10⁸ m/s) A)2200 N/C B)1000 N/C C)1100 N/C D)4100 N/C E)2000 N/C

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Quizplus · Accepted Answer

The rms value of the electric field in a laser beam is given by:$$E_{rms} = \sqrt{\frac{2P}{\varepsilon_0 c A}}$$where:* P is the power of the laser beam* $\varepsilon_0$ is the permittivity of free space* c is the speed of light* A is the area of the laser beamIn this problem, we are given that the power of the laser beam is 8.0 mW, the diameter of the laser beam is 0.90 mm, and the wavelength of the laser beam is not given. We can calculate the area of the laser beam using the formula:$$A = \pi r^2$$where r is the radius of the laser beam. The radius of the laser beam is half of the diameter, so:$$r = \frac{d}{2} = \frac{0.90 	ext{ mm}}{2} = 0.45 	ext{ mm} = 4.5 	imes 10^{-4} 	ext{ m}$$Therefore, the area of the laser beam is:$$A = \pi (4.5 	imes 10^{-4} 	ext{ m})^2 = 6.36 	imes 10^{-7} 	ext{ m}^2$$Now we can calculate the rms value of the electric field in the laser beam:$$E_{rms} = \sqrt{\frac{2P}{\varepsilon_0 c A}} = \sqrt{\frac{2(8.0 	imes 10^{-3} 	ext{ W})}{(8.85 	imes 10^{-12} 	ext{ C}^2/	ext{N} \cdot 	ext{m}^2)(3.0 	imes 10^8 	ext{ m/s})(6.36 	imes 10^{-7} 	ext{ m}^2)}} = 2200 	ext{ N/C}$$Therefore, the rms value of the electric field in the laser beam is 2200 N/C.

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