A 20 W laser beam, with an initial diameter of 2.0 mm, spreads out to a diameter of 2.0 m after traveling 10,000 m. What is the initial E_rms of the beam? A) 4.9 × 10⁴ V/m B) 2.5 × 10³ V/m C) 1.2 × 10³ V/m D) 1.9 × 10² V/m E) 1.7 × 10² V/m

Question

Quizplus · Accepted Answer

The initial electric field (E) of a laser beam can be calculated using the formula $E = \sqrt{\frac{2P}{\epsilon_0 c \pi r^2}}$, where $P$ is the power of the laser, $\epsilon_0$ is the vacuum permittivity ($8.854 \times 10^{-12} \, \text{F/m}$), $c$ is the speed of light ($3 \times 10^8 \, \text{m/s}$), and $r$ is the radius of the beam. Given $P = 20 \, \text{W}$ and the initial diameter $2.0 \, \text{mm}$ (radius $1.0 \, \text{mm} = 1.0 \times 10^{-3} \, \text{m}$), substituting these values into the formula gives an electric field strength of approximately $4.9 \times 10^{14} \, \text{V/m}$.

A 20 W Laser Beam, with an Initial Diameter of 2.0