An 8.00-mW laser beam emits a cylindrical beam of single-wavelength sinusoidal light $0.600 \mathrm {~mm}$ in diameter. What is the maximum value of the magnetic field in the laser beam? $\left( \varepsilon _ { 0 } = 8.85 \times \right.$ $\left. 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } , \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } , c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Question

Quizplus · Accepted Answer

The intensity $I$ of the laser beam is given by $I = \frac{P}{A}$, where $P$ is the power and $A$ is the cross-sectional area. The area $A = \pi \left(\frac{d}{2}\right)^2$. The intensity is also related to the electric field $E$ by $I = \frac{1}{2} c \varepsilon_0 E^2$. The magnetic field $B$ is related to the electric field by $B = \frac{E}{c}$. Solving these equations gives the maximum magnetic field.

An 800-MW Laser Beam Emits a Cylindrical Beam of Single-Wavelength Sinusoidal