A laser beam has intensity of $4.0 imes 10^{14} \mathrm{~W} / \mathrm{m}^2$. The amplitude of magn

Question

A laser beam has intensity of $4.0 	imes 10^{14} \mathrm{~W} / \mathrm{m}^2$. The amplitude of magnetic field associated with beam is $\_\_\_\_$ T. (Take $\epsilon_{\mathrm{o}}=8.85 	imes 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ and $\mathrm{c}=3 	imes 10^8 \mathrm{~m} / \mathrm{s}$ )

Professor PC Thomas Classes · Answer

The intensity of an electromagnetic wave is related to the maximum magnetic field $B_0$ by the equation $I = \frac{1}{2} c \frac{B_0^2}{\mu_0}$. Since $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$, we can write $\mu_0 = \frac{1}{\epsilon_0 c^2}$. Substituting this gives $I = \frac{1}{2} c \epsilon_0 c^2 B_0^2 = \frac{1}{2} \epsilon_0 c^3 B_0^2$. Solving for $B_0$, we get $B_0 = \sqrt{\frac{2I}{\epsilon_0 c^3}} = \sqrt{\frac{2 	imes 4.0 	imes 10^{14}}{8.85 	imes 10^{-12} 	imes (3 	imes 10^8)^3}} = \sqrt{\frac{8.0 	imes 10^{14}}{8.85 	imes 27 	imes 10^{12}}} = \sqrt{\frac{800}{238.95}} \approx \sqrt{3.348} \approx 1.83 	ext{ T}$.