A laser beam has intensity 17.7 times 10^{14} | vedclass

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(A) The intensity $I$ of an electromagnetic wave is related to the amplitude of the electric field $E_0$ by the formula: $I = \frac{1}{2} \epsilon_0 E

Vedclass · Accepted Answer

$\frac{2}{\sqrt{3}} 	imes 10^9 \ N \ C^{-1}$

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(A) The intensity $I$ of an electromagnetic wave is related to the amplitude of the electric field $E_0$ by the formula: $I = \frac{1}{2} \epsilon_0 E_0^2 c$ Given: $I = 17.7 	imes 10^{14} \ W/m^2$ $\epsilon_0 = 8.85 	imes 10^{-12} \ C^2 / (N \cdot m^2)$ $c = 3 	imes 10^8 \ m/s$ Substituting the values into the formula: $17.7 	imes 10^{14} = \frac{1}{2} 	imes (8.85 	imes 10^{-12}) 	imes E_0^2 	imes (3 	imes 10^8)$ $17.7 	imes 10^{14} = \frac{26.55 	imes 10^{-4}}{2} 	imes E_0^2$ $17.7 	imes 10^{14} = 13.275 	imes 10^{-4} 	imes E_0^2$ $E_0^2 = \frac{17.7 	imes 10^{14}}{13.275 	imes 10^{-4}} = \frac{17.7}{13.275} 	imes 10^{18} \approx 1.333 	imes 10^{18} = \frac{4}{3} 	imes 10^{18}$ Taking the square root: $E_0 = \sqrt{\frac{4}{3} 	imes 10^{18}} = \frac{2}{\sqrt{3}} 	imes 10^9 \ N \ C^{-1}$

$A$ laser beam has intensity $17.7 \times 10^{14} \ W/m^2$. The amplitude of the electric field is
[Use $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 / (N \cdot m^2)$]

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$A$ laser beam has intensity $17.7 \times 10^{14} \ W/m^2$. The amplitude of the electric field is [Use $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 / (N \cdot m^2)$]