Question 728: Electrostats & Capacitance

Question

An electron revolves around an infinite cylindrical wire having uniform linear charge density $$2 	imes 10^{-8} \mathrm{C} \mathrm{m}^{-1}$$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ___________ $$	imes 10^{6} \mathrm{~m} \mathrm{~s}^{-1}$$. Given mass of electron $$=9 	imes 10^{-31} \mathrm{~kg}$$

Accepted Answer

$$
\begin{aligned}
& e E=\frac{\mathrm{mV}^2}{r} \\
& e \cdot \frac{2 \mathrm{~K} \lambda}{r}=\frac{\mathrm{mV}^2}{r} \\
& V=\sqrt{\frac{e \cdot 2 \mathrm{k} \lambda}{\mathrm{m}}} \\
& =\sqrt{\frac{1.6 	imes 10^{-19} 	imes 2 	imes 9 	imes 10^9 	imes 2 	imes 10^{-8}}{9 	imes 10^{-31}}} \\
& =8 	imes 10^6 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$

Electrostats & Capacitance

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