Question 71 of 311

An infinitely long positively charged straight thread has a linear charge density $\lambda \mathrm{Cm}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

ABCD

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Answer: (C)

Electric field $\mathrm{E}$ at a distance $\mathrm{r}$ due to infinite long wire is $E=\frac{2 k \lambda}{r}$
Force of electron $\Rightarrow F=e E$
$\begin{aligned}
& F=e\left(\frac{2 k \lambda}{r}\right) \\
& F=\frac{2 k \lambda e}{r}
\end{aligned}$
This force will provide required centripetal force
$\begin{aligned}
\mathrm{F} & =\frac{\mathrm{m}^2}{\mathrm{r}}=\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{r}} \\
\mathrm{v} & =\sqrt{\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}} \\
\mathrm{KE} & =\frac{1}{2} \mathrm{mv}^2=\frac{1}{2} \mathrm{~m}\left(\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}\right) \\
& =\mathrm{k} \lambda \mathrm{e}
\end{aligned}$