An infinitely long positively charged straight thread has a linear charge density λ mathrm{Cm}^{-1}

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1. Electric Charges and Fields

hard

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 :

A

B

C

D

(JEE MAIN-2024)

Solution

Electric field $\mathrm{E}$ at a distance $\mathrm{r}$ due to infinite long wire is $E=\frac{2 \mathrm{k} \lambda}{\mathrm{r}}$

Force of electron $\Rightarrow \mathrm{F}=\mathrm{eE}$

$F=e\left(\frac{2 k \lambda}{r}\right)$

$F=\frac{2 k \lambda e}{r}$

This force will provide required centripetal force

$\mathrm{F} =\frac{\mathrm{mv}^2}{\mathrm{r}}=\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{r}}$

$\mathrm{v} =\sqrt{\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}}$

$\mathrm{KE} =\frac{1}{2} \mathrm{mv}^2=\frac{1}{2} \mathrm{~m}\left(\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}\right)$

$=\mathrm{k} \lambda \mathrm{e}$

This is constant so option $(2)$ is correct.

Standard 12

Physics

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