Q 12-01-045JEE MainJEE Main 2024 (4 Apr, Shift 1)Medium
An infinitely long positively charged straight thread has a linear charge density $\lambda\ \text{C m}^{-1}$. An electron revolves along a circular path having its axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of the electron as a function of the radius of the circular path from the wire is
Answer: (C) see figure
The field of the line charge provides the centripetal force:
$$\frac{mv^2}{r} = eE = \frac{e\lambda}{2\pi\varepsilon_0 r} \Rightarrow mv^2 = \frac{e\lambda}{2\pi\varepsilon_0}$$
So $KE = \dfrac12mv^2 = \dfrac{e\lambda}{4\pi\varepsilon_0}$, independent of $r$: a horizontal line, graph (C).
Solution by Sreeraj P, M.Sc Physics