Q 12-01-063JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then the time period will be given as: (Consider $k$ as Coulomb's constant)
Answer: (B) $T = 2\pi r\sqrt{\dfrac{m}{2k\lambda q}}$
Field of the line charge: $E = \dfrac{2k\lambda}{r}$. The attraction provides the centripetal force:
$$\frac{2k\lambda q}{r} = \frac{mv^2}{r} \Rightarrow v = \sqrt{\frac{2k\lambda q}{m}}$$
$$T = \frac{2\pi r}{v} = 2\pi r\sqrt{\frac{m}{2k\lambda q}}$$
Solution by Sreeraj P, M.Sc Physics