JEE PYQ: Electrostatics Question 39
Question 39 - 2019 (08 Apr Shift 2)
A positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density. The speed ($v$) of the point charge, as a function of instantaneous distance $r$ from line charge, is proportional to:
(1) $v \propto e^{+r/r_0}$
(2) $v \propto \sqrt{\ln\left(\frac{r}{r_0}\right)}$
(3) $v \propto \ln\left(\frac{r}{r_0}\right)$
(4) $v \propto \sqrt{\frac{r}{r_0}}$
Show Answer
Answer: (2)
Solution
Using energy conservation: $\frac{1}{2}mv^2 = q\int_{r_0}^{r} \frac{\lambda}{2\pi\varepsilon_0 r}dr = \frac{q\lambda}{2\pi\varepsilon_0}\ln\left(\frac{r}{r_0}\right)$. So $v \propto \sqrt{\ln(r/r_0)}$.
BETA
