JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2019
- Hard
- MCQ
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(v \propto \sqrt {\ln \left( {\frac{r}{{{r_0}}}} \right)} \)
Step-by-step Solution
Detailed explanation
\(\frac{1}{2} m V^{2}=-q\left(V_{f}-V_{i}\right)\)
\(E = \frac{\lambda }{{2\pi {\varepsilon _0}r}}\)
\(\Delta \mathrm{V}=\frac{\lambda}{2 \pi \varepsilon_{0}} \ln \left(\frac{\mathrm{r}_{0}}{\mathrm{r}}\right)\)
\(\frac{1}{2} m v^{2}=\frac{-q \lambda}{2 \pi \varepsilon_{0}} \ln \left(\frac{r_{0}}{r}\right)\)
\(v \propto \sqrt{\ln \left(\frac{r}{r_{0}}\right)}\)
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