| 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 :- |
| [JEE Main 8-4-2019 Afternoon] |
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A) \[\text{v}\propto {{\text{e}}^{+r/{{r}_{0}}}}\]
B) \[\text{v}\propto \ell n\left( \frac{r}{{{r}_{0}}} \right)\]
C) \[\text{v}\propto \left( \frac{r}{{{r}_{0}}} \right)\]
D) \[\text{v}\propto \sqrt{\ell n\left( \frac{r}{{{r}_{0}}} \right)}\]
Correct Answer: D
Solution :
| [d] \[\frac{1}{2}m{{V}^{2}}=-q({{V}_{f}}-{{V}_{i}})\] |
| \[E=\frac{\lambda }{2\pi {{\varepsilon }_{0}}r}\] |
| \[\Delta V=\frac{\lambda }{2\pi {{\varepsilon }_{0}}}\ell n\left( \frac{{{r}_{0}}}{r} \right)\] |
| \[\frac{1}{2}m{{v}^{2}}=\frac{-q\lambda }{2\pi {{\varepsilon }_{0}}}\ell n\left( \frac{{{r}_{0}}}{r} \right)\] |
| \[\text{v}\propto \sqrt{\ell n\left( \frac{r}{{{r}_{0}}} \right)}\] |
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