Q

Solve it, A Positive point charge is released from rest at a distance rofrom a positive line chage with unifrom density. The speed (v) of the point charge , as function of instantaneous distance r from line charge, is proportional to:

A Positive point charge is released from rest at a distance  ro from a positive line chage with unifrom density. The speed (v) of the point charge , as function of instantaneous distance r from line charge, is proportional to:

• Option 1)

$v \;\alpha \; e^{+r/r_{0}}$

• Option 2)

$v\; \alpha \;\sqrt{\ln \left ( \frac{r}{r_{0}} \right )}$

• Option 3)

$v\; \alpha \;\ln \left ( \frac{r}{r_{0}} \right )$

• Option 4)

$v\; \alpha \; \left ( \frac{r}{r_{0}} \right )$

Views

Apply Energy conservation

$\frac{1}{2}mv^{2}=q\left ( v_{f}-v_{i} \right )$

$E=\frac{\lambda }{2 \pi \epsilon_{0}r } , \Delta v=\frac{\lambda }{2 \pi \epsilon_{0}}\ln \left ( \frac{r_{0}}{r} \right )$

$\Rightarrow \frac{1}{2}mv^{2}=\frac{-q\lambda }{2 \pi \epsilon_{0}} \ln \left ( \frac{r_{0}}{r} \right )$

$\Rightarrow v\alpha \sqrt{\ln \left ( \frac{r}{r_{0}} \right )}$

Option 1)

$v \;\alpha \; e^{+r/r_{0}}$

Option 2)

$v\; \alpha \;\sqrt{\ln \left ( \frac{r}{r_{0}} \right )}$

Option 3)

$v\; \alpha \;\ln \left ( \frac{r}{r_{0}} \right )$

Option 4)

$v\; \alpha \; \left ( \frac{r}{r_{0}} \right )$

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