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 )

     

 

Answers (1)

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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