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 )

 

Preparation Products

Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
Buy Now
Rank Booster JEE Main 2020

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 9999/- ₹ 4999/-
Buy Now
Test Series JEE Main Sept 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 1999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions