Question 458: Electrostatics & Capacitance

Question

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 :-
![](https://imagex.cdn.examgoal.net/18hoxe66ijwb9xhtn/b6e44e06-f018-47fa-8ff5-6733c56d7eea/6b93d4b0-8330-11e9-8081-1d558b7f1d26/file-18hoxe66ijwb9xhto.png)

Accepted Answer

${1 \over 2}m{V^2} =  - q\left( {{V_f} - {V_i}} \right)$
$E = {\lambda  \over {2\pi {\varepsilon _0}r}}$
$\Delta V = {\lambda  \over {2\pi {\varepsilon _0}}}\ln \left( {{{{r_0}} \over r}} \right)$
${1 \over 2}m{v^2} = {{ - q\lambda } \over {2\pi {\varepsilon _0}}}\ln \left( {{{{r_0}} \over r}} \right)$
$v \propto \sqrt {\ln \left( {{r \over {{r_0}}}} \right)} $

Answer

$v \propto \left( {{r \over {{r_0}}}} \right)$

Answer

$v \propto \ln \left( {{r \over {{r_0}}}} \right)$

Answer

$v \propto {e^{ + r/{r_0}}}$

Answer

$v \propto \sqrt {\ln \left( {{r \over {{r_0}}}} \right)} $

Electrostatics & Capacitance

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 :-

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