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 :-

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 :-

Choose the correct answer: