Question

In free space, a particle $A$ of charge $1\mu C$ is held fixed at a point $P$. Another particle $B$ of the same charge and mass $4\mu g$ is kept at a distance of $1mm$ from $P$. if $B$ is released, then its velocity at a distance of $9mm$ from $P$ is :
$\left[\text{Take}\frac{1}{4\pi {\epsilon }_0}=9\times 10^{9}N{m}^2{C}^{-2}\right]$

• A. $2.0\times 10^{3}m/s$
• B. $3.0\times 10^{4}m/s$
• C. $1.5\times 10^{2}m/s$
• D. $1.0m/s$

Answer 1

Answer: (A)

$W_E=-\left[\Delta U\right]=U_i-U_F=\frac{1}{2}m{v}^2$
$U=\frac{k{q}_1{q}_2}{r}$
$\frac{\left(9\times 10^9\right)\times 10^{-12}}{10^{-3}}-\frac{\left(9\times 10^9\right)\times 10^{-12}}{9\times 10^{-3}}=\frac{1}{2}\times \left(4\times 10^{-6}\right)v^2$
$v^2=4\times 10^6$
$v=2\times 10^3\frac{m}{s}$