Question

Two charges $7\mu C$ and $-2\mu C$ are placed at $(-9cm,0,0)$ and $(+9cm,0,0)$ respectively. There is no external field on the system. Determine the electrostatic potential energy of this system.(b) How much work will be done in keeping the two charges at infinite distance from each other?

Answer 1

(a) $q_1=7\mu C$
$q_1=7\times {10}^{-6}C$
$q_2=-2pC$
$q_2=-2\times {10}^{-6}C$
$r=18cm$
$r=18\times {10}^{-2}m$
$\begin{array}{cc}\frac{1}{4\pi {\epsilon }_0}& =9\times {10}^9\frac{N-m^2}{C^2}\\ U& =\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r}\\ U& =\frac{9\times {10}^9\times (+7\times {10}^{-6})\times (-2\times {10}^{-6})}{18\times {10}^{-2}}\\ U& =-7\times {10}^{11}\times {10}^{-12}\\ U& =-0.7J\end{array}$
(b) Potential energy at infinity$U_2=0$
Potential energy at given position$U_1=-0.7J$
Work done in seperating the charges upto infinite$W=U_2-U_1$
$\Rightarrow W=0-(-0.7)$
$W=0.7J$