Question

Two charges $q_1$ and $q_2$ are located $30\text{cm}$ apart, as shown in the figure. A third charge $q_3$ is moved along tthe arc of a circle of radius $40\text{cm}$ from $C$ to $D$. The change in the potential energy of the system is $\frac{n{q}_2{q}_3}{4\pi {ϵ}_0}$. Find $n$.

Answer 1

$U_i=\frac{1}{4\pi {ϵ}_0}[\frac{q_1{q}_3}{\left(0.4\right)}+\frac{q_1{q}_2}{\left(0.3\right)}+\frac{q_2{q}_3}{\left(0.5\right)}]$
$U_f=\frac{1}{4\pi {ϵ}_0}[\frac{q_1{q}_3}{0.4}+\frac{q_1{q}_2}{0.3}+\frac{q_2{q}_3}{0.1}]$
$\Delta U=U_f-U_i=\frac{q_2{q}_3}{4\pi {ϵ}_0}(\frac{1}{0.1}-\frac{1}{0.5})$
$=\frac{q_3}{4\pi {ϵ}_0}\left(8q_2\right)$