Question

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

• A. $8q_2$
• B. $8q_1$
• C. $6q_2$
• D. $6q_1$

Answer 1

The correct option is A $8q_2$



Change in potential energy $\left(\Delta U\right)=U_f-U_i$
$\Rightarrow \Delta U=\frac{1}{4\pi {ϵ}_0}[(\frac{q_1{q}_3}{0.4}+\frac{q_2{q}_3}{0.1})-(\frac{q_1{q}_3}{0.4}+\frac{q_2{q}_3}{0.5})]$
$\Rightarrow \Delta U=\frac{1}{4\pi {ϵ}_0}\left[8q_2{q}_3\right]=\frac{q_3}{4\pi {ϵ}_0}\left(8q_2\right)$
$\therefore k=8q_2$