Question

Two charges $q_1$ and $q_2$ are placed 30cm apart, as shown in figure. A third charges $q_3$ 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 $\frac{q_3}{4\pi {ϵ}_0}\text{k}$, where k is

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

Answer 1

The correct option is A

$8q_2$

$\Delta \text{U}={\text{U}}_{\text{f}}-{\text{U}}_{\text{i}}$

$\frac{{\text{q}}_3}{4\pi {ϵ}_0}\text{k}=\frac{1}{4\pi {ϵ}_0}[\frac{q_1{q}_2}{0.3}+\frac{q_2{q}_3}{0.1}+\frac{q_1{q}_3}{0.4}]-\frac{1}{4\pi {ϵ}_0}[\frac{q_1{q}_2}{0.3}+\frac{q_2{q}_3}{0.5}+\frac{q_1{q}_3}{0.4}]$

${\text{q}}_3\text{k}={\text{q}}_2{\text{q}}_3[\frac{1}{0.1}-\frac{1}{0.5}]=8{\text{q}}_2{\text{q}}_3$

$k=8{\text{q}}_2$