Question

Two point charges are located on the x-axis: $q_1=-e$ at $x=0$ and $q_2=+e$ at $x=a$. A third point charge $q_3=+e$ is brought to $x=2a.$ The total potential energy of the system of three charges is :

• A. $\frac{e^2}{4\pi {\epsilon }_{0}a}$
• B. $\frac{e^2}{8\pi {\epsilon }_{0}a}$
• C. $\frac{-e^2}{8\pi {\epsilon }_{0}a}$
• D. $\frac{-e^2}{4\pi {\epsilon }_{0}a}$

Answer 1

The correct option is C $\frac{-e^2}{8\pi {\epsilon }_{0}a}$

Third charge $q_3$ is brought to $x=2a$.

Potential energy of $q_1,q_2$ system$=\frac{1}{4\pi {ϵ}_0}\frac{-e^2}{a}$

Potential energy of $q_2,q_3$ system$=\frac{1}{4\pi {ϵ}_0}\frac{+e^2}{a}$

Potential energy of $q_2,q_3$ system$=\frac{1}{4\pi {ϵ}_0}\frac{-e^2}{2a}$

Hence total energy of the system of three particles$=\frac{-e^2}{8\pi {ϵ}_{0}a}$