Question

Four electric charges are arranged as shown in the figure at the four corners of a square of side a . The potential energy of the system is:

• A. Zero
• B. Negative
• C. Positive
• D. Greater than $\frac{1}{4\pi {\epsilon }_0}\frac{2q^2}{a}$

Answer 1

The correct option is B Negative

Electrostatic potential energy is defined as $\frac{1}{4\pi ϵ}q1\frac{q2}{r}$.
P.E.=$2\frac{1}{4\pi ϵ}q\frac{-q}{a}+\frac{1}{4\pi ϵ}-q\frac{-q}{\sqrt{2}a}$ where a is radius of square.
P.E.=$-2\frac{1}{4\pi ϵ}\frac{q^2}{a}+\frac{1}{4\pi ϵ}\frac{q^2}{\sqrt{2}a}$
Hence the answer comes negative and the correct choice is B.