Question

In the following figure, a central particle of charge -2q is surrounded by a square array of charged particles, separated by either distance d or $\frac{d}{2}$ along the parimeter of the square. What is the magnitude and direction of the net electrostatic force on the central particle due to the other particles?

• A. $\frac{1}{4\pi {ϵ}_0}\frac{6q^2}{d^2}$ left
• B. Zero
• C. $\frac{1}{4\pi {ϵ}_0}\frac{6q^2}{d^2}$ right
• D. $\frac{1}{4\pi {ϵ}_0}\frac{2q^2}{d}$ left

Answer 1

The correct option is A $\frac{1}{4\pi {ϵ}_0}\frac{6q^2}{d^2}$ left

The net force here is only due to +3q because the forces due to all other charges cancel due to the symmetry considerations.
Hence the net force on -2q must be $\frac{1}{4\pi {ϵ}_0}\frac{\left(2q\right)\left(3q\right)}{d^2}$