Question

Two charges of equal magnitude 'q' are placed in air at a distance '$2a$' apart and third charge '$-2q$' is placed at midpoint. The potential energy of the system is ________.

(${ϵ}_0=$ permittivity of free space)

• A. $-\frac{q^2}{8\pi {ϵ}_{0}a}$
• B. $-\frac{3q^2}{8\pi {ϵ}_{0}a}$
• C. $-\frac{5q^2}{8\pi {ϵ}_{0}a}$
• D. $-\frac{7q^2}{8\pi {ϵ}_{0}a}$

Answer 1

Answer: (D)

$-\frac{7q^2}{8\pi {ϵ}_{0}a}$

The system of 3 charges can be thought of as three pairs of charges and the potential energy of each pair can be found individually. The total potential energy will be the sum of these energies.

Therefore, the potential energy of the system is given by:

$U=\frac{1}{4\pi {\epsilon }_0}[\frac{q^2}{2a}-\frac{{2q}^2}{a}-\frac{{2q}^2}{a}]=\frac{-7q^2}{8\pi {\epsilon }_{0}a}$