Question

Two charges of equal magnitude 'q' are placed in air at a distance '2a' apart and charge '-2q' is placed at midpoint. The potential energy of the system is ($\epsilon_0$ = permittivity of free space)

• A. -$\frac{q^2}{8\pi \epsilon_0 a}$
• B. -$\frac{3q^2}{8\pi \epsilon_0 a}$
• C. -$\frac{5q^2}{8\pi \epsilon_0 a}$
• D. -$\frac{7q^2}{8\pi \epsilon_0 a}$

Answer 1

Answer: (D)

-$\frac{7q^2}{8\pi \epsilon_0 a}$

Answer 2

The mutual potential energy is given by:

$U = k [ \frac{q \cdot q}{2a} + \frac{q \cdot (-2q)}{a} + \frac{q \cdot (-2q)}{a} ]$

$U = \frac{1}{4\pi\epsilon_0} [ \frac{q^2}{2a} - \frac{2q^2}{a} - \frac{2q^2}{a} ]$

$U = \frac{1}{4\pi\epsilon_0} [ \frac{q^2}{2a} - \frac{4q^2}{a} ]$

$U = \frac{1}{4\pi\epsilon_0} [ \frac{q^2 - 8q^2}{2a} ]$

$U = -\frac{7q^2}{8\pi\epsilon_0 a}$