Three particles, each having a charge of 10 μC, are placed at the vertices of an equilateral triangle of 10 mm. Find the work done by a person in pulling them apart to infinite separation.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -270 J
Charge on each particle, q = 10 μC = 10 × 10⁻⁶ C
Side of equilateral triangle, a = 10 mm = 0.01 m
Work done to separate charges = Electrostatic potential energy of the system:
For three charges at vertices of an equilateral triangle:
$W = k \left[\frac{q_1 q_2}{a} + \frac{q_1 q_3}{a} + \frac{q_2 q_3}{a}\right]$
All charges are equal:
$W = 3 k \frac{q^2}{a}$
Substitute values (k = 9 × 10⁹ N·m²/C²):
$W = 3 \cdot 9 \times 10^9 \cdot \frac{(10 \times 10^{-6})^2}{0.01}$
$W = 27 \times 10^9 \cdot \frac{100 \times 10^{-12}}{0.01}$
$W = 27 \times 10^9 \cdot 10^{-8} = 270\ \text{J}$
Since the work is done against the electrostatic repulsion to pull the charges apart, it is considered negative:
∴ Work done = -270 J