Two point charges, 4 μC and -3 μC (with no external field) are placed at (-6 cm, 0, 0) and (6 cm, 0, 0), respectively. The amount of work required to separate the two charges infinitely away from each other will be

0.9 J

The correct answer is Option (1) → 0.9 J

Given:

$q_1 = 4\ \mu C = 4 \times 10^{-6}\ C$

$q_2 = -3\ \mu C = -3 \times 10^{-6}\ C$

Distance between charges, $r = 6 - (-6) = 12\ \text{cm} = 0.12\ \text{m}$

Work required to separate them to infinity = Decrease in potential energy

$W = -U = -\left( \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r} \right)$

Magnitude: $W = \frac{1}{4 \pi \varepsilon_0} \frac{|q_1 q_2|}{r}$

Using $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9$

$W = 9 \times 10^9 \times \frac{(4 \times 10^{-6})(3 \times 10^{-6})}{0.12}$

$W = 9 \times 10^9 \times \frac{12 \times 10^{-12}}{0.12}$

$W = 9 \times 10^9 \times 10^{-10}$

$W = 9 \times 0.1 = 0.9\ \text{J}$

Work required = 0.9 J