A charge of magnitude $3 × 10^{-7} C$ is located at a distance of 0.09 m from a point P. Obtain the work done in bringing a charge of $2 × 10^{-9} C$ from infinity to the point P.

$6 × 10^{-5} J$

The correct answer is Option (3) → $6 × 10^{-5} J$

$\text{Given: } q_1 = 3 \times 10^{-7} \, \text{C}, \, q_2 = 2 \times 10^{-9} \, \text{C}, \, r = 0.09 \, \text{m}$

Work done in bringing $q_2$ from infinity to P is:

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

Substituting values:

$W = 9 \times 10^9 \times \frac{(3 \times 10^{-7})(2 \times 10^{-9})}{0.09}$

$W = 9 \times 10^9 \times \frac{6 \times 10^{-16}}{0.09}$

$W = 9 \times 10^9 \times 6.67 \times 10^{-15}$

$W = 6.0 \times 10^{-5} \, \text{J}$

$\text{Answer: } W = 6.0 \times 10^{-5} \, \text{J}$