Answer
The work done by the applied force is $8.45~J$
Work Step by Step
We can find the electric potential energy:
$U = \frac{k~q_1~q_2}{r}$
$U = \frac{(9.0\times 10^9~N~m^2/C^2)(6.5\times 10^{-6}~C)(6.5\times 10^{-6}~C)}{0.045~m}$
$U = 8.45~J$
When the charges are very far apart, we can assume that the electric potential energy is zero. Therefore, the work done by the applied force is $8.45~J$.
