Answer
The force is increasing at a rate of $~~7.2\times 10^{-4}~N/s$
Work Step by Step
We can find the rate at which the force is increasing:
$F = \frac{kq^2}{r^2}$
$\frac{dF}{dt} = \frac{2kq}{r^2}~\frac{dq}{dt}$
$\frac{dF}{dt} = \frac{(2)(9.0\times 10^9~N~m^2/C^2)(5.0\times 10^{-9}~C)}{(0.025~m)^2}~\cdot (5.0\times 10^{-9}~C/s)$
$\frac{dF}{dt} = 7.2\times 10^{-4}~N/s$
The force is increasing at a rate of $~~7.2\times 10^{-4}~N/s$
