Answer
$t=2.1days$
Work Step by Step
We can find the initial electric energy as
$U_i=3\times \frac{Kq^2}{a}$
$U_i=3\times \frac{9\times 10^9(0.12)^2}{1.7}=2.2871\times 10^8J$
We can find the final electric energy as
$U_f=2\times \frac{Kq^2}{\frac{a}{2}}+\frac{Kq^2}{a}$
We plug in the known values to obtain:
$U_f=2\times \frac{9\times 10^9\times (0.12)^2}{\frac{1.7}{2}}+\frac{9\times 10^9(0.12)^2}{1.7}=3.81176\times 10^8J$
Now,
$W=\Delta U=3.81176\times 10^8-2.2871\times 10^8=1.5247\times10^8J$
We can determine the time as
$t=\frac{W}{P}$
We plug in the known values to obtain:
$t=\frac{1.5247\times10^8}{0.83\times 10^3}=1.837\times 10^5s=2.1days$
