Answer
$1.16\times10^{-5}\;C$
Work Step by Step
Let the charge on one sphere is $+q\;C$
Then the charge on other sphere is $q^{'}=(5\times10^{-5}-q)\;C$
Magnitude of electrostatic force between them
$F=\frac{1}{4\pi\epsilon_0}\frac{q\times(5\times10^{-5}-q)}{2^2}\;N$
or, $1\;N=\frac{1}{4\pi\epsilon_0}\frac{q\times(5\times10^{-5}-q)}{4}\;N$
or, $9\times10^{9}q^2-4.5\times10^{5}q+4=0$
The solutions are:
$q=3.84\times10^{-5}\;C$ or $q=1.16\times10^{-5}\;C$
for, $q=3.84\times10^{-5}\;C$, the value of $q^{'}=1.16\times10^{-5}\;C$
and for $q=1.16\times10^{-5}\;C$, the value of $q^{'}=3.84\times10^{-5}\;C$
Therefore, the charge on the sphere with the smaller charge is $1.16\times10^{-5}\;C$
