Answer
it took just $8$ electrons to produce the charge on one of the objects.
Work Step by Step
Distance between the spherical objects is $r=1.80\times10^{-3}m$
suppose after acquiring electrons each object is charged to $-q$
since both the objects are equally charged we can write $q_{1}=q_{2}=-q$
and the magnitude of charges $|q_{1}|=|q_{2}| =q$
from coulombs law we know that magnitude of force between two charged objects is given by
$F=k\frac{|q_{1}|\times|q_{2}| }{r^2}$
in our problem it is given that magnitude of force
$F=4.55\times10^{-21}N$
$k=8.99\times10^{9}N.m^2/C^2$
$r=1.80\times10^{-3}m$
so putting these values we will get
$4.55\times10^{-21}N=8.99\times10^{9}N.m^2/C^2\times \frac{q\times q}{(1.80\times10^{-3}m)^2}$
$q^2=\frac{4.55\times10^{-21}N\times (1.80\times10^{-3}m)^2}{8.99\times10^{9}N.m^2/C^2}$
$q=\sqrt (1.63982\times10^{-36}C^2)$
$q=1.2805\times10^{-18}C$
magnitude of charge is $1.2805\times10^{-18}C$
$q_{1}=q_{2}=-q=-1.2805\times10^{-18}C$
$-1.6\times10^{-19}C$ is equal to $1$ electron
$-1C$ is equal to $\frac{1}{1.6\times10^{-19}} $electron
$-1.2805\times10^{-18}C$ is equal to $\frac{1.2805\times10^{-18}}{1.6\times10^{-19}} $electron = $0.8003\times10^{1}$ electrons
or approximately $8$ electrons.
