91Ó°ÊÓ

The force of attraction or repulsion that exists between two-point charges separated by some distance in space is known as electrostatic force.

(a)

The electrostatic force between two-point charges q and Q separated by some distancer is given as,

\(F = \frac{{KqQ}}{{{r^2}}}\)

When the separation between the charges is changed to \(r'\), the new electrostatic force is given as,

\(F' = \frac{{KqQ}}{{{{r'}^2}}}\)

Taking the ratio of equations (1.1) and (1.2),

\(\begin{aligned} \frac{F}{{F'}} &= \frac{{\frac{{KqQ}}{{{r^2}}}}}{{\frac{{KqQ}}{{{{r'}^2}}}}}\\\frac{F}{{F'}} &= {\left( {\frac{{r'}}{r}} \right)^2}\end{aligned}\)

Since \(F' = 10F\). Therefore,

\(\begin{aligned} \frac{F}{{10F}} &= {\left( {\frac{{r'}}{r}} \right)^2}\\{\left( {\frac{{r'}}{r}} \right)^2} &= \frac{1}{{10}}\\\frac{{r'}}{r} &= \frac{1}{{\sqrt {10} }}\\ &= 0.316\end{aligned}\)

Hence, the distance must be reduced by a factor of 0.316 in order to change the force between the point charges by a factor of 10.

(b)

Since the Coulomb force due to two-point charges is inversely proportional to the square of their separation. That is,

\({\rm{F}} \propto \frac{{\rm{1}}}{{{{\rm{r}}^{\rm{2}}}}}\)

Hence, to increase the force between two-point charges, the separation must be decreased.