91Ó°ÊÓ

The electric force exerted between two charges is directly proportional to the magnitude of charges and inversely proportional to the square of the separation distance.

The expression for the electric force is given as:

\(F = k\frac{{{Q_1}{Q_2}}}{{{r^2}}}\) … (i)

Here, k is the Coulomb’s constant,\({Q_1},\;{Q_2}\)are the charges and r is the separation between the charges.

The initial distance between the charged spheres is, \(r = 6.52\;{\rm{cm}}\)

From equation (i), the electric force is,

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

When the force is multiplied by the factor 3, the value of rwill reduce by factor \(\sqrt 3 \).

So, the new distance between the charged spheres is,

\(\begin{aligned}{l}r' = \frac{r}{{\sqrt 3 }}\\r' = \frac{{6.52\,{\rm{cm}}}}{{\sqrt 3 }}\\r' = 3.76\,{\rm{cm}}\end{aligned}\)

Thus, the distance between the charged spheres becomes \(3.76\,{\rm{cm}}\).