Question

Two identical spheres with charges $4q,-2q$ kept some distance apart exert a force $F$ on each other. If they are made to touch each other and replaced at their old positions, the force between them will be

• A. $\frac{1}{9}F$
• B. $\frac{1}{8}F$
• C. $\frac{9}{8}F$
• D. $\frac{8}{9}F$

Answer 1

Answer: (B)

When spheres are touched and separated, charge is
$q^{\prime }=\frac{4q-2q}{2}=\frac{2q}{2}=q$
From Coulomb's law
$F=\frac{1}{4\pi {\epsilon }_0}\frac{(4q)(-2q)}{r}$...(i)
When made to touch
$F^{\prime }=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r}$ ...(ii)
From Eqs. (i) and (ii), we get
$F^{\prime }=\frac{F}{8}$