Question

$A$ and $B$ are two identically spherical charged bodies which repel each other with force $F$, kept at a finite distance. A third uncharged sphere $C$ of the same size is brought in contact with sphere $B$ and removed. It is then kept at midpoint of $A$ and $B$. Find the magnitude of force on $C$.

• A. $\frac{F}{4}$
• B. $\frac{F}{8}$
• C. $F$
• D. zero

Answer 1

The correct option is C $F$

Initial force between the two spheres carrying charge (say $q$) is
$F=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}$

Further when an uncharged sphere is kept in touch with the sphere of charge $q$, the net charge on both become $\frac{q+0}{2}=\frac{q}{2}$.

Force on the 3rd charge, when placed at center of the first two:
$F_3=\frac{1}{4\pi {\epsilon }_0}\frac{q\left(\frac{q}{2}\right)}{{\left(\frac{r}{2}\right)}^2}-\frac{1}{4\pi {\epsilon }_0}\frac{{\left(\frac{q}{2}\right)}^2}{{\left(\frac{r}{2}\right)}^2}$$=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}[2-1]=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}=F$