Question

A metal sphere is suspended through a nylon thread. When another charged sphere (identical to A) is brought near to $A$ and kept at a distance $d$, a force of repulsion $F$ act between them. Now $A$ is brought in contact with an identical uncharged sphere $C$ and $B$ is also brought in contact with an identical uncharged sphere $D$ and then they are separated from each other. What will be the force between sphere $A$and$B$ when they are at a distance$\frac{d}{2}$

Answer 1

Suppose the first charged sphere is having charge $q$

So it will induce same amount of opposite charge.

So, charge on $A$ is $q$

Now with contact of another uncharged sphere, charge will be divided equally between these two spheres by $\frac{q}{2}$ and they will repel each other

So $F^{\prime }=k\frac{\frac{q}{2}\times \frac{q}{2}}{\frac{d^2}{4}}=\frac{k{q}^2}{d^2}=F$ and the nature is repulsive.