Question

Consider three metal spheres $A,B$ and $C$. Spheres $A$ carries charge $+6q$ and sphere $B$ carries charge $-3q$. Sphere $C$ carries no charge. Spheres $A$ and $B$ are touched together and then separated. Sphere $C$ is then touched to sphere $A$ and separated from it. Finally the sphere $C$ is touched to sphere $B$ and separated from it. Find the final charge on the sphere $C$.

Answer 1

When the two metal spheres are touched they will come to equal potential. And when the metal sphere are of same radius then the equal potential means equal charges.

Now the charge distribution at each steps will be-

1. Initially- A=+6q B=-3q C=0
2. Spheres A, B touched and seperated- A= +1.5q B=+1.5q C=0 ( charges will be equally distributed and total charge will be conserved for two spheres that are touched)
3. C and A are touched- A=+0.75q B=+1.5q C=+0.75q (same logic as above)
4. C and B are touched- A=+0.75q B=+1.125q C=1.125q

So the final charge on sphere C will be $q_c=+1.125q$.