Question

Two similarly and equally charged identical metal spheres A and B repel each other with a force of `2xx10^(-5)N`. A third identical unchared sphere C is touched with A and then placed at the midpoint between A and B. Find the net electric force on C.

Answer 1

Correct Answer - `2xx10^(-5)` N toward sphere B
Let charge on each sphere be q, then
`F=k(q^2)/(r^2)=2xx10^(-5) or (q^2)/(r^2)=(2xx10^(-5))/(9xx10^(9))`

When sphere C is touched by sphere A, charge gets equally divided between the two.
`F_(CA)=k(q^(2)//4)/(r^(2)//4)=k(q^2)/(4)xx(4)/(r^2)=(kq^2)/(r^2)`
`F_(CB)=k(q^(2)//4)/(r^(2)//4)=k(q^2)/(4)xx(4)/(r^2)=2k(q^2)/(r^2)`
`F_(C)=F_(CB)-F_(CA)=k(q^(2))/(r^(2))=2xx10^(-5)`N towards A.