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

Explanation

Suppose charge of each sphere isd q, the force between spheres A and B for separation r
`F=2.0xx10^(-5)=1/(4pi epsilon_(0))(q^(2))/(r^(2))`…….i

When uncharged sphere C is touched to the sphere A the charge on each one becomes q/2. Thus force between A and C
`F_(AC)=1/(4 p epsion_(0))((q//2)(q//2))/((r//2)^(2))=F`
force between B and C
`f_(BC)=1/(4pi epsilon_(0))((q/2)q)/((r/2)^(2))=2F`
Thus the net force on the sphere C
`=2F-F=F=2.0xx10^(-5)N` from C to A