Two hollow concentric non-conducting spheres of radius the a and `b (a gt b)` contain charges `Q_(a)` and `Q_(b)` respectively. Prove that potential difference between the two spheres is independent of charge on outer sphere. If outer sphere is given an extra charge, is there any change in potential difference ?

Explanation

`V_("inner sphere") = (KQ_(b))/(b) + (KQ_(a))/(a)`
`V_("outer sphere") = (KQ_(b))/(a) + (KQ_(a))/(a)`

`V_(inner sphere") - V_("Outer sphere") = (KQ_(b))/(b) - (KQ_(b))/(a)`

`Delta V = KQ_(b)[(1)/(b) - (1)/(a)]`
Which is independent of charge on outer sphere. If outer sphere in given any extra charge then there will be no change in potential difference.