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`
`:. DeltaV=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.