A small sphere of radius a carrying a positive charge q, is placed concentrically inside a larger hollow conducting shell of radius b (b a). This outer shell has charge Q on it . Show that if these spheres are connected by a conducting fire, charge will always flow from the inner sphere to the outer sphere, irrespective of the magnitude of the two charges.

(Why aren't induced charges, -q on the circumference of the inner sphere and Q+q on outer sphere considered since the spheres are conducting? If we consider them then Va= kq/a - kq/a + k(Q+q)/b and Vb= kq/b - kq/b + k(Q+q)/b. Thus, Va=Vb. Where is my mistake?)

Please have a look on the following solution. Hope this will clear your doubts.

The electric potential on the outer shell due to charge Q is given by,14π0.QbThe electric potential on the inner sphere due to q is14π0.qaThus, the total potential on the inner sphere will be given by,14π0.qa+14π0.QbThe electric potential on the outer sphere due to charge q is14π0.qbTherefore total potential on the outer sphere=14π0.qb+14π0.QbAnd so,V(a) -V(b)=14π0[qa-qb]=q4π0[1a-1b]   Since a<b, so  [1a-1b] =Positivei.e. V(a) -V(b)=Positive if q=PositiveIf two spheres are connected by a wire, charges will flow from inner sphere to outer sphere as V(a) >V(b) irrespective of magnitude of charges.

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