A small sphere of radius a carrying a positive charge q, is placed concentrically inside a larger hollow conducting shell - Physics - Electrostatic Potential And Capacitance

Question

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?)

Jyoti Pant · Accepted Answer

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,14π∈0 QbThe electric potential on the inner sphere due to q is14π∈0 qaThus, the total potential on the inner sphere will be given by,14π∈0 qa+14π∈0 QbThe electric potential on the outer sphere due to charge q is14π∈0 qbTherefore total potential on the outer sphere=14π∈0 qb+14π∈0 QbAnd so,V(a) -V(b)=14π∈0[qa-qb]=q4π∈0[1a-1b] Since aV(b) irrespective of magnitude of charges