(a)
(i) Due to the presence of charge #+Q# at the center of conducting hollow sphere, there is an induced charge of opposite nature on the surface of the conductor nearer to the charge.
#:.# Charge on the inner surface of conducting hollow sphere #-Q#.
(ii) When a charge #-Q# is induced on the inner surface of the sphere, equal and opposite charge appears on the outer surface of the sphere#-#Law of Conservation of Charge.
(b)F rom Gauss's Law we have
#int_(Area)vecEcdot vec(dA)=Q_(enc)/epsilon_0#
Due to symmetry above equation becomes
#vecE(4pir^2)=Q_(enc)/epsilon_0hatr#
#=>vecE=1/(4piepsilon_0)Q_(enc)/r^2hatr# .......(1)
Point #A#: Consider a Gaussian surface of radius #r_1# as a sphere having its center coinciding with the center of hollow sphere at #O#. Inserting charge enclosed by the Gaussian surface in (1) we get
#vecE_A=1/(4piepsilon_0)(+Q)/r_1^2hatr_1#
Point #B#: Consider a Gaussian surface of radius #r_2# as a sphere having its center coinciding with the center of hollow sphere at #O#. Inserting charge enclosed by the Gaussian surface in (1) we get
#vecE_B=0#
Point #C#: Consider a Gaussian surface of radius #r_3# as a sphere having its center coinciding with the center of hollow sphere at #O#. Inserting charge enclosed by the Gaussian surface in (1) we get
#vecE_C=1/(4piepsilon_0)(+Q)/r_3^2hatr_3#
