In Fig. 23-50, a solid sphere of radius a = 2.00 cm is concentric with a spherical conducting shell of
inner radius b = 2.00a and outer radius c = 2.40a. The sphere has a net uniform charge q1 = +5.00 fC; the shell has a net charge q2 = -q1' What is the magnitude of the electric field at radial distances (a) r = 0, (b) r = aI2.00, (c) r = a, (d) r = 1.50a, (e) r = 2.30a, and (f) r = 3.50a? What is the net charge on the (g) inner and (h) outer surface of the shell?
This is my attempt, i am confused at some points
a. r = 0; The Electric field is 0
b. At r = a/2.00; I verified the answer and it is non zero, but my understanding is that the net charge should be on the surface of the conductor. Hence the charge q1=5*10^-15 C, should go to the surface of the solid sphere. Hence the net charge below "a" should be 0 and the E field should be "0". But why is that the charge does not move to the surface?
If the answer is non zero, then i did the following calculation,
the charge is proportional to the volume hence
q' = q *r^3/R^3;
E= q'/(4πεο*r^2); => E = q*r/(4πεο*R^3); => E = (5*10^-15*9*10^9*a)/(2*a^3)
E= 45*10^-6/(2*4*10^-4) = 5.625*10^-2;
c. and d was easy.
E = q/(4πεο*r^2); r = a for c, r =1.5a for d;
e. r = 2.30a this is the area between the conducting shell, the charge on the inner shell is q2 = -q1. At this r, the net charge is 0 q2+q1=0; E=0;
f. r = 3.50a ; E=0 since the net charge is 0.
g. inner q2 = -q1
h. outer 0.
But my additional thinking let us say that q2 = -2q1;
then on the inner shell the charge will be q2 = -q1 since it has to compensate the solid sphere charge. The remaining charge of -q1 will be on the outer shell. Am I correct? Please advise.