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Suppose there are three concentric conducting spheres A,B,C having radius a,b,c (a<b<c).

We put charge q1, q2 and q3 on these three surfaces A,B,C respectively.

Now using gauss law, we can prove that

Charge on inner surface of A is 0

Charge on outer surface of A is q1.

Charge on inner surface of B is -q1

Charge on outer surface of B is q2+q1

Charge on inner surface of C is -q2-q1

Charge on outer surface of C is q1+q2+q3.

Now this is because electric field and therefore flux inside a conductor should be 0.

Now my text book asks me to find the Potential at A and B (considering potential at infinity is 0)

Now what I wanted to do is that since the field inside the conductor is 0 everywhere, the potential should be constant everywhere inside and therefore be equal to the potential at surface C

which is

k(q1+q2+q3)/c.

So this should be potential at A and B

However in the answer the potential at B is given as

k[q1/b +q2/b+q3/c]

And at A is given as k(q1/a+q2/b+q3/c).

i.e they have now considered the three sphere alone in calculating potential.

Is the text books solution right?

Where am I going wrong?

If the text book's solution is right, then isn't the potential not constant inside the sphere C, implying a non-zero electric field