# Electric Potential of three concentric spheres

Hey, i have a conceptual doubt.

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
Hey, i have a conceptual doubt.

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
The difficulty comes from what is meant by the word "inside". Inside refers to a location within the conducting material itself. It does not refer to every point interior to the outer surface of the sphere or spheres.

I assume that these conducting spheres are spherical shells which have a very small thickness, a thickness so small that it may be ignored when compared to the radius of each spherical shell. However, to be a physically feasible problem, the spheres must truly have a finite thickness.

No.The figure clearly shows these are three concentric solid conducting spheres.(not shells). That is all three are virtually in contact.

I in fact fail to get why there would be any charge on sphere A and B.It should all move to the surface C and reside there.

However, those are the exact lines stated in my book.

I think it's wrong.