Electric Potential of three concentric spheres

In summary, the conversation discusses the problem of finding potential at points A and B in a system of three concentric conducting spheres with charges q1, q2, and q3 placed on their respective surfaces. The textbook provides a solution that considers only the three spheres, while the individual discussing the problem believes the potential should be constant inside the spheres and equal to the potential at the outer surface of sphere C. It is unclear why the textbook's solution is valid and where the individual's understanding may be incorrect.
  • #1
emailanmol
296
0
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 textbook 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 textbooks solution right?

Where am I going wrong?


If the textbook's solution is right, then isn't the potential not constant inside the sphere C, implying a non-zero electric field
 
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  • #2
emailanmol said:
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 textbook 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 textbooks solution right?

Where am I going wrong?

If the textbook'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.
 
  • #3
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.
 

FAQ: Electric Potential of three concentric spheres

1. What is the concept of Electric Potential?

Electric Potential is the amount of electric potential energy per unit charge at a specific point in an electric field.

2. How is Electric Potential measured?

Electric Potential is measured in units of volts (V).

3. What is the formula for calculating Electric Potential?

The formula for calculating Electric Potential is V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge, and r is the distance between the two charges.

4. How does the Electric Potential of three concentric spheres differ from that of two concentric spheres?

In the case of three concentric spheres, the electric potential will depend on the distance from the center of the innermost sphere, as well as the charges on all three spheres. In contrast, for two concentric spheres, the electric potential will only depend on the distance from the center of the innermost sphere and the charges on the two spheres.

5. Can the Electric Potential of three concentric spheres be negative?

Yes, the Electric Potential of three concentric spheres can be negative if the charges on the spheres are of opposite signs and the distance from the center of the innermost sphere is large enough.

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