Electric potential inside an insulating sphere

In summary, the conversation discusses the calculation of electric potential using integration of the electric field from different reference points. The reference point can be chosen arbitrarily, with infinity being a convenient choice as it results in a 0 potential reference point where there is no charge. Integrating from a different reference point, such as the center of a sphere, would result in a different constant but would still yield the correct answer. There may be a small problem at r=0, but this depends on the type of charge being considered.
  • #1
UMath1
361
9
In the example my textbook has, the electric potential is calculating by integrating the electric field from infinity to R, radius of sphere, and then integrating the electric field from R to r, radius of point inside sphere. What I don't understand is why is the field integrated from infinity to r, why not 0 to r? How do you decide on the reference point? In an uniform electric field, the potential is calculated by integrating from to 0 to r.
 
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  • #2
The integration is alwaysstarting from your reference (0 potential) location.
 
  • #3
All kinds of potential have an arbitrary zero point, which is essentially a constant of integration. Infinity is just a handy choice of a zero point. Since the field of a charge drops off to 0 at infinity, setting a reference point at infinity is like setting a 0 potential reference point where there is no charge at all.
 
  • #4
What about if you integrated the field from r=0 to r=R, radius of sphere? Why would that ot give you the right answer? Conceptually what is the difference in value?
 
  • #5
You could certainly do that. The result would differ by a constant from the usual formula, which is fine. It would simply mean that you are taking the center as your reference instead of infinity.
 
  • #6
You might find a small problem at r=0.
 
  • #7
So it's just that integrating from infinity is more convenient as the voltage at infinity would be zero, correct?
 
  • #8
Yup
 
  • #9
Khashishi said:
You might find a small problem at r=0.
I think that he is considering a sphere of charge, not a point charge. So there shouldn't be a problem at r=0.
 

1. What is electric potential inside an insulating sphere?

Electric potential inside an insulating sphere is the measure of the electric potential energy per unit charge at any point inside the sphere. It is a scalar quantity that represents the potential difference between two points in the sphere.

2. How is the electric potential inside an insulating sphere calculated?

The electric potential inside an insulating sphere can be calculated using the formula V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere.

3. Does the electric potential inside an insulating sphere vary at different points?

Yes, the electric potential inside an insulating sphere varies at different points. The potential is highest at the center of the sphere and decreases as you move towards the surface. It is zero at the surface of the sphere.

4. How does the charge of the sphere affect the electric potential inside it?

The charge of the sphere directly affects the electric potential inside it. As the charge increases, the potential also increases. This is because the electric potential is directly proportional to the charge of the sphere.

5. Can the electric potential inside an insulating sphere be negative?

Yes, the electric potential inside an insulating sphere can be negative. This happens when the sphere has a negative charge, which causes the potential to be negative. However, the potential is always measured relative to a reference point, so it is possible for the potential to be positive or negative depending on the chosen reference point.

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