# I Electric potential inside an insulating sphere

1. Mar 22, 2016

### UMath1

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.

2. Mar 22, 2016

### Staff: Mentor

The integration is alwaysstarting from your reference (0 potential) location.

3. Mar 22, 2016

### Khashishi

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. Mar 22, 2016

### UMath1

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. Mar 23, 2016

### Staff: Mentor

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. Mar 23, 2016

### Khashishi

You might find a small problem at r=0.

7. Mar 23, 2016

### UMath1

So it's just that integrating from infinity is more convenient as the voltage at infinity would be zero, correct?

8. Mar 23, 2016

### Khashishi

Yup

9. Mar 23, 2016

### Staff: Mentor

I think that he is considering a sphere of charge, not a point charge. So there shouldn't be a problem at r=0.