Electric potential inside an insulating sphere

[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.

 

[Dale]

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

 

[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.

 

[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?

 

[Dale]

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.

 

[Khashishi]

You might find a small problem at r=0.

 

[UMath1]

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

 

[Khashishi]

Yup

 

[Dale]

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.