Voltage of a charged conducting sphere

[maccha]

I've recently learned that the voltage of a charged conduction sphere remains constant inside the sphere all the way to the surface, as the electric field inside is zero. What I don't understand is how the voltage can be the same on the surface as it is inside- since there is an electric field on the surface, wouldn't the potential change?

 

[collinsmark]

I've recently learned that the voltage of a charged conduction sphere remains constant inside the sphere all the way to the surface, as the electric field inside is zero. What I don't understand is how the voltage can be the same on the surface as it is inside- since there is an electric field on the surface, wouldn't the potential change?

As you increase r to the surface, the potential does change, but infinitesimally with any infinitesimal increase in r. The electric field can change dramatically, as you have pointed out. But you need to integrate E to get V.

If it helps, let me pose you this question. Consider a step function where y jumps straight up from 0 to 1 at x = 10. What's the area under the curve from x = 0 to x = 9.999999? What's the area under the curve from x = 0 to x = 10.0001?