Electric Potential: Solving for Center of Sphere

[collegeconfid]

Homework Statement

What is the electric potential at the center of a uniformly charged sphere?

Homework Equations

Ed=-V

The Attempt at a Solution

Integrate from infinity to the center of the sphere and be sure to account for the changing electric potential. I was told that the answer might be zero, but I believe that that is not right. So, am I right?

 

[xcvxcvvc]

Homework Statement

What is the electric potential at the center of a uniformly charged sphere?

Homework Equations

Ed=-V

The Attempt at a Solution

Integrate from infinity to the center of the sphere and be sure to account for the changing electric potential. I was told that the answer might be zero, but I believe that that is not right. So, am I right?

The answer is not zero, so you're right about that. Think about it this way: what if instead of a sphere of continual charge, you had billions of little, positive point charges in the shape of a sphere. You could calculate the voltage of each one and sum them together to get the total voltage at that point. Well, voltage for a positive charge is always positive and never zero. Therefore, all the point charges would always add and never subtract from the voltage at some point p inside the sphere.

By the way, you know that voltage is the -integral of electric field dx. You also know form Gauss that that sphere of charge up until the surface behaves like a point charge. You also know that the electric field within a conducting sphere is zero. So your voltage calculation is the same as that of a point charge up until r = R (where R is the radius of the sphere) and then the voltage stops becoming bigger - it remains constant throughout the inside of the conductor. This makes sense since the E field is zero in there - it takes no work (no force) to move the charge around at a constant velocity(you needn't push or pull to prevent the electrical force from accelerating it)