A conducting sphere with radius R is charged until the magnitude of the electric field just outside its surface is E. The electric potential of the sphere, relative to the potential for away, is:

Question

Quizplus · Accepted Answer

Since the sphere is a conductor, its electric potential is constant throughout its surface. Therefore, the potential difference between the surface and infinity is equal to the work required to move a unit charge from infinity to the surface, which is equal to the electric potential. The work done is given by W = ∫E•ds, where E is the electric field just outside the surface and ds is the displacement from infinity to the surface. Since the electric field is constant, we have E•ds = E(R-∞) = ER. Therefore, the electric potential of the sphere relative to infinity is ER.

A Conducting Sphere with Radius R Is Charged Until the Magnitude