The
absolute potential at a point is the work done against
electric forces in carrying a unit positive test-charge from
infinity to that point. Hnece the absolute potential at a point
B is the difference in potential from
A = ∞ to
B.
Consider a point charge q in vacuum and a point P at a distance r from the point charge. The absolute potential at P due to the charge q is:
V = k · q / r
where k = 8.99 · 1092 / C2 is the Coulomb constant. The absolute potential at infinity (at r = ∞) is zero.
Becuase of the superposition principle and the scalar nature of potential difference, the absolute potential at a point due to a number of point charges is:
V = k · Σ qi / ri
where the ri are the distances of the charges qi from the point in question. Negative q's contribuet negative terms to the potential, while positive q's contribute positive terms.
The absolute potential due to a uniformly charged sphere, at points outside the sphere or on its surface is V = kq / r, where q is the charge on the sphere. THis potential is the same as that due to a point charge q placed at the position of the sphere's center.