Electric Potential and Voltage

Every point in space near a charge has a potential, a number in volts that tells you how much potential energy each coulomb of charge would gain by being there. It's defined as V = PE/q, or built directly from a source charge as V = kq/r, where k = 8.99 x 10⁹ N m²/C^2. Potential is a property of the location and the source charge creating the field there. It exists whether or not you ever place a test charge at that point.

This is why the bird on the power line is fine. The wire sits at a high potential, maybe 10,000 volts above the ground, but the bird's two feet are both touching the same wire, at essentially the same potential. No potential difference means no energy hill between the bird's feet, so no current flows through the bird. Current and shock come from voltage differences, not from voltage itself. A lineman gets hurt by touching the wire and a grounded pole at the same time, because that creates a huge potential difference across his body.

Potential connects directly to potential energy through PE = qV: multiply the potential at a point by the charge you actually place there, and you get the energy that charge has. It connects to the electric field too, since field is what tells you how fast potential changes with distance. Unlike field and force, which are vectors, potential is a scalar, so potentials from multiple charges simply add, with sign, making problems with several charges far easier than vector field problems.