Electric Potential
Electric potential is the electric potential energy per unit charge at a point in an electric field, measured in volts, providing a scalar alternative to the vector electric field for describing electrostatic effects.
Curious
A 9-volt battery, a wall socket at 230 V, a static shock of thousands of volts — voltage (electric potential, or more precisely the potential difference between two points) is one of the most everyday physics quantities. Just as water flows from high ground to low ground, positive charge naturally tends to move from high potential to low potential, releasing energy as it goes — the basis of every battery-powered device.
Crucially, voltage measures energy per charge, not force — it tells you how much energy each coulomb of charge would gain or lose moving between two points, regardless of how much charge actually moves. This is why a shock from a 20,000 V static spark, despite the huge voltage, is usually harmless: very little actual charge moves, so very little total energy is transferred.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| V | Electric potential | volt (V) = J/C |
| U | Electric potential energy | joule (J) |
| q | Charge | coulomb (C) |
The relationship E = −dV/dx (in one dimension; more generally E = −∇V) shows that the electric field points in the direction of steepest decrease of potential — exactly analogous to how a ball rolls downhill in the direction of steepest decrease of gravitational potential energy. This is why the electric field is often more convenient to compute via the potential (a scalar) rather than directly, since scalar addition is far simpler than vector addition when combining contributions from multiple charges.
Worked example: A point charge of +2 µC creates a potential at a distance of 0.4 m. V = kQ/r = (8.99×10⁹)(2×10⁻⁶)/0.4 = 17,980/0.4 = 44,950 V ≈ 4.50 × 10⁴ V.
Deep Dive
The volt is named for Alessandro Volta, whose 1800 invention of the voltaic pile (the first true electric battery, made from alternating discs of zinc and copper separated by brine-soaked cloth) provided, for the first time, a steady and controllable source of electric current — a crucial practical advance that made systematic experimentation with circuits and electromagnetism possible.
Path independence: Electric potential is a well-defined scalar function of position specifically because the electrostatic field is conservative (∇×E = 0 in the static case, following from Faraday's law with no time-varying magnetic field). This guarantees that the work done moving a charge between two points is independent of the path taken — a property that fails once time-varying magnetic fields are present, where induced electric fields are no longer conservative and a single-valued potential can no longer be defined in the same simple way.
For a system of point charges, the total potential at any point is the scalar sum of each charge's individual contribution (V = kΣqᵢ/rᵢ), a considerably simpler calculation than vector-summing the electric field directly — one of the main practical reasons potential is used as an intermediate step in solving many electrostatics problems.
Concept Relationship Map
Requires: electric field, potential energy [PENDING FULL ENTRY]
Enables: capacitance, circuit analysis
Commonly confused with: electric field (related by E = −∇V, but not the same quantity) and current
Sources
- Volta, A. (1800). Philosophical Transactions of the Royal Society of London, 90, 403–431.
- Griffiths, D.J. (2017). Introduction to Electrodynamics, 4th ed. Cambridge University Press, Ch. 2.