Potenziale

Potenziale is a term used in physics and mathematics to denote a field from which forces or energies can be derived. In its broad sense, a potential function assigns a scalar (or vector) value to every point in space, such that the physical force acting on a particle is the negative gradient of that function. This makes many forces conservative: the work done moving a particle between two points depends only on the endpoints, not on the path taken.

In physics, several standard potentials are used. Electric potential, V, is defined so that the electric field equals the negative gradient of V (E = -∇V). The potential difference between two points equals the work done per unit charge to move a test charge between those points. Gravitational potential, Φ, is the potential per unit mass, with the gravitational field g = -∇Φ and the potential energy U = mΦ for a mass m. The concept of potential is extended by the magnetic vector potential, A, from which the magnetic field is obtained as B = ∇×A; in electromagnetism, E and B can be expressed in terms of both scalar and vector potentials, subject to gauge freedom.

In mathematics, potential theory studies harmonic and subharmonic functions, governed by equations like Laplace’s equation ∇^2φ = 0 and Poisson’s equation ∇^2φ = -ρ/ε0. The Newtonian potential, proportional to 1/|x| in three dimensions, plays a central role in field theories.

Applications span classical mechanics, fluid dynamics (velocity potentials for irrotational flows), electromagnetism, quantum mechanics (potential energy in the Schrödinger equation), and various areas of analysis. The concept of Potenziale thus provides a unifying framework for describing how forces emerge from underlying fields.