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In physics, a potential is a scalar quantity that can be used to analyze the effects of complicated vectorial forces and similar quantities by means of simple conservation laws. The most common examples are forms of potential energy (and the related case of electrical potential). Technically, it is a scalar field used to describe a conservative (curl-free) vector field V, such that the vector field is the gradient of the potential (possibly multiplied by a constant).
A related concept is that of a vector potential: a vector field describing a divergence free vector field (having only "closed" field lines) that is its curl. The most common example is the magnetic vector potential A, where the magnetic field B is ∇ × A.
Because the physically observable field is a spatial derivative of its potential, adding an arbitrary constant field to it—a gauge transformation—will not change anything in the physics of a system. This is an example of the general concept of gauge invariance.
In quantum theory, gauge invariance leads to Aharonov-Bohm effects where an effect of a potential is observable even in regions where the corresponding classical field is zero.
In classical mechanics, the force generated by the field is -1 times the gradient of the potential energy (so that the system is pushed towards a lower-energy configuration).
In electromagnetism, the electric field (a force per unit charge) is -1 times the gradient of the electric (scalar) potential (an energy per unit charge), closely related to the classical mechanics usage. This electric potential, typically measured in Volts, provides a simple way to analyze electric circuits without requiring detailed knowledge of the circuit shape or the fields within it. This potential is also generalized for the case of circuits with inductance, handling the case of non-conservative electric fields (which occur when there is a time-varying magnetic flux), by including an effective potential difference equal to the integral of electric field around the closed circuit (zero for a conservative field). In such cases, this effective potential difference is sometimes confusingly called the electromotive force (emf), although it is not strictly a "force". Note also that the electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.
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