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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 mechanicsClassical mechanics is a model of the physics of forces acting upon bodies. It is often referred to as Newtonian mechanics after Newton and his laws of motion. Classical mechanics is subdivided into statics (which models objects at rest), kinematics (whic, 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 electromagnetismElectromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. The electric field is produced by stationary electric charges, and gives rise to the electric force, t, the electric fieldIn physics, an electric field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. Definition and derivation The mathematical definition of the electric field is developed as follows. Coulomb's law gives the (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 VoltThe volt is the SI derived unit for electric potential and voltage (derived from the ampere and watt). It is named in honor of Alessandro Volta, who, in 1800, invented the voltaic pile, the first chemical battery. The volt is defined as the potential diffs, provides a simple way to analyze electric circuitAn electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. It can be as small as an integrated circuit on a silicon chip, or as large as an els 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 forceAn electromotive force ( emf is the "force", measured in volts, that is produced by interaction between a current and a magnetic field, at least one of which is changing. Since the word " force" now has a very specific meaning in physics, and an emf is no (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.
