An electric potential is the amount of work needed to move a unit of charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point can be used. In classical electrostatics, the electrostatic field is a vector quantity which is expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ, equal to the electric potential energy of any charged particle at any location divided by the charge of that particle. By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself. In short, electric potential is the electric potential energy per unit charge. This value can be calculated in either a static or a dynamic electric field at a specific time in units of joules per coulomb, or volts. The electric potential at infinity is assumed to be zero. In electrodynamics, when time-varying fields are present, the electric field cannot be expressed only in terms of a scalar potential. Instead, the electric field can be expressed in terms of both the scalar electric potential and the magnetic vector potential. 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. Practically, electric potential is always a continuous function in space; Otherwise, the spatial derivative of it will yield a field with infinite magnitude, which is practically impossible. Even an idealized point charge has potential, which is continuous everywhere except the origin. The electric field is not continuous across an idealized surface charge, but it is not infinite at any point. Therefore, the electric potential is continuous across an idealized surface charge. An idealized linear charge has potential, which is continuous everywhere except on the linear charge.
Introduction
explores concepts such as force, energy, potential, etc. Force and potential energy are directly related. A net force acting on any object will cause it to accelerate. As an object moves in the direction in which the force accelerates it, its potential energy decreases. For example, the gravitational potential energy of a cannonball at the top of a hill is greater than at the base of the hill. As it rolls downhill its potential energy decreases, being translated to motion, kinetic energy. It is possible to define the potential of certain force fields so that the potential energy of an object in that field depends only on the position of the object with respect to the field. Two such force fields are the gravitational field and an electric field. Such fields must affect objects due to the intrinsic properties of the object and the position of the object. Objects may possess a property known as electric charge and an electric field exerts a force on charged objects. If the charged object has a positive charge the force will be in the direction of the electric field vector at that point while if the charge is negative the force will be in the opposite direction. The magnitude of the force is given by the quantity of the charge multiplied by the magnitude of the electric field vector.
Electrostatics
The electric potential at a point r in a static electric fieldE is given by the line integral where C is an arbitrary path connecting the point with zero potential to r. When the curl is zero, the line integral above does not depend on the specific path C chosen but only on its endpoints. In this case, the electric field is conservative and determined by the gradient of the potential: Then, by Gauss's law, the potential satisfies Poisson's equation: where ρ is the total charge density and ∇· denotes the divergence. The concept of electric potential is closely linked with potential energy. A test chargeq has an electric potential energy UE given by The potential energy and hence also the electric potential is only defined up to an additive constant: one must arbitrarily choose a position where the potential energy and the electric potential are zero. These equations cannot be used if the curl, i.e., in the case of a non-conservative electric field. The generalization of electric potential to this case is described below.
Electric potential due to a point charge
The electric potential arising from a point charge Q, at a distance r from the charge is observed to be where ε0 is the permittivity of vacuum. is known as the Coulomb potential. The electric potential for a system of point charges is equal to the sum of the point charges' individual potentials. This fact simplifies calculations significantly, because addition of potential fields is much easier than addition of the electric fields. Specifically, the potential of a set of discrete point charges qi at points ri becomes and the potential of a continuous charge distribution ρ becomes The equations given above for the electric potential are in the forms required by SI units. In some other systems of units, such as CGS-Gaussian, many of these equations would be altered.
Generalization to electrodynamics
When time-varying magnetic fields are present, it is not possible to describe the electric field simply in terms of a scalar potential V because the electric field is no longer conservative: is path-dependent because . Instead, one can still define a scalar potential by also including the magnetic vector potential A. In particular, A is defined to satisfy: where B is the magnetic field. Because the divergence of the magnetic field is always zero due to the absence of magnetic monopoles, such an A can always be found. Given this, the quantity is a conservative field by Faraday's law and one can therefore write where V is the scalar potential defined by the conservative field F. The electrostatic potential is simply the special case of this definition where A is time-invariant. On the other hand, for time-varying fields, unlike electrostatics.
Inside metals, the energy of an electron is affected not only by the electric potential, but also by the specific atomic environment that it is in. When a voltmeter is connected between two different types of metal, it measures not the electric potential difference, but instead the potential difference corrected for the different atomic environments. The quantity measured by a voltmeter is called electrochemical potential or fermi level, while the pure unadjusted electric potential V is sometimes called Galvani potential. The terms "voltage" and "electric potential" are a bit ambiguous in that, in practice, they can refer toeither of these in different contexts.
