Electric potential
Electric potential | ||
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SI unit volt | | |
Other units | statvolt | |
In SI base units | V = kg⋅m2⋅s−3⋅A−1 | |
Extensive? | yes | |
Dimension | M L2 T−3 I−1 |
Articles about |
Electromagnetism |
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Electric potential (also called the electric field potential, potential drop, the electrostatic potential) is defined as the amount of
In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ,[1] equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured in coulombs). By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself. In short, an electric potential is the electric potential energy per unit charge.
This value can be calculated in either a static (time-invariant) or a dynamic (time-varying) electric field at a specific time with the unit joules per coulomb (J⋅C−1) or volt (V). The electric potential at infinity is assumed to be zero.
In
Practically, the electric potential is a
Introduction
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 a gravitational field and an electric field (in the absence of time-varying magnetic fields). Such fields affect objects because of the intrinsic properties (e.g., mass or charge) and positions of the objects.
An object may possess a property known as
The magnitude of force is given by the quantity of the charge multiplied by the magnitude of the electric field vector,
Electrostatics
An electric potential at a point r in a static electric field E is given by the line integral
where C is an arbitrary path from some fixed reference point to r; it is uniquely determined up to a constant that is added or subtracted from the integral. In electrostatics, the
This states that the electric field points "downhill" towards lower voltages. By Gauss's law, the potential can also be found to satisfy Poisson's equation:
where ρ is the total charge density and denotes the divergence.
The concept of electric potential is closely linked with
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 , i.e., in the case of a non-conservative electric field (caused by a changing magnetic field; see Maxwell's equations). The generalization of electric potential to this case is described in the section § Generalization to electrodynamics.
Electric potential due to a point charge
The electric potential arising from a point charge, Q, at a distance, r, from the location of Q is observed to be
The electric potential at any location, r, in a system of point charges is equal to the sum of the individual electric potentials due to every point charge in the system. This fact simplifies calculations significantly, because addition of potential (scalar) fields is much easier than addition of the electric (vector) fields. Specifically, the potential of a set of discrete point charges qi at points ri becomes
where
- r is a point at which the potential is evaluated;
- ri is a point at which there is a nonzero charge; and
- qi is the charge at the point ri.
And the potential of a continuous charge distribution ρ(r) becomes
where
- r is a point at which the potential is evaluated;
- R is a region containing all the points at which the charge density is nonzero;
- r' is a point inside R; and
- ρ(r') is the charge density at the point r'.
The equations given above for the electric potential (and all the equations used here) are in the forms required by
Generalization to electrodynamics
When time-varying magnetic fields are present (which is true whenever there are time-varying electric fields and vice versa), it is not possible to describe the electric field simply as a scalar potential V because the electric field is no longer conservative: is path-dependent because (due to the
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
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,
Gauge freedom
The electrostatic potential could have any constant added to it without affecting the electric field. In electrodynamics, the electric potential has infinitely many degrees of freedom. For any (possibly time-varying or space-varying) scalar field, 𝜓, we can perform the following
Given different choices of gauge, the electric potential could have quite different properties. In the
just like in electrostatics. However, in the Lorenz gauge, the electric potential is a retarded potential that propagates at the speed of light and is the solution to an inhomogeneous wave equation:
Units
The SI derived unit of electric potential is the volt (in honor of Alessandro Volta), denoted as V, which is why the electric potential difference between two points in space is known as a voltage. Older units are rarely used today. Variants of the centimetre–gram–second system of units included a number of different units for electric potential, including the abvolt and the statvolt.
Galvani potential versus electrochemical potential
Inside metals (and other solids and liquids), 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 the potential difference corrected for the different atomic environments.[6] The quantity measured by a voltmeter is called electrochemical potential or fermi level, while the pure unadjusted electric potential, V, is sometimes called the Galvani potential, ϕ. The terms "voltage" and "electric potential" are a bit ambiguous but one may refer to either of these in different contexts.
See also
References
- ISBN 0201025108.
- ISBN 978-81-203-1601-0.
- ^ Young, Hugh A.; Freedman, Roger D. (2012). Sears and Zemansky's University Physics with Modern Physics (13th ed.). Boston: Addison-Wesley. p. 754.
- ^ "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ISBN 013805326X.
- ISBN 978-0-471-70058-6.
Further reading
- Politzer P, Truhlar DG (1981). Chemical Applications of Atomic and Molecular Electrostatic Potentials: Reactivity, Structure, Scattering, and Energetics of Organic, Inorganic, and Biological Systems. Boston, MA: Springer US. ISBN 978-1-4757-9634-6.
- Sen K, Murray JS (1996). Molecular Electrostatic Potentials: Concepts and Applications. Amsterdam: Elsevier. ISBN 978-0-444-82353-3.
- Griffiths DJ (1999). Introduction to Electrodynamics (3rd. ed.). Prentice Hall. ISBN 0-13-805326-X.
- Jackson JD (1999). Classical Electrodynamics (3rd. ed.). USA: John Wiley & Sons, Inc. ISBN 978-0-471-30932-1.
- Wangsness RK (1986). Electromagnetic Fields (2nd., Revised, illustrated ed.). Wiley. ISBN 978-0-471-81186-2.