(redirected from potentiality)
Also found in: Dictionary, Thesaurus, Medical, Legal, Wikipedia.


A function or set of functions of position in space, from whose first derivatives a vector can be formed, such as that of a static field intensity.



in the broad sense, the means, reserves, and sources that are available and capable of being mobilized, set in action, or used to attain a certain goal, carry out a plan, or solve some problem; the possibilities open to an individual, society, or state in a field, for example, economic potential or production potential.



(also potential function), a concept characteristic of a broad class of physical force fields, such as electric and gravitational fields, and, in general, fields of any physical quantities representable by vectors, such as the velocity field in a fluid. For an electrostatic field, the potential is introduced as an auxiliary function whose spatial derivatives are the components of the electric field intensity at a given point. In hydrodynamics, they are the components of the velocity at a given point. In many cases, the potential also has another important physical meaning. Thus, in an electrostatic field it is numerically equal to the negative of the energy necessary to remove a unit positive charge from a given point to infinity.

In the general case of the potential of a vector field a(x, y, z), there is a scalar function u(x, y, z) such that a = grad u; that is, ax = ∂u/∂x, ay = ∂u/∂y, and az = ∂u/∂z, where ax, ay, and az are the components of field a in the Cartesian coordinate system Oxyz. If such a function can be introduced, then vector field a is called a potential field. In electrostatics, the potential can also be designated by the function U = — u. The potential of a vector field a is not determined unambiguously but only to the accuracy offactor. Therefore, only differences in potential between various points in the field are of interest in the study of a potential field. Geometrically, the equation u(x, y, z) = c represents a surface at all points of which the potential has the same value. Such surfaces are called equipotential surfaces.

For a gravitational field formed by a point mass m placed at point A(ξ, η, ξ), the potential, here called the Newtonian potential, at point P(x, y, z) has the form

(1) u(x, y, z) = Gm/r

where Potential and G is the gravitational constant. When fields are superposed on one another, their potentials are algebraically added. If a gravitational field is set up by some mass of density p(ξ, η, ξ) occupying a volume T, then it may be considered as a result of the superposition of the elementary fields formed by infinitesimally small bodies of mass ρdξdηdξ. The Newtonian potential of such a field is given by the integral

The potential u(x, y, z), together with its partial derivatives of the first order, is a continuous function throughout all space. Outside the body of volume T, the function u(x, y, z) satisfies the Laplace equation and, within the body, the Poisson equation.

If the attracting masses are distributed with a density psur over a surface S as a single layer, then the potential of the field formed by them is given by the integral

The potential of the single layer v(x, y, z) is a continuous function throughout all space outside of S. When the surface S is crossed, however, the normal derivative of the function v(x, y, z) experiences a discontinuity equal to 4πG/psur. By bringing together without limit two surfaces on which single layers with densities ρsur and —ρsur are located and by simultaneously increasing psur to infinity in such a way that the limit is lim npsur = μ, where η is the perpendicular distance between the surfaces, we reach the concept of the potential of a double layer:

The potential of the double layer w(x, y, z) is a continuous function throughout all space outside of S. When the surface S is crossed, the function w(x, y, z) experiences a discontinuity, which is equal to 4πμ. The functions v(x, y, z) and w(x, y, z) both satisfy the Laplace equation.

If a body of volume T is an infinite cylinder of cross section D and if the density ρ of the matter in the cylinder is constant along every line parallel to the generatrices of the cylinder, then equation (2) leads to the concept of the logarithmic potential:

(5) u(x,y) = G ∫∫D ρ In (1/r) ds

Any harmonic function can be represented as the sum of the potentials of a single and double layer; this helps to explain the importance attached to potential theory.


Giunter, N. M. Teorii apotentsiala i eeprimenenie k osnovnym zadacham matematicheskoi fiziki. Moscow, 1953.
Sretenskii, L. N. Teorii n’iutonovskogo potentsiala. Moscow-Leningrad, 1946.
Tamm, I. E. Osnovy teorii elektrichestva, 7th ed. Moscow, 1957.
Idel’son, N. I. Teoriia potentsiala s prilozheniiami k teorii figury Zemli i geofizike, 2nd ed. Leningrad-Moscow, 1936.


References in periodicals archive ?
Proponents of this account claim that practices of development no longer aim to give hope to the poor--to tackle their perceived 'absence of aspiration' (Galbraith, 1979: 61-62, quoted in Pupavac, 2005: 165)--but to contain what is perceived as an inherent potentiality (Duffield, 2005: 152), withholding them from the political and transformative experience taken to characterise hope (Evans and Reid, 2014: 195).
Latency and accuracy were analyzed by means of repeated measures ANOVAs including the factors Potentiality (real vs.
For the first half of After Live, Sack's vehicle for examining potentiality is the figure of Herman Melville's "Bartleby, the Scrivener.
A generic conceptualization of potentiality explains how a child is able to grow up to be a particular type of person with a particular role in society (a statesman for example).
Once I have explained the scientific image, I will use it to describe spirit as our wave of potentiality and probability and body as our actualization of that potential.
Weak utopianism is the experience of the potentiality of utopianism without the command to make this utopianism a determinate, materialized form or shape.
Utilizing Debord and Warburg, Murray considers that cinema in particular is able to disrupt the smooth narratives of history and reveal what is understood to be the potentiality of gesture.
In chapters 2-7, the concept of potentiality leads first to a study of several student writers, then to a discussion of William Butler Yeats.
Each of the four chapters relates potentiality to questions emerging from a specific topic.
For men who work in the diving industry, I really think there is a high potentiality for problems there," she said.
And his national scale research, written up in the book Toward a Democratic Left, suggested through a very sophisticated design and empirical assemblage, the structure of real political potentiality and the immense work required for its actualization in electoral politics.