Potential

potential

[pə′ten·chəl] (electricity) electric potential (physics) 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.

Potential

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.

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, a_x = ∂u/∂x, a_y = ∂u/∂y, and a_z = ∂u/∂z, where a_x, a_y, and a_z 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 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 p_sur 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/p_sur. By bringing together without limit two surfaces on which single layers with densities ρ_sur and —ρ_sur are located and by simultaneously increasing p_sur to infinity in such a way that the limit is lim np_sur = 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.

REFERENCES

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.

V. I. BITIUTSKOV

potential

[po-ten´shal] existing and ready for action, but not active.electric tension or pressure.action potential see action potential.after-potential the period following termination of the potential" >spike potential.auditory evoked potential in electroencephalography, changes in waves in response to sound; see also potential" >brainstem auditory evoked potential.brainstem auditory evoked potential that portion of the potential" >auditory evoked potential that comes from the brainstem; abnormalities can be analyzed to evaluate comas, to support diagnosis of multiple sclerosis, and to detect early posterior fossa tumors.cognitive event--related p's a diagnostic study that uses electroencephalographic equipment and a computer dedicated to analyze brain wave P300; this wave is a measure of the brain's active cognitive processing of information. The patient is instructed to complete a task that requires attention and information processing. A recording of brain wave activity as well as information related to cognitive function is produced.diastolic potential the transmembrane potential of the cell during electrical diastole" >diastole.maximal diastolic potential the most negative level attained during the cycle" >cardiac cycle by the cell membrane of a fiber that does not have a constant resting potential, occurring at the end of phase 3 of the action potential. In pacemaker cells this is a point of hyperpolarization.membrane potential the electric potential that exists on the two sides of a membrane or across the wall of a cell.resting potential (resting membrane potential) the difference in potential across the membrane of a cell when it is at rest, i.e., fully repolarized. In cardiac physiology this occurs during electrical diastole in pacemaker cells and continuously in nonpacemaker cells.spike potential the initial, very large change in potential of the membrane of an excitable cell during excitation.threshold potential the transmembrane potential that must be achieved before a membrane channel can open; it differs among the various cardiac membrane channels.potential (omaha) in the omaha system, a modifier" >problem modifier on the third level of the problem classification scheme, defined as the presence of health patterns, behaviors, or risk factors that may preclude optimal health even though specific signs and symptoms are absent.

po·ten·tial

(pō-tent'shăl), Avoid the redundant use of this adjective with a noun whose sense includes the notion of possibility, as potential danger and potential hazard.1. Capable of doing or being, although not yet in course of doing or being; possible, but not actual. 2. A state of tension in an electric source enabling it to do work under suitable conditions; in relation to electricity, potential is analogous to the temperature in relation to heat. [L. potentia, power, potency]

potential

Vox populi 1. The difference in electric charge between 2 points in a circuit, expressed in volts or mV. See Action potential, Evoked potential, Inhibitory post-synaptic potential, Late potential, Membrane potential, Spike potential, Ventricular late potential, Zeta potential.2. The inherent capacity to occur. See Biological hazard potential, Biopotential, Biotic potential, Chemical potential, Health potential, Maximum life-span potential.

po·ten·tial

(pŏ-ten'shăl) 1. Capable of doing or being, although not yet doing or being; possible, but not actual. 2. A state of tension in an electric source enabling it to do work under suitable conditions; in relation to electricity, potential is analogous to the temperature in relation to heat. [L. potentia, power, potency]

potential

The amount of energy required to transfer a unit of positive charge from one point in an electrical field to another (potential difference). It is typically measured in volts.
action potential The electric current generated in an axon of a nerve cell in response to a stimulus. The stimulus must be above a certain threshold value to have an effect. The sodium pump (or sodium/potassium pump) which transports most sodium ions outside the cell and potassium ions inside the cell ceases to function and the sodium ions rush in making the interior of the axon a positive voltage with respect to the outside. The voltage changes from about −70 mV to +40 mV and then falls rapidly back to the resting membrane potential as the sodium pump regains its effect. The whole process takes less than one millisecond and its amplitude is always the same (all or none law) for a given axon, whatever the magnitude of the stimulus. The action potential is followed by an inexcitable period called the refractory period, which usually lasts one or two milliseconds. The action potential travels as a wave in both directions from the point of stimulation and the speed is faster in myelinated than in unmyelinated nerve fibres. Syn. nerve impulse. See adaptation; Schwann cell; neuron; receptor potential; resting membrane potential; synapse.
dark potential of the eye See resting potential of the eye.
early receptor potential (ERP) This is an early rapid response that can be detected when the retina is stimulated with an intense flash of light, approximately 10⁶ times brighter than that required to elicit the ERG. It is completed within 1.5 ms and is followed by the a-wave of the ERG. It is primarily, in man, a cone-generated potential. See electroretinogram.
graded potential A depolarization or a hyperpolarization (e.g. in the photoreceptors) generated by a neuron in response to a stimulus. The amplitude of the response varies with the intensity of the stimulus. If the neuron becomes depolarized to threshold an action potential is triggered in its axon.
membrane potential See resting membrane potential.
oscillatory p's . (OP) Subwaves of low amplitude but high frequency (70-140 Hz) superimposed on the b-wave of the electroretinogram. The amplitude of these oscillatory responses is usually enhanced by a filtering technique. These potentials are presumed to originate from the vicinity of the inner plexiform layer of the retina (probably the amacrine cells) and may reflect disturbances of that part of the retina.
receptor potential Difference in potential occurring in a receptor in response to a stimulus. This is a graded type of response with an amplitude proportional to the intensity of the stimulus (graded potential). The photoreceptors and the bipolar cells produce a receptor potential but, surprisingly, it is a hyperpolarization, i.e. the inside of the membrane becomes more negative with respect to the outside. The ganglion cells respond with action potentials. See action potential; rhodopsin.
resting membrane potential Difference in direct current potential between the inside and outside of a living cell. The inside of the cell is usually about −70 mV compared to the outside, but this value depends on the quantity of potassium (mainly), sodium and chloride ions on both sides of the membrane, and the permeability to these ions of the membrane itself. Syn. membrane potential; transmembrane potential. See depolarization; hyperpolarization; action potential; tonus.
resting potential of the eye A direct current potential which exists between the anterior and posterior poles of the eye, the cornea being positive relative to the back of the eye. It is of the order of several mV in humans. This potential is used in recording the electrooculogram. Syn. dark potential of the eye; standing potential of the eye. See electrooculogram.
standing potential of the eye See resting potential of the eye.
standing potential See electrooculogram.
transmembrane potential See resting membrane potential.
visual evoked cortical potential (VECP) An electrical potential measured at the level of the occipital cortex in response to a light stimulation. Recording requires repetition of the stimulus and a computer synchronized with the onset of that stimulus, to average out the background noise produced by the spontaneous brain potentials (e.g. alpha, beta, delta, theta waves). This potential has clinical application and is used to objectively measure refraction, visual acuity, amblyopia, binocular anomalies and help in the diagnosis of some demyelinating diseases (e.g. multiple sclerosis), etc. Many abbreviations are also used, although they are not strictly correct. They are EP (evoked potential), VEP (visually evoked potential), VER (visual evoked response), and pVER (indicating that this potential is pattern-elicited). See objective accommodation; artifact; electrodiagnostic procedures.

po·ten·tial

(pŏ-ten'shăl) Capable of doing or being, although not yet in course of doing or being; possible, but not actual. [L. potentia, power, potency]

potential

po·ten·tial

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po•ten•tial

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potential formal date

realize (one's) potential

realize one's potential

Potential

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REFERENCES

potential

potential

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adj possible

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adj hidden

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noun ability

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adj capable of being but not yet in existence

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adj capable of favorable development

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noun the inherent capacity for growth or development

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noun the inherent capacity for coming into being

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noun the difference in electrical charge between two points in a circuit expressed in volts

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adj existing in possibility

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adj expected to become or be

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