# Definitions for scalar potentialscalar poten·tial

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1. Scalar potential

Scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity. A scalar potential is a fundamental concept in vector analysis and physics (the adjective scalar is frequently omitted if there is no danger of confusion with vector potential). The scalar potential is an example of a scalar field. Given a vector field F, the scalar potential P is defined such that: F = − ∇ P = − ( ∂ P ∂ x , ∂ P ∂ y , ∂ P ∂ z ) , {\displaystyle \mathbf {F} =-\nabla P=-\left({\frac {\partial P}{\partial x}},{\frac {\partial P}{\partial y}},{\frac {\partial P}{\partial z}}\right),} where ∇P is the gradient of P and the second part of the equation is minus the gradient for a function of the Cartesian coordinates x, y, z. In some cases, mathematicians may use a positive sign in front of the gradient to define the potential. Because of this definition of P in terms of the gradient, the direction of F at any point is the direction of the steepest decrease of P at that point, its magnitude is the rate of that decrease per unit length.

### Numerology

1. Chaldean Numerology

The numerical value of scalar potential in Chaldean Numerology is: 6

2. Pythagorean Numerology

The numerical value of scalar potential in Pythagorean Numerology is: 4

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"scalar potential." Definitions.net. STANDS4 LLC, 2021. Web. 28 Nov. 2021. <https://www.definitions.net/definition/scalar+potential>.

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##### diverge from the expected
• A. descant
• B. aberrate