Math 2.0

Real functions Concept

Scalar potential

Builds on Gradient

Summary

A scalar potential of a vector field is a scalar function whose gradient is the field, or minus the field in the physics convention. A field has a scalar potential exactly when it is conservative.

Reading path

To understand this page from the ground up, read these 8 pages in order. The foundations come first.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptTotal derivative, concept, no evidence levelTotal derivativeconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptDifferentiable function of several variables, concept, no evidence levelDifferentiable functi…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptGradient, concept, no evidence levelGradientconceptScalar potential, concept, no evidence levelScalar potentialconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Total derivative concept
  4. Function of several variables concept
  5. Differentiable function of several variables concept
  6. Partial derivative concept
  7. Gradient concept
  8. Scalar potential concept

Where this leads

1 page builds on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Scalar_potential, lead section
About this page
Tag0H7C3T1GJY
URIm2://0H7C3T1GJY
Aliasespotential-function
Kindconcept
WritingW1 stated
MSC26B12
UsesGradient
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