## Sscalar field – Summary

Sscalar field . The concept of scalar field dates from the 19th century and its application is oriented to the description of phenomena related to the distribution of temperatures within a body, the pressures inside fluids, the electrostatic potential, the potential energy in a gravitational system, population densities or of any magnitude the nature of which can approximate a continuous distribution.

## Summary

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• 1 in mathematics
• 2 Representation
• 4 Source

## In math

A scalar field associates a scalar value to each point in space. The value can be a mathematical number or a physical quantity. Scalar fields are often used in physics, in particular, to indicate temperature distribution across space, or air pressure.

Physically a scalar field represents the spatial distribution of a scalar magnitude.

Mathematically a scalar field is a scalar function of the coordinates whose physical representation is shown in Figure 1

The representations of these fields in a three-dimensional space require four dimensions, making it impossible to graph them in three dimensions, but they can be used as optimization tools for modeling cases where different variables intervene.

## Representation

Scalar fields are represented by the function that defines them or by equipotential lines or surfaces.

An equipotential surface or line is defined as the locus of points such that: Φ = cte On a relief map, for example, there is a scalar field corresponding to elevation above sea level as a function of the latitude and geographic longitude coordinates. This case corresponds to a scalar field defined in two mathematical dimensions.

In this case, the equipotential surfaces are called contour lines, and as it follows from the definition, all the points belonging to a contour line have the same elevation above sea level.