# Definition:Field (Physics)

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*This page is about Field in the context of Physics. For other uses, see Field.*

## Definition

A **field**, in the context of physics, is a region of space which is acted on by a point-function.

That is, in which a physical quantity is associated with every point of spacetime.

The physical quantity in question may be either in vector or scalar form.

## Scalar Field

Let $F$ be a field which acts on a region of space $S$.

Let the point-function giving rise to $F$ be a scalar quantity.

Then $F$ is a **scalar field**.

## Vector Field

Let $F$ be a field which acts on a region of space $S$.

Let the point-function giving rise to $F$ be a vector quantity.

Then $F$ is a **vector field**.

## Sources

- 1951: B. Hague:
*An Introduction to Vector Analysis*(5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $5$. Scalar and Vector Fields