Definition:Field (Physics)

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.

Also see

• Results about fields in the context of physics can be found here.

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
• 1976: Ralph J. Smith: Circuits, Devices and Systems (3rd ed.) ... (previous) ... (next): Chapter $1$: Electrical Quantities: Introduction: Forces and Fields