Definition:Scalar Field (Physics)

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

Definition

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.

Examples

Temperature Distribution

The distribution of temperature throughout a body is an example of a scalar field.

Density

The (mass) density of a body is an example of a scalar field.

Electric Charge Density

The electric charge density within a region of space is an example of a scalar field.

Electric Potential

The electric potential within a region of space is an example of a scalar field.

Also see

• Results about scalar 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
• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.3$ Electric Fields in Matter: $1.3.1$ The atomic charge density
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): field: 2. (field of force, force field)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): field: 2. (field of force, force field)