Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
A vector field is a mathematical function that assigns a vector to each point in space. It describes the direction and magnitude of a physical quantity at every point.
A scalar field is similar to a vector field, but it assigns only a scalar value (magnitude) to each point in space, without specifying any direction.
Gradient: The gradient of a scalar field measures how rapidly the scalar quantity changes from one point to another.
Flux: Flux is the flow rate of a vector field through an imaginary surface. It represents how much of the vector quantity passes through the surface per unit area.