Citation:
A scalar field is a mathematical function that assigns only a scalar value (magnitude) to each point in space, without specifying any direction. It describes quantities like temperature or pressure.
In contrast to a scalar field, which only assigns magnitudes, a vector field assigns both magnitude and direction to each point in space.
Gradient: The gradient of a scalar field measures how rapidly the scalar quantity changes from one point to another.
Potential energy can be described using scalar fields. It represents stored energy that depends on position or configuration.