In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space $${\displaystyle \mathbb {R} ^{n}}$$. A vector field on a plane can be visualized as a collection of … See more

Line integral
A common technique in physics is to integrate a vector field along a curve, also called determining its See more

Michael Faraday, in his concept of lines of force, emphasized that the field itself should be an object of study, which it has become throughout … See more

Replacing vectors by p-vectors (pth exterior power of vectors) yields p-vector fields; taking the dual space and exterior powers yields See more

Vector fields on subsets of Euclidean space
Given a subset S of R , a vector field is represented by a vector-valued function V: S → R in standard See more

• A vector field for the movement of air on Earth will associate for every point on the surface of the Earth a vector with the wind speed and direction for that point. This can be drawn using arrows to represent the wind; the length (magnitude) of the arrow will be an indication … See more

Consider the flow of a fluid through a region of space. At any given time, any point of the fluid has a particular velocity associated with it; thus there is a vector field associated to any flow. The converse is also true: it is possible to associate a flow to a vector … See more