Vector field
![A portion of the vector field (sin y, sin x)](/Images/godic/202502/19/VectorField.svg2434.png")
![Two representations of the same vector field: v(x, y) = −r. The arrows depict the field at discrete points, however, the field exists everywhere.](/Images/godic/202502/19/Radial_vector_field_sparse.svg2434.png")
![Dense vector field representation.](/Images/godic/202502/19/Radial_vector_field_dense.svg2434.png")
![A vector field on a sphere](/Images/godic/202502/19/Vector_sphere.svg2434.png")
In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane (for instance), can be visualised as: a collection of arrows with a given magnitude and direction, each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.