# Vector Field Model

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A Vector Field Model is a field model that represents some field by using vector field functions.

**Context:**- It can range from being a 2D Vector Field, to being a 3D Vector Field to being a k-Dimensional Vector Field.
- It can range from being a Divergent Vector Field to being a Convergent Vector Field also to being a constant Vector Field.
- It can (often) be used to model a Physical Field (such as a magnetic field, gravity field or fluid flow field)

**Example(s):**- The flow of a fluid can be considered as a constant vector field. Mathematically the field can be represented as [math]\displaystyle{ V=i+j }[/math].Here [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math] are the unit vectors along x-axis and y-axis respectively. This is a constant vector field where each vector is of magnitude [math]\displaystyle{ \sqrt{2} }[/math] and direction [math]\displaystyle{ 45^o }[/math]angle with respect to x-axis.
- [math]\displaystyle{ \vec{V}(x,y) = xi+yj }[/math] is an example of a divergent vector field. In this vector field the vectors can have all possible magnitude and direction, pointing away from the origin.
- [math]\displaystyle{ \vec{V}(x,y) = -xi-yj }[/math] is an example of a convergent vector field. In this vector field the vectors can have all possible magnitude and direction, pointing towards the origin.
- [math]\displaystyle{ \vec{V}(x,y) = -yi+xj }[/math] such that [math]\displaystyle{ x^2 +y^2=1 }[/math] is an example of a rotational vector field. Here all the vectors are of unit magnitude and all possible direction but the starting point of a vector is the point on the circle [math]\displaystyle{ x^2 +y^2=1 }[/math].
- Gradient vector field to a surface is a vector field which consist of all the vectors normal to the surface.
- Velocity field. At ant instant the velocity vectors of a rotating body constitute a vector field, called velocity field of rotation.

**See:**Scalar Field, Tensor Field.