Force field (physics)

Plot of a two-dimensional slice of the gravitational potential in and around a uniform spherical body. The inflection points of the cross-section are at the surface of the body.

In physics a Force Field is a special kind of vector field that models the intensity of a non-contact force at various positions in space-time. The term appears to have been coined by Michael Faraday^[1].

Advantages and Restrictions

An important point to remember when employing force fields is that the vector field in question does not exist. It is a map of the vectors which would exist, were a particle in that location in that moment; this kind of mathematical tool is called a Kuhnian construct. The force field is linked inseparably from the lines of force one object exerts on another object or a collection of other objects. The force field is simple to collection of many of these lines in one location.

Examples of force fields

A local Newtonian gravitational field near Earth ground typically consists of a uniform array of vectors pointing in one direction---downwards, towards the ground; its force field is represented by the Cartesian vector ${\vec {F}}=m\cdot g(-{\hat {z}})$ , where ${\hat {z}}$ points in a direction away from the ground, and m refers to the mass, and g refers to the acceleration due to gravity.
A global Gravitational field consists of a spherical array of vectors pointing towards the center of gravity. Its classical force field, in spherical coordinates, is represented by the vector, ${\vec {F}}={\frac {GmM}{r^{2}}}(-{\hat {r}})$ , which is just Newton's Law of Gravity, with the radial unit ${\hat {r}}$ vector pointing towards the origin of the sphere (center of the Earth).
A conservative Electric field has an electric charge (or a smeared plum pudding of electric charges) as its source object. In the case of the point charges, the force field is represented by ${\vec {F}}={\frac {kqQ}{r^{2}}}(-{\vec {R}})$ , where ${\vec {R}}$ is the position vector that represents the straightest line between the source charge and the other charge.
A static Magnetic field has a magnetic charge (a magnetic monopole or a charge distribution).