Vector Force Field

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. A vector field defines a direction at all points in space; a field line for that vector field may be constructed by tracing a topographic path in the direction of the vector field. More precisely, the tangent line to the path at each point is required to be parallel to the vector field at that point. A complete description of the geometry of all the field lines of a vector field is sufficient to completely specify the direction of the vector field everywhere. In order to also depict the magnitude, a selection of field lines is drawn such that the density of field lines (number of field lines per unit perpendicular area) at any location is proportional to the magnitude of the vector field at that point. As a result of the divergence theorem, field lines start at sources and end at sinks of the vector field. (A "source" is wherever the divergence of the vector field is positive, a "sink" is wherever it is negative.) In physics, drawings of field lines are mainly useful in cases where the sources and sinks, if any, have a physical meaning, as opposed to e.g. the case of a force field of a radial harmonic oscillator.

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 ,

where points in a direction away from the ground, and m refers to the mass, and g refers to the acceleration due to gravity.