Originally a term coined by Michael Faraday to provide an intuitive paradigm, but theoretical construct (in the Kuhnian sense), for the behavior of electromagnetic fields, the term force field refers to the lines of force one object (the "source object") exerts on another object or a collection of other objects. An object might be a mass particle or an electric or magnetic charge, for example. The lines do not have to be straight, in the Euclidean geometry case, but may be curved. Faraday called these theoretical connections between objects lines of force because the objects are most directly connected to the source object along this line. Michael Faraday, FRS (September 22, 1791 – August 25, 1867) was an English chemist and physicist (or natural philosopher, in the terminology of that time) who contributed significantly to the fields of electromagnetism and electrochemistry. ... Thomas Samuel Kuhn, philosopher and historian of science Alfred Kuhn, a social systems theorist Fritz Kuhn, German Green Party politician Fritz Kuhn, leader of the German-American Bund Richard Kuhn, winner of the Nobel Prize in Chemistry 1938 An Atlantic Island A French manufacterer of agricultural machinery, especially mowers and... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. ...

A conservative force field is a special kind of vector field that can be represented as the gradient of a potential. Conservatism is a political philosophy that generally favors free markets, traditional values and strong foreign defense. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ... Horizontal line (use sparingly)d grade for the grade or gradient of roads and other geographic features. ... It has been suggested that this article or section be merged with Scalar potential. ...

Note that a force field does not exist in reality, per se, but it is really a Kuhnian construct that allows scientists to visualize the effects of objects on other objects; in other words, it makes the math easy.

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.
• 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, , which is just Newton's Law of Gravity, with the radial unit 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 , where 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).
• The electromagnetic force is given by the Lorentz force formula, which in SI units is, .