# Force field

A physical force field is a field whose field strength exerts a force on a test specimen . The force depends on the location of the specimen in the field and on the charge of the specimen with respect to the interaction concerned . ${\ displaystyle {\ vec {r}}}$ ${\ displaystyle q}$

The effect of the test specimen on the field is assumed to be negligibly small, in this way a test specimen is idealized and only reacts passively. If the force field is caused by the electromagnetic interaction , the electric charge is ; the body is then called a test charge . In the gravitational field , the charge is the mass , the body is then called the test mass . ${\ displaystyle q}$ ${\ displaystyle m}$

Mathematically, the force on a test specimen in a force field, a vector-valued function of the place: . Force fields can be represented with the help of field lines . ${\ displaystyle {\ vec {F}} ({\ vec {r}}, q)}$

In the literature, the use of the term is not uniform: on the one hand, the term can be understood synonymously with field strength in such a way that it is the field that exists independently of the presence of a test body and does not have the dimension of a force; such a field still has the charge of the specimen are multiplied to get the force on this: . Other authors, on the other hand, understand the force field to be a field function with the dimension of a force that depends on the test specimen used. Here, too, the dependence on the test specimen is to be understood without the test specimen affecting the existing field. ${\ displaystyle {\ vec {E}} ({\ vec {r}})}$${\ displaystyle {\ vec {F}} ({\ vec {r}}, q) = q \ cdot {\ vec {E}} ({\ vec {r}})}$

## Examples

A force field is obtained from an electric field by multiplying the electric field strength by the electric charge on the specimen. Are obtained analogously in a gravitational field by multiplying the gravitational field strength (i. E. The gravitational acceleration) with the mass of the specimen, the force of gravity . If the specimen is moved in the force field along a path s from A to B, the work becomes

${\ displaystyle W = \ int _ {A} ^ {B} {\ vec {F}} ({\ vec {r}}) \ cdot \ mathrm {d} {\ vec {r}}}$

performed. If it is moved back from B to A along another path s ' , the work done W' for conservative force fields is equal to -W, but can deviate from it for force fields which, like the magnetic field, are not a gradient of a potential .

In the simplest case, the force field is homogeneous, so the force is the same in all places. This represents an idealization that is a sensible approximation, for example for the gravitational field near the earth's surface or the electric field between two capacitor plates.

## history

### Classic field term from 1830

The term force field was developed around 1830 by Michael Faraday based on his observations on electricity and magnetism and specified using the image of the field lines . According to this, there is a certain field strength at every point in space , which can be detected and measured by its force on a test specimen. Soon gravitation was also described by a gravitational field. A field is produced by another body, the source of the field . This replaced the image of remote action , which was viewed as philosophically problematic : one body no longer acts directly on another through empty space, but creates a field around itself, which in turn exerts its effect at the location of the other body.

The fact that a field has physical reality regardless of its source was shown in 1886 by Heinrich Hertz's discovery that free electromagnetic fields exist and spread in the form of waves. In 1905 it emerged from Albert Einstein's special theory of relativity that these fields exist in a vacuum without any material substrate (“ ether ”) and do not spread infinitely quickly, but at the speed of light. The thought that this must also apply to the gravitational field led Einstein to the general theory of relativity in 1916 .

In 1900 Max Planck made the discovery that the free electromagnetic field can only absorb or release its energy in certain portions. In 1905 Einstein referred to these as light quanta , later as photons . This marks the beginning of quantum physics .

### Quantum field theory from 1927

From 1927 Paul Dirac , Werner Heisenberg , Wolfgang Pauli a . a. apply the rules of quantum mechanics to fields. Accordingly, the photons are the elementary levels of excitation of the free electromagnetic field. In addition, it emerges that photons can exist in “virtual states” that would be forbidden according to the classical field equations. In such states, the photons cannot be detected directly, but they are responsible for all observable electrical and magnetic effects. Thus, in quantum electrodynamics , they are behind the electromagnetic interaction as exchange particles and in particular also cause Faraday force fields.

The corresponding field quanta for the second force field in classical physics, the gravitational field, are called gravitons . It is currently unknown whether they really exist. A satisfactory quantum field theory for gravity has not yet been found.

## Individual evidence

1. a b Ludwig Bergmann, Clemens Schaefer: Textbook of Experimental Physics, Volume 1: Mechanics, Relativity, Warmth . Walter de Gruyter, Hamburg 1998, ISBN 978-3-11-012870-3 , p. 188 ( online ).
2. ^ Christian Gerthsen: Gerthsen Physics . Ed .: Dieter Meschede. Supervised by Helmut Vogel up to the 20th edition. Springer, Berlin 2010, ISBN 978-3-642-12893-6 , pp. 28 ( online ).

## literature

Friedrich Hund: History of physical terms (Vol. 2) . 2nd Edition. BI university pocket books , Mannheim 1978, ISBN 3-411-05543-X .