# Test particle

In physical theories, a

**test particle**is an idealized model of an object whose physical properties (usuallymass ,charge , or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system. The concept of a test particle often simplifies problems, and can provide a good approximation for physical phenomena. In addition to its uses in the simplification of the dynamics of a system in particular limits, it is also used as a diagnostic incomputer simulations of physical processes.**Classical Gravity**The easiest case for the application of a test particle arises in Newtonian gravity. The general expression for the gravitational force between two masses $m\_1$ and $m\_2$ is:

:$F(r)\; =\; -G\; frac\{m\_1\; m\_2\}\{(r\_1-r\_2)^2\}$

where $r\_1$ and $r\_2$ represent the position of each particle in space. In the general solution for this equation, both masses rotate around their

center of mass , in this specific case::$R\; =\; frac\{m\_1r\_1+m\_2r\_2\}\{m\_1+m\_2\}$cite book

date = 1980

title = Classical Mechanics, 2nd Ed.

pages =p.5

publisher =Addison-Wesley

author =Herbert Goldstein ]In the case where one of the masses is much larger than the other ($m\_1>>m\_2$), one can assume than the smaller mass moves as a test particle in a gravitational field generated by the larger mass, which does not accelerate. By defining the gravitational field as

$g(r)\; =\; frac\{Gm\_1\}\{r^2\}$

with $r$ as the distance between the two objects, the equation for the motion of the smaller mass reduces to

$a(r)\; =\; frac\{F(r)\}\{m\_2\}\; =\; -g(r)$

and thus only contains one variable, for which the solution can be calculated more easily. This approach gives very good approximations for many practical problems, e.g. the orbits of

satellites , whose mass is relatively small compared to that of theearth .**Test particles in general relativity**In metric theories of gravitation, particularly

general relativity , a test particle is an idealized model of a small object whose mass is so small that it does not appreciably disturb the ambientgravitational field .According to the

Einstein field equation , the gravitational field is locally coupled not only to the distribution of non-gravitationalmass-energy , but also to the distribution ofmomentum and stress (e.g. pressure, viscous stresses in a perfect fluid).In the case of test particles in a

vacuum solution orelectrovacuum solution , this turns out to imply that in addition to the tidal acceleration experienced by small clouds of test particles (spinning or not), "spinning" test particles may experience additionalacceleration s due tospin-spin force s.cite web | author=Poisson, Eric | title=The Motion of Point Particles in Curved Spacetime | work=Living Reviews in Relativity | url=http://relativity.livingreviews.org/Articles/lrr-2004-6/index.html | accessmonthday=March 26 | accessyear=2004]**Test particles in plasma physics or electrodynamics**In simulations with

electromagnetic fields the most important characteristics of a**test particle**is itselectric charge and itsmass . In this situation it is often referred to as a**test charge**.An electric field is defined by $extbf\{E\}\; =\; kfrac\{q\}\{r^2\}\; hat\{r\}$. Multiplying the field by a test charge $q\_\; extrm\{test\}$ gives an electric force exerted by the field on a test charge. Note that both the force and the electric field are vector quantities, so a positive test charge will experience a force in the direction of the electric field.

In a

magnetic field , the behavior of a test charge is determined by effects ofspecial relativity described by theLorentz force . In this case, a positive test charge will be deflected clockwise if moving perpendicular to a magnetic field pointing toward you, and counterclockwise if moving perpendicular to a magnetic field directed away from you.**ee also***

Papapetrou-Dixon equations

*Magnetogravitic tensor and theBel decomposition of the Riemann tensor

*point mass

*point charge **References**

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