In physical theories, a test particle is an idealized model of an object whose physical properties (usually
mass, 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 in computer simulationsof physical processes.
The easiest case for the application of a test particle arises in Newtonian gravity. The general expression for the gravitational force between two masses and is:
where and 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:
date = 1980
title = Classical Mechanics, 2nd Ed.
In the case where one of the masses is much larger than the other (), 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
with as the distance between the two objects, the equation for the motion of the smaller mass reduces to
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 the earth.
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 ambient gravitational field.
According to the
Einstein field equation, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentumand stress (e.g. pressure, viscous stresses in a perfect fluid).
In the case of test particles in a
vacuum solutionor electrovacuum 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 additional accelerations due to spin-spin forces.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 fieldsthe most important characteristics of a test particle is its electric chargeand its mass. In this situation it is often referred to as a test charge.
An electric field is defined by . Multiplying the field by a test charge 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.
magnetic field, the behavior of a test charge is determined by effects of special relativitydescribed by the Lorentz 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.
Magnetogravitic tensorand the Bel decompositionof the Riemann tensor
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