Test particle

Test particle

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 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 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 momentum and stress (e.g. pressure, viscous stresses in a perfect fluid).

In the case of test particles in a vacuum solution or 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 fields the most important characteristics of a test particle is its electric charge and its mass. 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 of special relativity described 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.

ee also

*Papapetrou-Dixon equations
*Magnetogravitic tensor and the Bel decomposition of the Riemann tensor
*point mass
*point charge

References


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • test particle — bandomoji dalelė statusas T sritis fizika atitikmenys: angl. test particle vok. Sondenteilchen, n; Testpartikel, f; Testteilchen, n rus. пробная частица, f pranc. particule d’épreuve, f; particule témoin, f …   Fizikos terminų žodynas

  • Particle filter — Particle filters, also known as sequential Monte Carlo methods (SMC), are sophisticated model estimation techniques based on simulation. They are usually used to estimate Bayesian models and are the sequential ( on line ) analogue of Markov chain …   Wikipedia

  • Particle counter — A particle counter is an instrument that detects and counts particles. Applications of particle counters are separated into two primary categories:*Aerosol particle counters *Liquid particle countersAerosol particle countersAerosol Particle… …   Wikipedia

  • particle accelerator — accelerator (def. 7). [1945 50] * * * Device that accelerates a beam of fast moving, electrically charged atoms (ions) or subatomic particles. Accelerators are used to study the structure of atomic nuclei (see atom) and the nature of subatomic… …   Universalium

  • test — 1. To prove; to try a substance; to determine the chemical nature of a substance by means of reagents. 2. A method of examination, as to determine the presence or absence of a definite disease or of some substance in any of the fluids, tissues,… …   Medical dictionary

  • particle-size analysis — granuliometrinė analizė statusas T sritis chemija apibrėžtis Medžiagos dalelių rūšiavimas pagal matmenis ir jų kiekio nustatymas. atitikmenys: angl. granulometric analysis; mechanical analysis; particle size analysis; size analysis; size test;… …   Chemijos terminų aiškinamasis žodynas

  • Magnetic-particle inspection — (MPI) is a non destructive testing (NDT) process for detecting surface and subsurface discontinuities in ferroelectric materials such as iron, nickel, cobalt, and some of their alloys. The process puts a magnetic field into the part. The piece… …   Wikipedia

  • subatomic particle — or elementary particle Any of various self contained units of matter or energy. Discovery of the electron in 1897 and of the atomic nucleus in 1911 established that the atom is actually a composite of a cloud of electrons surrounding a tiny but… …   Universalium

  • Mechanics of planar particle motion — Classical mechanics Newton s Second Law History of classical mechanics  …   Wikipedia

  • GRE Physics Test — The GRE physics test is an examination administered by the Educational Testing Service (ETS). The test attempts to determine the extent of the examinees understanding of fundamental principles of physics and their ability to apply them to problem …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”