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| {{Redirect|Test mass|other uses|Proof mass}}
| | The author's title is Andera and she believes it seems quite [http://www.weddingwall.com.au/groups/easy-advice-for-successful-personal-development-today/ good psychic]. The preferred pastime for him and his kids is to play lacross and he would never give it up. Office supervising is what she does for a living. My spouse and I live in Kentucky. |
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| In [[Theoretical physics|physical theories]], a '''test particle''' is an idealized model of an object whose physical properties (usually [[mass]], [[charge (physics)|charge]], or [[volume|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.
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| ==Classical Gravity==
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| The easiest case for the application of a test particle arises in [[Newton's law of universal gravitation|Newtonian gravity]]. The general expression for the gravitational force between two masses <math>m_1</math> and <math>m_2</math> is:
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| :<math>F(r) = -G \frac{m_1 m_2}{(r_1-r_2)^2}</math>
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| where <math>r_1</math> and <math>r_2</math> 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:
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| :<math>R = \frac{m_1r_1+m_2r_2}{m_1+m_2}</math><ref name=goldstein>{{cite book
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| | year = 1980
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| | title = Classical Mechanics, 2nd Ed.
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| | publisher =Addison-Wesley
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| | author = [[Herbert Goldstein]]
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| | page =5
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| }}
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| </ref>
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| In the case where one of the masses is much larger than the other (<math>m_1>>m_2</math>), one can assume that the smaller mass moves as a test particle in a [[Classical field theory|gravitational field]] generated by the larger mass, which does not accelerate. By defining the gravitational field as
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| <math>g(r) = \frac{Gm_1}{r^2}</math>
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| with <math>r</math> as the distance between the two objects, the [[Equations of motion|equation for the motion]] of the smaller mass reduces to
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| <math>a(r) = \frac{F(r)}{m_2} = -g(r)</math>
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| 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]].
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| ==Test particles in general relativity==
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| 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]].
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| 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 (physics)|stress]] (e.g. pressure, viscous stresses in a [[fluid solution|perfect fluid]]).
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| 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 [[acceleration]]s due to [[spin-spin force]]s.<ref name = poisson>{{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 | accessdate=March 26, 2004}}</ref>
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| ==Test particles in plasma physics or electrodynamics==
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| 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'''.
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| An electric field is defined by <math> \textbf{E} = k\frac{q}{r^2} \hat{r} </math>. Multiplying the field by a test charge <math>q_\textrm{test}</math> 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.
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| 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.
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| == See also ==
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| * [[Magnetogravitic tensor]] and the [[Bel decomposition]] of the Riemann tensor
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| * [[Papapetrou-Dixon equations]]
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| * [[Point mass]]
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| * [[Point charge]]
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| == References ==
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| {{Reflist}}
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| [[Category:Mathematical methods in general relativity]]
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The author's title is Andera and she believes it seems quite good psychic. The preferred pastime for him and his kids is to play lacross and he would never give it up. Office supervising is what she does for a living. My spouse and I live in Kentucky.