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Concept
Test particle
Summary
In physical theories, a test particle, or test charge, 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.
The easiest case for the application of a test particle arises in Newtonian gravity. The general expression for the gravitational force between any two point 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 R, in this specific case:
In the case where one of the masses is much larger than the other (), one can assume that the smaller mass moves as a test particle in a gravitational field generated by the larger mass, which does not accelerate. We can define the gravitational field as
with as the distance between the massive object and the test particle, and is the unit vector in the direction going from the massive object to the test mass. Newton's second law of 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.
In simulations with electric 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.
Similar to the case of classical gravitation, the electric field created by a point charge q is defined by
where k is the Coulomb constant.
Official source
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