11. The concept of a test particle often simplifies problems, and can provide a good approximation for physical phenomena. 12. Thus, when a test particle is forced to approach the electron, it causes changes that can be measured. 13. Notably, in order to deflect a test particle from its geodesic path, an external force must be applied. 14. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles . 15. Analogously, the world lines of test particles in free fall are spacetime geodesics, the straightest possible lines in spacetime. 16. Where such objects are concerned, the laws governing the behavior of test particles are sufficient to describe what happens. 17. The equations for the motion of test particles in the Kerr spacetime may be obtained using proper Hamilton-Jacobi equations. 18. To go with the section on test particles above, here are the equations for the fields in which they move. 19. The area enclosed by the test particles does not change and there is no motion along the direction of propagation. 20. In simulations with electromagnetic fields the most important characteristics of a "'test particle "'is its electric charge and its mass.
