Selected Fields
To go with the section on test particles above, here are the equations for the fields in which they move. The equations below pertain to the fields in which the test particles described above move and allow the calculation of those fields. The equations below will not give you the equations of motion of a test particle in the field but will instead give you the potential (field) induced by quantities such as mass or charge density at any point . For example, in the case of Newtonian gravity, the Lagrangian density integrated over space-time gives you an equation which, if solved, would yield . This, when substituted back in equation (1), the Lagrangian equation for the test particle in a Newtonian gravitational field, provides the information needed to calculate the acceleration of the particle.
Read more about this topic: Lagrangian
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