Vector field approach Mathematical descriptions of the electromagnetic field

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the common description of electromagnetic field uses 2 three-dimensional vector fields called electric field , magnetic field. these vector fields each have value defined @ every point of space , time , regarded functions of space , time coordinates. such, written e(x, y, z, t) (electric field) , b(x, y, z, t) (magnetic field).


if electric field (e) non-zero, , constant in time, field said electrostatic field. similarly, if magnetic field (b) non-zero , constant in time, field said magnetostatic field. however, if either electric or magnetic field has time-dependence, both fields must considered coupled electromagnetic field using maxwell s equations.


maxwell s equations in vector field approach

the behaviour of electric , magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics (electromagnetic fields), governed maxwell s equations:







where ρ charge density, can (and does) depend on time , position, ε0 electric constant, μ0 magnetic constant, , j current per unit area, function of time , position. equations take form international system of quantities.


when dealing nondispersive isotropic linear materials, maxwell s equations modified ignore bound charges replacing permeability , permittivity of free space permeability , permittivity of linear material in question. materials have more complex responses electromagnetic fields, these properties can represented tensors, time-dependence related material s ability respond rapid field changes (dispersion (optics), green–kubo relations), , possibly field dependencies representing nonlinear and/or nonlocal material responses large amplitude fields (nonlinear optics).







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