Magnetostatics as a special case of Maxwell's equations
Maxwell's equations and assuming that charges are either fixed or move as a steady current , the equations separate into two equations for the
electric field (see
electrostatics) and two for the
 The fields are independent of time and each other. The magnetostatic equations, in both differential and integral forms, are shown in the table below.
Where ∇ with the dot denotes
divergence, and B is the
magnetic flux density, the first integral is over a surface with oriented surface element . Where ∇ with the cross denotes
curl, J is the
current density and H is the
magnetic field intensity, the second integral is a line integral around a closed loop with line element . The current going through the loop is .
The quality of this approximation may be guessed by comparing the above equations with the full version of
Maxwell's equations and considering the importance of the terms that have been removed. Of particular significance is the comparison of the term against the term. If the term is substantially larger, then the smaller term may be ignored without significant loss of accuracy.
Re-introducing Faraday's law
A common technique is to solve a series of magnetostatic problems at incremental time steps and then use these solutions to approximate the term . Plugging this result into
Faraday's Law finds a value for (which had previously been ignored). This method is not a true solution of
Maxwell's equations but can provide a good approximation for slowly changing fields.