Magnetostatic field

Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static — as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic recording devices.

Starting from Maxwell's equations and assuming that charges are either fixed or move as a steady current ${\displaystyle \scriptstyle \mathbf {J} }$, the equations separate into two equations for the electric field (see electrostatics) and two for the magnetic field. 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 ∇ denotes divergence, and B is the magnetic flux density, the first integral is over a surface ${\displaystyle \scriptstyle S}$ with oriented surface element ${\displaystyle \scriptstyle d\mathbf {S} }$. Where J is the current density and H is the magnetic field intensity, the second integral is a line integral around a closed loop ${\displaystyle \scriptstyle C}$ with line element ${\displaystyle \scriptstyle \mathbf {l} }$. The current going through the loop is ${\displaystyle \scriptstyle I_{\text{enc}}}$.

...
Wikipedia