Quasistatic approximation
Encyclopedia
In Electromagnetism, Magnetostatics equations such as Ampère's Law
or the more general Biot-Savart law
allow one to solve for the magnetic fields produced by steady electrical currents. Often, however, one may want to calculate the magnetic field due to time varying currents (accelerating charge) or other forms of moving charge. Strictly speaking, in these cases the aforementioned equations are invalid, as the field measured at the observer must incorporate distances measured at the retarded time, that is the observation time minus the time it took for the field (traveling at the speed of light) to reach the observer. It is important to realize that the retarded time is different for every point of a charged object, hence the resulting equations are quite complicated; often it is easier to formulate the problem in terms of potentials; see retarded potential
and Jefimenko's equations
.
In most situations, however, provided that the velocities involved are small compared to the speed of light, one may invoke the quasistatic approximation. This simply permits one to assume that the magnetostatic equations will yield approximately correct values provided the v/c fraction remains small. (Indeed, to first order, the mistake of using only Biot-Savart's law rather than both terms of Jefimenko's magnetic field equation and using time instead of retarded time will fortuitously cancel).
Ampère's law
In classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the integrated magnetic field around a closed loop to the electric current passing through the loop...
or the more general Biot-Savart law
Biot-Savart law
The Biot–Savart law is an equation in electromagnetism that describes the magnetic field B generated by an electric current. The vector field B depends on the magnitude, direction, length, and proximity of the electric current, and also on a fundamental constant called the magnetic constant...
allow one to solve for the magnetic fields produced by steady electrical currents. Often, however, one may want to calculate the magnetic field due to time varying currents (accelerating charge) or other forms of moving charge. Strictly speaking, in these cases the aforementioned equations are invalid, as the field measured at the observer must incorporate distances measured at the retarded time, that is the observation time minus the time it took for the field (traveling at the speed of light) to reach the observer. It is important to realize that the retarded time is different for every point of a charged object, hence the resulting equations are quite complicated; often it is easier to formulate the problem in terms of potentials; see retarded potential
Retarded potential
The retarded potential formulae describe the scalar or vector potential for electromagnetic fields of a time-varying current or charge distribution. The retardation of the influence connecting cause and effect is thereby essential; e.g...
and Jefimenko's equations
Jefimenko's equations
In electromagnetism, Jefimenko's equations describe the behavior of the electric and magnetic fields in terms of the charge and current distributions at retarded times....
.
In most situations, however, provided that the velocities involved are small compared to the speed of light, one may invoke the quasistatic approximation. This simply permits one to assume that the magnetostatic equations will yield approximately correct values provided the v/c fraction remains small. (Indeed, to first order, the mistake of using only Biot-Savart's law rather than both terms of Jefimenko's magnetic field equation and using time instead of retarded time will fortuitously cancel).