Biot - Savart Law and time - variable current

Question

Is the Biot Savart law valid also with currents which are functions of time (for instance a sine wave)?

Answer 1

Strictly speaking, the Biot-Savart law is only valid in magnetostatics, i.e. when there are no time-varying currents. Jefimenko's equations need to be solved instead.

However, in the quasi-static approximation of electromagnetism which is valid for currents with time variations that are "sufficiently slow", it is safe to use the Biot-Savart law. One way of judging the validity of the quasi-static approximation is by comparing the system size to the wavelength associated with time scales of interest ($\lambda = c/f$, where $f$ is a dominant frequency with which the current is varying and $c$ is the speed of light in the relevant medium, often air/vacuum). If the system is much smaller compared to this wavelength, the quasi-static approximation typically works very well.