0
$\begingroup$

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

Improve this question
$\endgroup$
0

1 Answer 1

Reset to default
1
$\begingroup$

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.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Hello, I have a pair of questions which are similar to that I asked in this topic. Is the coulomb law for electric field (E = k Q/r^2) true also in electrodynamics (Q = Q(t))? Moreover, consider a conductor which is supplied with a DC voltage: are we in electrostatics (since current is constant in time) or electrodynamics (since charges move)? $\endgroup$
    – Kinka-Byo
    Commented Mar 3, 2020 at 17:18
  • 1
    $\begingroup$ Coulomb's law is not strictly valid in electrodynamics. Again, Jefimenko's equations are what you would use instead. Steady currents are usually the realm of magnetostatics, but I don't know what best to call it if you're only concerned with the E-field, perhaps a special case of electrodynamics. What is important is that all fields in this case are static, and this means you can use Coulomb's law to calculate the E-field due to a fixed charge distribution even in the presence of DC currents. $\endgroup$
    – Puk
    Commented Mar 4, 2020 at 18:52