When can the Biot-Savart law be applied to time-varying currents?

[LeoPedranjo]

Guys, I'm having trouble with some concepts on the Biot-Savart Law. Lots of texts compare this law with Coulomb Law, but doesn't affirm that B-S is only applicable on a static case (constant current). What are the real physical conditions in which Biot-Savart Law can be directly applied? Does it covers the instant eletromagnetic effects with the distance (as the Coulomb Law doesn't)?
Also, to surpass the instant effects over distance, could I aplly the Ampere-Maxwell law?

Thanks!

 

[jfizzix]

Long story short, The Biot-savart law applies in magnetostatics, where currents are constant in time.
Similarly, Coulomb's law, applies in electrostatics, where charge densities are constant in time (though individual charges may be moving)

These laws are special cases of what are known as the Jeffimenko equations, which completely describe the electric and magnetic field generated from an arbitrarily changing collection of charges (both Wikipedia and Griffith's E&M book have good introductions).