# The Conditions for Biot-Savart Law to Ampere's Law

Mathematically, what conditions must a B-field that obeys the Biot-Savart Law satisfy before it will obey Ampere's Law?

Additionally, what conditions must the B-field obey in order to satisfy Faraday's Law?

The Biot-Savart and Ampere's Law are equivalent. The condition for their validity is that (a) all fields are time-independent and (b) that the stationary current obeys the (reduced) continuity equation ##\vec{\nabla} \cdot \vec{j}=0##. See

http://th.physik.uni-frankfurt.de/~hees/publ/ampere-law-discussion-ver2.pdf
http://dx.doi.org/10.1088/0143-0807/35/5/058001

thanks. I wanted to apply this to Faraday's Law since it also follows Stokes' theorem.

vanhees71