Ampere’s circuital law is not new in content from Biot-Savart law Both relate the magnetic field and the current, and both express the same
physical consequences of a steady electrical current Ampere’s law is to
Biot-Savart law, what Gauss’s law is to Coulomb’s law Both, Ampere’s
and Gauss’s law relate a physical quantity on the periphery or boundary
(magnetic or electric field) to another physical quantity, namely, the source,
in the interior (current or charge)