Question

Equations derived from ampere's law that are valid for free space

Answer 1

In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law that André-Marie Ampère discovered in 1823[1]) relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell (not Ampère) derived it using hydrodynamics in his 1861 paper "On Physical Lines of Force"[2] and it is now one of the Maxwell equations, which form the basis of classical electromagnetism.
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