Question

explain why do we find ampere circuital law inconsistent when applied to charging of a capacitor? how is it resolved by introducing the concept of displacement current? justify mathematically.

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.