Ampere-maxwell Law

NCERT Class 12, Chapter 8 (Electromagnetic Waves) recounts how the original Ampere's law related the magnetic field around a loop only to the conduction current threading it. Maxwell noticed this failed for the region between charging capacitor plates: if one chooses an Amperian loop and stretches the bounding surface to pass between the plates, no conduction current pierces it, yet a magnetic field is undeniably present around the wire. He resolved the inconsistency by adding a displacement current term, ε₀(dΦ_E/dt), proportional to the time rate of change of electric flux, producing the Ampere-Maxwell law. This addition also made the set of equations symmetric with Faraday's law and ultimately predicted electromagnetic waves. The option invoking a rate of change of magnetic flux describes Faraday's law of induction, a different equation entirely. Replacing conduction current with magnetisation current is incorrect, since magnetisation current pertains to magnetic materials and does not fix the capacitor-gap problem. Removing the dependence on enclosed current would break the law even for ordinary steady currents. A consistency check shows that the added term makes the total current continuous through the capacitor, preserving the law universally, so the displacement current modification is correct.