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Asked in GUJCET 2024 · Maxwell's equations and what each asserts
Idea: Ampere's circuital law ties the line integral of ⃗B round a closed loop to the current threading it. Maxwell found it incomplete for a charging capacitor, where no conduction current crosses the gap.
What the gap does carry is a changing electric flux, and ε₀(dφ_E)/(dt) is the displacement current that continues the conduction current across it.
So the complete law keeps the line integral of ⃗B on the left and carries both currents on the right:
∮ B⃗ · dl⃗ = μ₀ i_c + μ₀ε₀(dφ_E)/(dt).
Two things identify it: the element must be d⃗l, and the flux in the extra term must be the electric one.
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