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As indicated below which one is the equation of Ampere-Maxwell law?

Asked in GUJCET 2024 · Maxwell's equations and what each asserts

Answer: (1) ∮ B⃗ · dl⃗ = μ₀ i_c + μ₀ε₀(dφ_E)/(dt)

Step-by-step solution

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.

Why the other options are wrong

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