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Asked in GSEB Board July 2023 · Maxwell's equations and what each asserts
Idea: the Ampere-Maxwell law is Ampere's circuital law with Maxwell's extra term, so it must have the line integral of ⃗B round a closed loop on the left and two sources on the right.
The first source is the conduction current i_c threading the loop, the familiar μ₀ i_c of Ampere's law.
The second is the displacement current, μ₀ε₀(dΦ_E)/(dt), which supplies the missing contribution wherever the electric flux changes and no charge flows -- in the gap of a charging capacitor, for instance.
So the equation is ∮ ⃗B· d⃗l = μ₀ i_c + μ₀ε₀(dΦ_E)/(dt).
The other three options are the remaining members of Maxwell's set: the two Gauss laws and Faraday's law. It is this added term that lets the set predict electromagnetic waves at all.
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