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Which of the following equations represents the Ampere-Maxwell law?

Asked in GSEB Board July 2023 · Maxwell's equations and what each asserts

Answer: (1) ∮ ⃗B· d⃗l = μ₀ i_c + μ₀ε₀(dΦ_E)/(dt)

Step-by-step solution

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.

Why the other options are wrong

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