Maxwell’s equations

Ampère’s circuital Law

Ampère’s circuital law, with a correction due to Maxwell, relates the circulation of a magnetic field around an area to the Current density passing through it:

∮𝜕Ω⃗𝐁⋅𝑑⃗ℓ=𝜇0(∬Σ⃗𝐉⋅𝑑⃗𝐚+𝜖0𝑑𝑑𝑡∬Σ⃗𝐄⋅𝑑⃗𝐚)=𝜇0(𝐼Σ+𝜖0𝜕Φ𝐸,Σ𝜕𝑡)

or equivalently by Stokes’s theorem

⃗∇×⃗𝐁=𝜇0(⃗𝐉+𝜖0𝜕⃗𝐄𝜕𝑡)

See also Ampère’s law for magnets

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