Faraday's law of induction

Faraday's law of induction describes how a changing magnetic field results in an electromotive force and thus current flow, and vice versa,

E = \oint 𝜕 Σ ⃗ 𝐄 \cdot 𝑑 ⃗ ℓ = - 𝜕 𝜕 𝑡 \iint Σ ⃗ 𝐁 \cdot 𝑑 ⃗ 𝐚 = - 𝑑 Φ 𝐵 𝑑 𝑡

or equivalently by Stokes's theorem

⃗ \nabla \times ⃗ 𝐄 = - 𝜕 ⃗ 𝐁 𝜕 𝑡

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