In general, the relation between the emf E in a wire loop encircling a surface Σ, and the electric field E in the wire is given by E = ∮ ∮ ∂ ∂ Σ Σ E ⋅ ⋅ d ℓ ℓ where d ℓ is an element of contour of the surface Σ, combining this with the definition of flux Φ Φ B = ∫ ∫ Σ Σ B ⋅ ⋅ d A , we can write the integral form of the Maxwell–Faraday equation ∮ ∮ ∂ ∂ Σ Σ E ⋅ ⋅ d ℓ ℓ = − − d d t ∫ ∫ Σ Σ B ⋅ ⋅ d A