So we have, the Maxwell Faraday equation: ∮ ∮ ∂ ∂ Σ Σ ( t ) d ℓ ℓ ⋅ ⋅ E ( r , t ) = − − ∫ ∫ Σ Σ ( t ) d A ⋅ ⋅ d B ( r , t ) d t and the Faraday Law, ∮ ∮ ∂ ∂ Σ Σ ( t ) d ℓ ℓ ⋅ ⋅ F / q ( r , t ) = − − d d t ∫ ∫ Σ Σ ( t ) d A ⋅ ⋅ B ( r , t ) .