Given a loop of wire in a magnetic field, Faraday's law of induction states the induced electromotive force (EMF) in the wire is: E = − − d Φ Φ B d t where Φ Φ B = ∫ ∫ Σ Σ ( t ) d A ⋅ ⋅ B ( r , t ) is the magnetic flux through the loop, B is the magnetic field, Σ(t) is a surface bounded by the closed contour ∂Σ(t), at time t, d A is an infinitesimal vector area element of Σ(t) (magnitude is the area of an infinitesimal patch of surface, direction is orthogonal to that surface patch).