Let Σ(t) be the moving wire, moving together without rotation and with constant velocity v and Σ(t) be the internal surface of the wire. The EMF around the closed path ∂Σ(t) is given by: E = ∮ ∮ ∂ ∂ Σ Σ ( t ) d ℓ ℓ ⋅ ⋅ F / q where E = F / q is the electric field and d ℓ is an infinitesimal vector element of the contour ∂Σ(t).