${\displaystyle U_{\text{l}}=-\frac{\text{d}}{\text{d}t}{\displaystyle {\oint }_{\text{C}}A\text{d}r}=-\frac{\text{d}}{\text{d}t}{\displaystyle {\int }_{\text{S}}B\cdot e_{\text{n}}\text{d}A}=-\frac{\text{d}}{\text{d}t}\Psi }$

where A is the magnetic vector potential at a point of the path C, dr is a vector line element of C, B is the magnetic flux density at a point on a surface S delimited by the curve C, e_ndA is a vector surface element of S, Ψ is the total flux through this surface, and t is time

Note 1 to entry: The loop voltage is often wrongly denoted as the induced voltage; this is only true when no current is flowing through the path C.

Note 2 to entry: The coherent SI unit of the loop voltage is volt, V = s⁻³ m² kg A⁻¹.