Ui=rb∫ra(C)(− ∂ A∂ t+v×B)⋅dr
where A and B are respectively a magnetic vector potential and the magnetic flux density at a point of the path C, v is the velocity with which that point is moving, r is position vector of the point, and t is time
Note 1 to entry: If the points a and b are at rest, i.e. their velocities are zero (va = vb = 0), the induced voltage is equal to the time derivative of the protoflux corresponding to the path C, with a positive or negative sign according to the convention in IEC 60375.
Note 2 to entry: The first term in the integrand results from Faraday’s law (see Maxwell equations) and the second one from the non-relativistic Lorentz transformation of the electromagnetic field tensor.
U i = ∫ r a ( C ) r b ( − ∂ A ∂ t +v×B )⋅dr MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiaadwfadaWgaaWcbaGaaeyAaaqabaGccqGH9aqpdaWdXbqaamaabmaabaGaeyOeI0IaaGjbVpaalaaabaaccaGae8NaIyRaaGjbVJqadiaa+feaaeaacqWFciITcaaMi8UaaGjbVlaadshaaaGaey4kaSIaamODaiabgEna0kaa+jeaaiaawIcacaGLPaaacqGHflY1caqGKbGaamOCaaWcbaGaamOCamaaBaaameaacaqGHbaabeaalmaabmaabaGaae4qaaGaayjkaiaawMcaaaqaaiaadkhadaWgaaadbaGaaeOyaaqabaaaniabgUIiYdaaaa@574C@
Note 1 to entry: If the points a and b are at rest, i.e. their velocities are zero (va = vb = 0), the induced voltage is equal to the time derivative of the protoflux corresponding to the path C, with a positive or negative sign according to the convention in IEC 60375.