# Maxwell’s magnetic theory

Still a question that has to be answered is why conductivity electrons are moving in the magnetic field in the conducting circuit. (Figure 37). Maxwell introduced the concept of vortex magnetic fields, that help to answer this question.

These magnetic field lines are closed. The source of this vortex electric field is a variable magnetic field. These forces are distributing the conduction electrons and provoke the appearance of EMF in the conductor, and the EMF of the static conductor in the variable magnetic field. The vortex electric field is also characterised by the E vector. The following equations are valid:

${\epsilon }_{i}={\int }_{C}{E}_{r}dr,{\epsilon }_{i}=–\frac{d\Phi }{dt}$

. As far as the magnet flux

$\Phi ={\int }_{\Sigma }{B}_{n}dS$

then

${\int }_{C}{E}_{r}dr=–\frac{d}{dt}{\int }_{\Sigma }{B}_{n}dS$