Rotation induced in a coil moving in an electric field

The integral form of the fourth Maxwell's equation is often written in two different ways: in the first, the partial derivative of Electric field appears, while the second contains a time derivative of electric flux integral. It would be useful, from a didactic point of view, to discriminate between the two different interpretations. In this paper, starting from a previous work about Faraday's law, we analyze the derivative of the flux of the electric field and we shed light on the right way to write the Maxwell equations. We introduce a "magnetomotive force" and we find, from the corresponding generalization of the second Laplace's law, the effect of a rotation induced in a coil embedded in an electric field