Faraday's law of electromagnetic induction must have been learned by everyone, that is, when the flux (i.e., magnetic flux) of magnetic induction intensity B passing through a coil changes, an induced current is generated in the coil (i.e., a vortex electric field E is generated to do work on electrons in the coil). I think smart people have already felt it by this time. The magnetic flux here is the flux of curl ▽×F to curved surface S in Stokes formula, and Joule heat generated in the coil is the work done by eddy current electric field E to electrons in the coil along the coil, that is, the loop integration of F to closed curve in Stokes formula. I think everyone has an intuitive imagination of Faraday's law of electromagnetic induction. The faster the magnetic flux changes, the greater the Joule heat in the coil, which is a physical phenomenon that both sides of Stokes formula are equal, that is, the flux of vortex field to curved surface is equal to the loop flux of its vortex source to curved surface. If it is assumed that there is current in the coil, there will be magnetic flux in the curved surface. Similarly, you can imagine that both sides of the equation are still equal. Of course, I must emphasize two points here: there is a negative sign difference between the vortex field generated by the first current and the right hand rule of current, because both current and magnetic induction intensity hinder each other. I think people who have studied electromagnetic fields and electromagnetic waves or electrodynamics still clearly remember the negative sign of the second equation of Maxwell's equations, and the eddy magnetic field generated by eddy electric field is anti-right-handed. Second: I want to emphasize that the electric field here is not an electrostatic field. At present, electromagnetic field thinks that there are two forms of electric field, namely electrostatic field and eddy current electric field, or you can think that electrostatic field is a special case of eddy current electric field, which doesn't matter. Because we all know that electrostatic field does not produce magnetic field, only changing the electric field produces magnetic field, then changing the magnetic field produces electric field, and then two "fly with me" forms electromagnetic wave!
Read a small blog as a student. I want to emphasize that advanced mathematics is a mathematical summary of living examples in life. Unless you are a Ph.D. student in pure mathematics, most of the mathematics we face is nothing more than a mathematical summary of physical phenomena around us. Of course, nothing is absolute, and mathematics is ahead of engineering. When you study modern mathematics, such as the concept of time and space involves four dimensions, you can only imagine it, because we are three-dimensional people and can't find four dimensions. Finally, I wish you success in your studies. Can realize their social and personal values, and gain something in life!