How does an inductor generate back emf equal to a source driving it

circuit analysiselectromagnetisminductor

I have a question about the way inductors fundamentally work. How can an inductor be modeled as accurately as possible?

I tried to approach this problem from the basics of electromagnetic fields, but I am still having some problems understanding the matter

When we connect the ends of a inductor across a battery:

  1. The end at lower potential pushes the electrons in the inductor by applying electromotive force on it
  2. due to this push the electrons gain acceleration
  3. because of this acceleration a change in current with respect to time di/dt occurs
  4. because of this di/dt an electric field is developed in the inductor to oppose it
  5. now there are two forces acting on the electrons that is the force due to battery and the force due to induced electric field in the battery
  6. now we see that under these two opposing forces the net acceleration of electrons has decreased and there is anew value of di/dt at that instant now since the di/dt has reduced the induced emf this time will be less compared to previous now again under the influence of these two forces a new acceleration will come and according to it will come a new di/dt
  7. and so there is a jerk like increment as well as decrease in the di/dt so the problem is what is happening inside because in textbooks they write that in simple inductor and battery circuits the di/dt is constant?

Another question I have is about the induced emf to be equal to the external battery if the induced emf(opposing emf induced in loop) is equal to the external battery then how in the world is di/dt not equal to zero because if there is are two fields exactly same in magnitude and in opposite directions then how come the current increases with time?

If external emf and induced emf are same then the energy given to electrons in completing the circuit is equal to the energy taken by the inductor from the electrons then how is their kinetic energy (current) increasing?

Best Answer

One way to think of a inductor from the circuit's point of view is that it gives inertia to current. This gives you some intuitive feel for why current builds up slowly as voltage is applied, and why the voltage goes as high as it needs to on a attempt to shut off the current abruptly. This isn't how the physics works, but this can be a very useful mental model for understanding and designing circuits with inductors.

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