# Can someone please clear this doubt regarding Lenz's Law?

In Lenz's Law or Faraday's Law of Electromagnetic Induction, whenever there is a change in magnetic flux in a solenoid due to an external magnetic field like an approaching magnet there is an EMF generated, this EMF then generates a current and that current's magnetic field opposes the original cause of change of magnetic flux (which in our case is an approaching magnet).

This can be formally stated as follows: $$\textrm{emf}_b = -N\frac{d\phi}{dt}$$ I understand the basic concept but I have a few doubts. Let's say the magnet approaches the solenoid with instantaneous velocity $$v_0$$ at some time $$t_0$$. Since the change in flux is happening we will apply the above equation to calculate the EMF value ($$\textrm{emf}_b$$). Then we can calculate the current by ohm's law: $$I=\textrm{emf}_b/R$$. This $$I$$ provides the necessary opposing magnetic field to push back the approaching magnet.

Doubt 1: If there are two objects pushing at each other with equal amount of force there should be no motion at all? But be know that the approaching magnet slows down or stops, but the motion happens. Why is that? Is it due to the fact that there are power losses in the solenoid too given by $$P_l= I^2R$$. Is that what is creating the imbalance?

Doubt 2: If we put in an iron core in the solenoid there would be eddy currents (if I am correct) and these eddy currents too would cause some losses. Does that mean the capability of the solenoid to 'push back' the approaching magnet decreases even further, creating more imbalance?

Doubt 3: If I reduce $$R$$ exponentially (say by increasing the cross section area of the wire) can I make the current's arbitrarily large?! The equation says so. but that means I can increase the power losses as much as I want with same/limited EMF?! I am a bit unclear but that shouldn't be possible.

Can someone please clarify where my understanding is wrong (I am sure it is somewhere).