Faraday's Law (Emf Induction)

Question

Let say there is a sharp decrease in current, all the way to zero in a coil connected to a power supply, will the emf induced in another coil placed close to it in a bar form (see first picture) or spike form (as in the second picture).

The red colored ink is the answer, and the black one is my attempt of solution. I am confused because the gradient of the sharp decrease in current is constant. Shouldn't the emf induced in the other coil be a constant too, since the gradient of the magnetic flux with respect to time is equal to the emf induced?

Answer 1

If the secondary coil is open, opening the switch on the primary will remove all current from both coils. The magnetic flux will collapse producing a large voltage spike in both coils. This is how spark plugs are powered in an old combustion engine. In an engine, there is generally a capacitor across the switch. This gives the switch time to open without arcing. If arcing occurs, then the collapse is not so fast, and you may not get enough voltage to span the gap in the plug. (It will also destroy the switch.)