As we know, a capacitor will maintain the same voltage across its poles even if it is disconnected from a battery source. For example, in this problem:
http://www.unm.edu/~toolson/rc_circuit.gif
This is because the charge on the plates stays the same, and it is clear that the charge difference would maintain the same voltage.
So this brings me to my question. Switch the cap in that circuit for an inductor, and everything changes. As I have been told many times, now it is the current that stays the same. Indeed, almost counterintuitively, if an inductor is instantly disconnected from its power source and put into a series circuit with more resistance, the voltage across its terminals gets even bigger, even though there is more resistance.
So, I know that an inductor stores its energy in a magnetic field, and I am aware of the relation between the voltage across its poles and the change in current ($V=-L\frac{dI}{dt}$), but this does not tell me why the current should stay the same (at the very least, it isn't obvious).
It's clear that current would still continue to flow, but why is it the same current? Why does it maintain the status quo?
Best Answer
There is energy stored in the magnetic field, and the magnetic field is proportional to the current.
In order for the current to change, the magnetic field must change.
By conservation of energy, that means the magnetic field energy must be transformed to some other kind of energy. Until you provide a mechanism for that to happen (for example a resistor that can turn the energy into heat), the current must remain constant.