Theory

Now for the fun part everyone has been waiting for: the physics that can describe the behavior of inductors!

I'm not able to go into a whole lot of detail and don't by any means understand everything myself, but my goal is to explain a few of the key mechanisms and calculations related to inductors.

Lenz's Law

Inductors tend to resist changes in current. This is explained by Lenz's Law, which states that the induced voltage will oppose change in current. One can think of it like a flywheel on a shaft with a clutch that allows some slipping. The flywheel wants to resist change in angular velocity, and if the shaft quickly speeds up, the clutch will slip initially, but the flywheel will eventually catch up to match the rotational speed of the shaft. Conversely, if the shaft slows down suddenly, the flywheel will continue to turn, applying a torque to the shaft in the direction of rotation (resisting the slowing). In the same way, when electricity is flowing through an inductor and suddenly drops, the energy stored in the magnetic field of the inductor is converted or "induced" back into an electrical current.

Maxwell-Faraday Law of Induction

The Maxwell-Faraday Law of Induction describes how a changing magnetic field will always cause an changing electrical field, and the other way around. The two are directly related to each other. In inductors it explains how the energy can be stored as a magnetic field and converted back and forth between electrical and magnetic fields.

One misconception about transformers that I had when I was younger is that they could magically step up or down any voltage. This is not true, and the reason they can only transform alternating current (AC), not direct current (DC) is due to the magnetic effects outlined by this law. A stationary permanent magnet in a coil of wire cannot cause a current to flow in the wire. This would violate the conservation of energy law and allow for the building of a perpetual motion machine/generator. However, if that magnet moves inside the coil, it can induce a current. Likewise, a stationary magnetic field generated by electricity flowing in another coil cannot induce a current in another coil. But similarly, if the magnetic field generated by one coil is "moving" in the case of AC, then a current will be induced in the other coil if the two coils are magnetically coupled.

An example of how this equation works is this: if perfect sine wave alternating current is applied through an inductor, a sinusoidal voltage will be produced. However, it will be 90° out of phase with the current, not just following the voltage. Looking at voltage, as it goes up and up, the inductor resists that change more and more and at the peak voltage, the current will be reduced to zero. And then as the voltage swings through its middle point, the current goes to its maximum value (on the voltage graph this is in the middle of peaks where the absolute value of the slope hits its maximum).

A last note I wanted to make is on the similarities and differences between inductors and capacitors. These two types of components are similar in that they store electrical energy. However, an inductor uses a magnetic field while a capacitor uses an electric field to accomplish this. The other main difference is that capacitors want to keep a consant voltage, while inductors strive for a steady current. This difference makes both of them useful in circuits, but capacitors are probably a bit more important.