Self-Inductance and Back EMF

A coil's current builds a magnetic field through its own loops. If that current changes, the flux through the coil changes too, and by Faraday's law a changing flux induces an emf. This self-induced emf always points to oppose the change that made it, a consequence of Lenz's law. So if you try to ramp current up, the coil pushes back against the increase; if you try to cut current off, the coil pushes to keep it flowing. That pushback is called back emf, and it is why inductors feel sluggish compared to resistors.

The size of the effect depends on the inductor's geometry through a constant called inductance, L, measured in henries. The back emf is written as emf = -L dI/dt: the minus sign is Lenz's law in symbols, and the magnitude is just L times how fast the current is changing. No change in current means no back emf, no matter how much current is flowing. This is the key fact that trips people up, and it mirrors how a capacitor with constant charge has constant voltage but zero current.

This sits right next to capacitors in the way the two components behave like opposites: a capacitor resists sudden changes in voltage, an inductor resists sudden changes in current. That symmetry is what drives the next topic, where inductors and capacitors trade energy back and forth in LC circuits, each one fighting to keep its own favorite quantity from changing.