Energy Stored in an Inductor

A steady current in a coil looks static, nothing visibly moving the way a stretched spring or lifted mass does. But the coil built a magnetic field to get to that steady current, and building that field cost work. While the current was ramping up from zero, the changing flux induced a back-EMF that opposed the increase, and the source had to push against it. That pushed-in energy did not vanish once the current stopped changing. It stays stored in the magnetic field, ready to be released if the current is allowed to drop.

To find how much energy got stored, go back to the fight itself. At any instant the source supplies power P = I V, and the inductor's voltage is V = L dI/dt. So the power delivered is L I dI/dt, and the energy delivered is the integral of L I dI as I climbs from 0 to its final value. That integral gives (1/2) L I² directly, the same way integrating a spring force k x dx gives (1/2) k x^2. A bigger inductance or a bigger current means a harder fight and more stored energy.

This sits right next to capacitor energy as the magnetic twin of an electric idea. A capacitor stores (1/2) C V² in its electric field; an inductor stores (1/2) L I² in its magnetic field. Written as energy densities, u_E = (1/2) epsilon₀ E² and u_B = B² / (2 mu₀) have the same skeleton: a constant from empty space times field strength squared. That parallel is the bridge into circuits where inductors and capacitors trade energy back and forth, oscillating between electric and magnetic storage.