Energy stored in an inductor

Also called Inductor energy, Magnetic field energy, U_L

The energy stored in an inductor sits in the magnetic field created by its own current, and equals one half the inductance times the square of that current. The AP Physics C E and M sheet prints it; AP Physics 2 has no inductors at all.

Statement 13.4.A.2 says it plainly: inductors store energy in the magnetic field that is generated by current in the inductor. The equation is

U_L = \tfrac{1}{2} L I^2

and it is printed on the AP Physics C: Electricity and Magnetism equation sheet, in one form only. Unlike the capacitor, there is no algebraic alternative to memorise, because $L$ and $I$ are the only two quantities involved.

Scope, stated cleanly. The words inductor and inductance appear nowhere in the AP Physics 2 course description, nowhere in AP Physics 1, and nowhere in AP Physics C: Mechanics. This is a Physics C: E&M quantity and only that.

Why the current cannot jump. Energy proportional to $I^2$ means changing the current means changing the stored energy, and doing that in zero time would demand infinite power. So an inductor's current is continuous through a switching event, which is the mechanical analogue of a mass refusing to change speed instantly. Set $\tfrac{1}{2}LI^2$ beside $\tfrac{1}{2}mv^2$ and inductance plays the part of mass.

The CED tracks where that energy goes: it can be dissipated through a resistor or used to charge a capacitor (13.4.A.2.i), and the transfer to other forms obeys conservation laws (13.4.A.2.ii). Those two destinations are exactly the LR circuit and the LC circuit.

Compare energy stored in a capacitor, which is held in an electric field instead and is the only such quantity AP Physics 2 examines.

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