Energy of the magnetic field
The magnetic field around a current-carrying coil has energy: while the current is raised from zero to I, the source does work against the self-induced EMF, and this work is stored as field energy. Since the flux Φ = L·I is proportional to the current, the graph Φ(I) is a straight line and the work equals the area of the triangle under it: A = I·Φ/2. Hence W = I·Φ/2 = L·I²/2: the energy is proportional to the inductance and to the square of the current. If the current doubles the energy becomes four times larger; L plays the role of mass and I the role of speed, so W = LI²/2 resembles the kinetic energy mυ²/2. When the current is broken, this energy does not vanish: it is released as the self-induction current, or as the heat and light of a spark. A coil with a ferromagnetic core has a large L and so more energy at the same current; electromagnetic cranes use the force of such a field to lift loads.
In your notebook compute W for L = 2 H and I = 1, 2, 3, 4 A and draw the graph of W against I (a parabola). In real life only a specialist connects and breaks the circuit of a coil with a large inductance: a high voltage and a spark can appear when it is broken.