Define self inductance and give its SI unit. Derive an expression for the self inductance of a long air-cored solenoid, and write the energy stored in an inductor.

1. 1 · Define. Self inductance L = NΦ/I, the flux linkage per unit current; ε = −L dI/dt. SI unit henry (H).
2. 2 · Describe the solenoid. Length l, area A, n turns per unit length, current I; total turns N = nl.
3. 3 · Draw it. [Long solenoid with current arrows; field lines inside parallel to the axis; l and A marked]
4. 4 · Find the flux linkage. B = μ₀nI; NΦ = (nl)(μ₀nI)A = μ₀n²AlI.
5. 5 · Get L. L = μ₀n²Al; with a core, L = μrμ₀n²Al.
6. 6 · Energy stored. Work against the back emf: dW = LI dI, so W = ½LI², stored in the magnetic field.
7. 7 · Real life. The spark at a switch when a motor is turned off shows a large back emf.
8. 8 · Close in one line. So, L depends only on geometry and core, and an inductor stores ½LI².

Scoring tip: Write B = μ₀nI before using it, and say that you are ignoring edge effects.