The physics
A current in a coil sends a magnetic flux through the coil itself. When the current changes, the flux changes. So the coil makes an emf in itself. This is self-induction.
ε = L |Δi| / Δt L in henry (H)
The emf opposes the change. A falling current gets a push along it. A rising current gets a push against it.
A fast switch-off gives a big kick. It can light a neon lamp across the coil, far above the cell's voltage.
E − i R − L di/dt = 0 VB − VA = −iR + E − L di/dt
In an induction coil, breaking the primary's current makes an emf in the secondary. Its size is M di/dt. It can reach kilovolts and make a spark.
ε₂ = M I / t