A current-carrying coil produces a magnetic field that links its own turns. If the current in the coil changes the amount of magnetic flux linking the coil changes and, by Faraday’s law, an emf is produced in the coil. This emf is called a self-induced emf.
Let the coil have N turns. Assume that the same amount of magnetic flux F links each turn of the coil. The net flux linking the coil is then NF. This net flux is proportional to the magnetic field, which, in turn, is proportional to the current I in the coil. Thus we can write NF ยต I. This proportionality can be turned into an equation by introducing a constant. Call this constant L, the self-inductance (or simply inductance) of the coil:
As with mutual inductance, the unit of self-inductance is the henry.
The self-induced emf can now be calculated using Faraday’s law:
The above formula is the emf due to self-induction.
Example
Find the formula for the self-inductance of a solenoid of N turns, length l, and cross-sectional area A.
Assume that the solenoid carries a current I. Then the magnetic flux in the solenoid is
