To calculate the self-inductance of a long solenoid of cross-sectional area A and length l, having n turns per unit length. The magnetic field due to a current I flowing in the solenoid is B = µ0 n I (neglecting edge effects, as before). The total flux linked with the solenoid is
where nl is the total number of turns. Thus, the self-inductance is,
If we fill the inside of the solenoid with a material of relative permeability µr (for example soft iron, which has a high value of relative permiability), then,
The self-inductance of the coil depends on its geometry and on the permeability of the medium.
The self-induced emf is also called the back emf as it opposes any change in the current in a circuit.
