- Self Induction Definition: Self induction is a phenomenon where a changing electric current induces an emf across the coil itself.
- Self Inductance: Self inductance is the ratio of the induced emf across a coil to the rate of change of current through it, denoted by L and measured in Henry (H).
- Lenz’s Law: The induced emf opposes the change in current, which is why there is a negative sign in the equation, following Lenz’s Law.
- Faraday’s Law: By applying Faraday’s Law of Electromagnetic Induction, the induced emf in a coil can be calculated from the changing magnetic flux.
- Inductive Reactance: In AC circuits, self-inductance results in inductive reactance (XL = 2πfL), which depends on the frequency of the AC supply.
Self Induction
Self induction is a phenomenon by which a changing electric current produces an induced emf across the coil itself.
Self Inductance
Self inductance is the ratio of the induced emf (electromotive force) across a coil to the rate of change of current through the coil. We denote self inductance with the letter L, and its unit is Henry (H).
Since, the induced emf (E) is proportional to the current changing rate, we can write, 
But the actual equation is
Why there is Minus (-) sign?
According to Lenz’s Law, the induced emf opposes the direction of the rate of change of current. So their value is same but sign differs.
Derivation of Inductance
For the DC source, when the switch is ON, i.e. just at t = 0+, a current starts flowing from its zero value to a certain value and with respect to time, there will be a rate of change in current momentarily. This current produces changing flux (φ) through the coil. As current changes flux (φ) also changes and the rate of change with respect to the time is 
Now by apply Faraday’s Law of Electromagnetic Induction, we get,
Where, N is the number of turn of the coil and e is the induced EMF across this coil.
By considering Lenz’s law, we can modify the equation to show the induced emf as:
Now, we can modify this equation to calculate the value of inductance.
So,
[B is the flux density i.e. B =φ/A, A is area of the coil],
[Nφ or Li is called magnetic flux Linkage and it is denoted by Ѱ]
Where H is the magnetizing force due to which magnetic flux lines flow from south to north pole inside the coil, l (small L) is the effective length of the coil and
r is the radius of the coil cross-sectional area.
Self inductance (L) is a geometric quantity, depending on the solenoid’s dimensions and the number of turns. In a DC circuit, self-inductance only has a momentary effect when the switch is first closed. After a while, the current steadies, and the effect of self-inductance fades.
In an AC circuit, the alternating current constantly causes self-induction in the coil. This self-inductance results in inductive reactance (XL = 2πfL), which depends on the frequency of the AC supply.
