Self-inductance of a coil

 Self-inductance of a coil

1) Self-inductance is the property of a coil by virtue of which a coil opposes any change of current through the coil.

2) This opposition is done by inducing an emf by the coil itself.

3) When a constant current is flowing through a coil then there is no self-inductance.

4) But when there is a change in the amount of current passing  through the coil, then there is a problem. That is the self-inductance.

5) Suppose there is a coil  having

n = no of turns per unit length of the coil

l = length of the coil

A = area of cross-section of the coil

I = current flowing through the coil

5) Then according to inductance

 

Where L is a proportionality constant  called co-efficient of self-inductance.

Now

N  = n l

Then the induce emf is

6) Magnetic field inside the coil is

But we know

So,

Now for N no of turns

But we know N  = n l

 

Since 

So,

Or

Which is the co-efficient of self-inductance.