Self Inductance Simplified Explanation

Self Inductance :

It is defined as the induction of a voltage in a current carrying wire when the current in the wire is itself changed. Hence changing current in a circuit generates a new voltage in the circuit. Hence it is called self inductance.  
                  [or]
It is the property of a coil/conductor by which it opposes change in current in itself.

We know that B ∝ I and  Φ ∝ B

∴ Φ ∝ I

∴ Φ= LI 
 (where L is the coefficient of self induction)

If current in the coil changes at a rate ΔI = dI/dt, then EMF induced in coil due to change in its own current is: e= dΦ/dt

 (where e is induced EMF)

∴ e= L[dI /dt] 
This is the magnitude. The induced EMF always opposes the very cause producing it.

∴ with direction it is written as 

e= - L[dI /dt]

Here's the explanation:

We have taken two circuits. In the 1st one, we have a battery with EMF = E, a galvanometer, a resistance R, and of course connecting wires.

In the 2nd circuit, all the components remain the same as in the first circuit except that we have added a loop in the circuit.

When we complete the circuit in case 1, when we apply ohms law [ V=IR], the value of current is E/R. The reading of the galvanometer suddenly increases E/R. This is because there is not much resistance in the circuit.

Now lets talk about case 2. When we complete the circuit, current flows in the loop. Due to this the loop produces a magnetic field. In the time taken to reach E/R, the current in the circuit is increasing. The current in the loop produces a magnetic field. Now, while the current is increasing in the loop, the magnitude of the magnetic field also changes(it increases). Since the magnitude of magnetic field is changing, the magnetic flux associated with the loop is also changing in that small time interval from 0 current to E/R. 

Hence, change in value of current creates a change in the magnitude of magneric field of the loop which causes a change in the magnetic flux associated with the loop.

To oppose the change in magnetic flux the loop generates its own EMF and hence induces a current which flows opposite to the original current.

In the above picture, the red arrows depict the direction of induces current in the loop. Because of this extra resistance of current, the current in the circuit rises slower compared to the first circuit. Hence the galvanometer takes more time to reach E/R. But this is only when the current in the circuit is rising, one it reaches E/R, there would no longer be a change in magnetic flux and hence the induced current disappears. 


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