Inductor and its inductance

 

Inductor and its inductance

A current in a conductor produces a magnetic field surround it.  The strength of this field depends upon the value of current passing through the conductor. The direction of the magnetic field is found by using   

 Right hand grip rule which shown in the figure. If you hold the current carrying conductor by your right hand as shown in the figure the thumb shows the direction of current whereas the other four finger indicate the direction of magnetic flux lines

Here the flux pattern for this magnetic field would be number of concentric circle perpendicular to the direction of current.    now if we wound the conductor in the form of a coil or solenoid it can be assumed that there will be concentric circular flux lines for each individual turn of the coil as shown but it is not possible practically as if concentric circular flux lines for each individual turn exist they will intersect each other however since lines of flux cannot intersect the flux lines for individual turn will distort they form complete flux loops around the whole coil as shown this flux pattern of the current carrying coil is similar to a flux pattern of a bar magnet as shown.  Now if the current through the coil is changed the magnetic flux produced by it will also be changed at the same rate as the flux is around the coil this changing flux obviously links the coil now according to faraday’s law of electromagnetic induction if changing flux links with a coil there will be an induced EMF in it. And according to lenz’s law this induced EMF opposes every cause of producing it hence the induced EMF is in opposite of the applied voltage across the coil. hence self-induced EMF in the coil is produced due to some changing flux and the changing flux is caused by changing current in the coil so it can be concluded that self-induced EMF is ultimately due to changing current in the coil and self-inductance is the property of a coil or solenoid which causes the self-induced EMF to be produced in the coil or solenoid

When the current through it changes now mathematically this can be written as

-

Where minus shows that the induced EMF opposes the supply voltage and  is the rate of change of current through the coil with respect to time the above equation can also be written as

                      -                   (1)

 

where L is the constant of proportionality and the (L) is defined as the self-inductance of the coil or solenoid determines how much EMF induced in a coil for a specific rate of change of current through it however the induced EMF is basically due to the rate of change of flux linkages. Thus the EMF may also be calculated by faraday’s law of electromagnetic induction as follows

                       -                   (2)

Where (N) is the number of turns in the coil and  is the rate of change of flux linkage with respect to time with one turn now from equation (1) and (2) we get

 =

Integrating both side

                           

 (3)

From the above expression inductance can also be defined as if the current (I) Flown