Concept of Self Inductance

Self Inductance or Inductance is defined as the property of a material due to which it opposes the flow of current through it. It is usually denoted by ‘L’ and its SI unit is Henry. How a material possess such property? To understand, let us consider a coil having N number of turns and connect the coil through an AC source.

Qualitative Analysis of Self Inductance

Let the current flowing through the coil is i = ImSinωt. Since the current is changing through the coil, therefore the magnetic field will also change. If the cross sectional area of the coil is assumed to be A then magnetic flux linking a coil will be BA where B is magnetic flux density.

Total flux linkage through N turns Ø = NBA

According to Faraday’s Law of Electromagnetic Induction, the changing magnetic flux will cause an emf to develop. This induced emf in the coil will oppose the cause as per Lenz’s Law. Here cause is alternating current. Therefore the coil will oppose the flow of current. Thus at this point we came to know how current opposing property came in picture for a coil. But the next important thing is to have a mathematical determination of this property which is called as Self Inductance or Inductance.

Quantative Analysis of Self Inductance

Suppose the magnetic flux passing through a single coil carrying a current I is Ø. Then the self inductance or inductance of coil is defined as “flux linking the coil per unit current”.

Self Inductance

Therefore,

L = Ø / I

SI Unit: Tesla / Ampere which is known as Henry.

Calculation of Self Inductance of Solenoid

Based on the above quantative analysis, we will calculate the self inductance of a solenoid. Let us consider a solenoid of N turns having cross sectional area of ‘A’ and length be ‘L’ as shown below.

Self Inductance or Inductance

The magnetic field through the center of solenoid B = µ0NI / L

“It shall be noted here at this point that the magnetic field inside a long solenoid is uniform. But the filed outside the solenoid is almost zero. Here long solenoid does not mean solenoid of infinite length rather it means that length of solenoid is much larger than its radius.”

Therefore,

Total flux linking the solenoid Ø = B x number of turns x A

                                                    = µ0N2IA / L

Hence,

Self Inductance / Inductance of Solenoid = Ø / I

                                                                  = µ0N2IA / LI

                                                                  = µ0N2A / L

From the above expression of self inductance, it is clear that self inductance or inductance does not depend on the flux or current. It only depends on the geometry of the material. If you take an example of single phase transmission line then inductance of transmission line = 4πx10-7log(D/0.7788r) where D is the separation between the conductors and r is the radius. In this case also, inductance only depends on the geometry.

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