Self Induction

When a current is established in a conductor, a magnetic field is produced in its vicinity. We can visualize this field in terms of magnetic flux. If steady current flows the number of lines of force at a given place would remain the same. But if the current changes with time, the flux associated with the loop changes and hence an e.m.f is induced in the loop. This phenomenon is called as self induction.

Self-induction is the property of a coil, which enables the induction of an EMF in it when the current in the coil changes.

Consider a coil carrying a current I having N turns and lets the magnetic flux f be linked with the coil. If the current in the coil is changed, the flux link also changes. Thus, according to Faraday's law of electromagnetic induction, induces an EMF on to itself. This EMF is called self-induced EMF and this phenomenon is called self-induction.

It is found that the flux linkage is proportional to the current through it.

i.e., f a I or f = LI

Here, L is constant and is called self-inductance of the coil or coefficient of self-induction.

S.I., the unit of self-inductance, is Henry

i.e., 1 Henry = 1 Weber turns / Ampereor 1 Henry = 1 Volt / ampere/second

Sub Topics

Definition
Self - Inductance of a Long Solenoid
Self Inductance of a Plane Coil
Energy Associated with Self-Inductance

Definition

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Self-inductance of a coil is 1 Henry when a current changes at the rate of 1 amp/sec through the coil induces EMF of 1 volt in the coil.

Self - Inductance of a Long Solenoid

A long solenoid is a wire whose length is very large as compared to its radius of turn. The magnetic field B at any point inside, such a solenoid is given by:

where N is number of turns

I is current

l is length of solenoid

The Magnetic flux linked with each turn of the solenoid is

Since q = 0

f = BA cos q

f = BA

Total magnetic flux linked with the solenoid = flux through each turn x total number of turns in the solenoid.

But f = LI

on comparing the two equations, we get

If an iron core is introduced inside the solenoid like

Then, if m_r is relative permeability of iron ore

Self Inductance of a Plane Coil

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If we consider a plane coil of radius r through which a current I ampere is flowing. If N is the number of turns of the coil, magnetic field at the center of the coil.

Magnetic flux per turn of the coil = BA

Total magnetic flux linked with N turns

But f = L I

Energy Associated with Self-Inductance

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If 'i' amperes of current is established in a coil in time 'dt', then 'dw' amount of work done if 'e' stands for the induced e.m.f.

dw = -eIdt

The total work done to build up current from 0 to i₀_.