Law of Self Inductance and How they Function

An electric current can be induced in a coil by flux change produced by another coil in its proximity or flux change produced by the same coil. In both cases, the flux through the coil is proportional to the current. 

That is-  ∅B∝I

For a closely looped coil of N turns, the same magnetic flux is linked with all the turns. When the flux ∅B through the coil changes, each turn contributes to the generated electromotive force. This is described using the term flux linkage which is equal to N∅B for a closely wound coil. In such a case- 

N∅B∝I

The constant of proportionality in this context is called inductance. It is affected by the shape of the coil and core material properties. It is a scalar quantity. Henry is the SI unit of inductance. It is denoted by H. It is named after Joseph Henry, an eminent physicist who discovered electromagnetic induction in the USA, independently of Faraday in England.

Law of Self Inductance

Sometimes, induction can happen when only a single device is present. When the flow of current is disturbed in a device, it also disturbs the magnetic field of that device and that can induce an opposing voltage in the same device. It is known as self-inductance. This opposing voltage acts as a second battery to the main one, opposing the primary voltage source and making it work more to do the same task. Henry is the SI unit of inductance. It is denoted by L. 

Self-inductance depends on the shape of the circuit. Straight wires have a small L, while wires in a loop have a large L.

The formula for the law of self-inductance is

L= N∅ (i)/ i

Where, 

N= number of turns

i= current in the circuit

∅ (i)= magnetic flux in the circuit due to the current.

Uses of self-inductance

Self-inductance is used in the following appliances-

• Tuning circuits
• Sensors
• Transformers
• Induction motors
• Chokes 
• Metal detectors
• Traffic lights 

Self-inductance is also used to store energy in a device. 

Characteristics of self-inductance

• It is a form of electromagnetic induction.
• Only one coil or wire or solenoid etc is used and a change in its current results in the generation of voltage.
• The voltage in the coil is self-induced
• The circuit element possessing the property of inductance is known as an inductor.
• Self-inductance follows Faraday’s law. 
• The number of turns of the coil is directly proportional to the amount of voltage in the coil. 
• Inductive reactance can be described as the fall in the current flow of a circuit due to induction. 
• Any metal object in the path of the circuit affects self-inductance. 
• Self-inductance also follows Lenz’s law. 
• The induced electromotive force in self-inductance across an inductor always opposes the change in the current. 
• Thus, if the current is increasing, the electromotive force will oppose the increase, if it is decreasing, the electromotive force will oppose the decrease and if the current is constant, there will be no electromotive force. 

Factors that affect self-inductance

The factors that affect self-inductance are as follows-

• The cross-sectional area of the coil
• Number of turns made by the coil
• The angle of the turns made by the coil
• The amount of space between the two coils
• The magnetic property of the medium in the coil that has the flux. 

Functioning of self-inductance

• A magnetic field is created when current passes through a coil. This magnetic field affects the wires or coils near it, as seen with mutual inductance. However, this magnetic field also affects the circuit from which it is set up. 
• The magnetic field can be imagined as a concentric circle and when the loops of the concentric circle merge, it forms self-coupling within the coil. 
• When the current in the coil changes, it results in the induction of voltage in the different loops due to self-inductance. 

Distinction between mutual inductance and self-inductance

Conclusion

Self-inductance can be described as the electromotive force induced when a coil’s magnetic field opposes the change of voltage and current in itself. Due to the change in the current in the circuit, the magnetic field is affected and voltage is induced opposing it. Henry is the SI unit of inductance. It is denoted by L.  When the primary current of the coil decreases, the secondary current opposes the decay of current in the coil. When the primary current of the coil increases, the secondary current opposes the increase of current in the coil. Self-inductance is used in traffic lights, sensors, Transformers, Induction motors, Chokes, etc.