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Self-inductance, a salient concept in the study of electromagnetism, talks about a coil or a circuit with varying current and its ability to induce an EMF(electromotive force) that opposes the EMF initially set up in the coil or circuit. An American physicist, Joseph Henry, was the first person to introduce the world to the concept of self-inductance. The unit of inductance has been named in his honour. The implication of self-inductance can be found in its application in a solenoid coil or an RL circuit. Self-induction depends on factors such as a coil’s length, geometry, and the medium used.
What is self inductance?
In the study of physics, some well-known facts help us understand the concept of self-inductance. These are:
- A current-carrying coil or circuit will generate a magnetic field
- With a change in the magnetic field lines that are linked to a coil or circuit, electromagnetic induction causes an EMF to be induced in the coil or circuit
- As a result, whenever a current-carrying coil or circuit experiences a change in the flow of electric current, a self-induced EMF is generated
As per the famous law of electromagnetism by the physicist Emil Lenz, popularly known as Lenz’s Law, by flowing in a direction opposite to the change, self-induced EMF strives to resist the cause which created it.
As a result, it was determined that self-inductance is the phenomenon of generating a self-induced EMF that then resists any change in the electrical state of a coil or a circuit.
ƐL (the EMF) is known as a self-induced emf.
How self inductance works
The electromotive force (EMF) generated across the coil during the self-inductance process is in proportion to the change in electric current (w.r.t. time) across the same coil.
We can say,
Electromotive force (EMF) ∝ Rate of change in current
e ∝ di∕dt |
Or,
e = L di∕dt |
Or,
L = e∕(di∕dt) |
Where,
‘L’ is self-inductance or the coefficient of self-induction.
The working of self-inductance can be described in the following steps:
- When the electric current (I) flows in a coil or circuit, some electric flux (𝛟) is produced inside the coil.
- At that moment of the self-induction phenomenon, the induced EMF generated inside the same coil opposes the rate of change of current in the coil.
- For DC cells, when the switch is on, that is when time (t) is just equal to 0+, a current will flow from its zeroth value to a certain value. Concerning time, there will be a rate of change in current momentarily, i.e. (di∕dt).
- The current produces magnetic field lines through the coil. As current changes its value from zero to a certain value, that is why magnetic flux (𝛟) gets a rate of change w.r.t. time, i.e. (d𝛟∕dt).
- Applying Faraday’s law in this coil,
e = N d𝛟∕dt |
Where,
N signifies the number of turns in the coil.
e signifies the EMF that is induced across this coil.
Also,
e = L di∕dt |
So
L i = N 𝛟 = NBA |
And
B = 𝛟∕A |
Where
A is the area (cross-sectional) of the coil
B is the flux density of the coil
Li or N𝛟 is the magnetic flux linkage and is denoted by Ѱ
Again
Hl = Ni |
Where
H is the magnetising force due to which magnetic flux lines flow from south to north pole inside the coil
L is the length of the used coil
L = NBA/i = N2BA/Ni = N2 𝛍HA∕Ni = N2 𝛍A∕L |
Or
L = 𝛍N2A∕L = 𝛍N2πr2∕L |
Where,
R is the radius of the coil’s cross-sectional area
The factors that influence self inductance
The factors that influence the constant of self-inductance ‘L’ are as follows:
- The coil geometry: More magnetic field lines are likely to be trapped by an arrangement with a coiled structure rather than a straight one
- The medium between coils: When a ferromagnetic material that is insulated is utilised as the coil’s core material, additional magnetic field lines are likely to become linked. As a result, the coefficient of self-inductance would increase in value
- The coil length: A longer coil induces a magnetic flux (ɸ) less than the one induced in a coil of a shorter length
Unit of self inductance
In the SI system, the units of self-inductance can be derived as
[Potential]∕{[charge]∕[time]2} -> Volts ∕ (Amp∕sec) |
- 1 Volt∕(Amp sec-1) is equivalent to 1 Henry.
A coil or a circuit is said to have a self-inductance of one henry if the magnetic flux linked with it equals one weber due to a current of one ampere in the same coil or circuit.
Or
A coil or a circuit is said to have a self-inductance of one henry when the current changes at the rate of 1 ampere per second, and the induced emf, set up in it, equals one volt.
The implication of self inductance
1. In a solenoid:
Assume that we have a solenoid that is uniformly wound with N turns and a length of L.
- Assuming that length L is much larger than the radius of the solenoid
The magnetic flux, through each turn of area (A), can be written as:
𝛟B = B A = 𝛍 n I A = 𝛍 (N∕L) I A |
The self-inductance is:
L = (N𝛟B)∕I = (𝛍 N2 A)∕I = 𝛍n2V |
Thus it is confirmed that the length L depends on the geometry of the solenoid.
2. In an RL circuit:
A circuit element with a high self-inductance is known as an inductor.
- We assume that the rest of the circuit’s self-inductance is negligible compared to the inductor
- A circuit will have some self inductance even if it does not have a coil
Conclusion
The phenomenon of self-inductance involves a change in the flow of electric current in a coil or a circuit. This coil itself opposes the changes by inducing an EMF within the same coil, implying that any other coil is not involved. The coefficient of self-inductance depends on the geometrical structure of the coil and the nature of the medium linked with the coil or circuit. The implication of self-inductance is found in its applications when used with an RL circuit or in a solenoid. It is observed that a circuit will have some self-inductance even if it does not have a coil, assuming that the rest of the circuit’s self-inductance is negligible.
