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Induction is the magnetic flux that is relative to the rate of change of the magnetic field. The induced EMF across a coil is directly proportional to the rate of change of current through it. The proportionality constant in that relationship is known as inductance. The SI Unit of inductance is H (henry). It is represented as L. 1 H (Henry) is defined as the amount of inductance required to produce an EMF of 1 (V) volt in a coil when the current change in the coil is at the rate of 1 Henry.
Read Also: Magnetism and Matter
Key Terms: Magnetic Flux, Magnetic Field, EMF, Inductance, Electromagnetism, Faraday’s law, Electromagnetic Induction, Electric current,
What is Inductance?
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Inductance is the ability of an inductor to store energy in the magnetic field created by the flow of electrical current. Energy helps to set up the magnetic field and should be released when the field falls.
Inductance is used in two ways:
- Self Inductance
Self-inductance is the property of a circuit, often a coil. A change in current causes a change in voltage in that circuit due to magnetic effect of caused by the current flow. Self-inductance applies to a single circuit, typically within a single coil. This effect is used in single coils or chokes.
- Mutual Inductance
Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.
Inductance
Factors Affecting Inductance
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According to the factors that affect the inductance:
- Number of turns in the wire
A higher number of turns of wire in the coil leads to greater inductance. Fewer turns of wire in the coil results in lesser inductance. In comparison, more coils of wires cause a greater amount of magnetic field force for a given amount of coil current.
- Permeability of the Core
The greater the coil area, the greater the inductance. A lesser coil area results in less inductance. A greater coil area presents less opposition to the formation of magnetic field flux, for a given amount of field force.
- Area of the Coil
The greater the magnetic permeability of the core to which the coil is wrapped around, the greater the inductance; the lesser the permeability of the core, the lesser the inductance.
- Length of the Coil
The longer the coil’s length, the lesser the inductance. The shorter the coil’s length, the greater the inductance.
Faraday Laws of Electromagnetic Induction
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Faraday’s law of electromagnetic induction is a basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction and is simply referred to as Faraday's law.
Based on his experiments, Faraday derived two laws circulating around Electromagnetic Induction:
- Faraday’s First Law states that “Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced which is called induced current.”
- Faraday’s Second Law states that “the induced EMF in a coil is equal to the rate of change of flux linkage.
Formula For Magnetic Induction
From Faraday’s law, the EMF induced in a closed circuit is given by –
\(\epsilon = \frac{d\Phi_{b} }{dt}\)
Here, Φb is the magnetic flux, t is the time and ε is the EMF induced.
Note:
\(\Phi_{b} = \oint\vec{B}\cdot d\vec{s}\)Where B = magnetic field and “ds” is a very small area.
In a coil of wire with N turns, the EMF will be- \(\epsilon = \frac{d\Phi_{b} }{dt}\)
The induced EMF sets up a current in such a way that the magnetic effect produced by it competes with the very cause producing it.
Solved Example on Faraday’s Law of Magnetic InductionExample: A loop of area 200 cm2 is positioned perpendicular to a uniform magnetic field. Without changing in direction of the magnetic field, its magnitude is reduced by 0.08T in the time interval 0.02s. Find the average induced emf in the loop? Solution: As per Faraday's law of induction equation, a changing magnetic flux through a closed surface bounded by a wire, creates an emf with a magnitude of \(\mathcal{E}=|\frac{\Delta \Phi_m}{\Delta t}|\). Flux through a surface area A is defined as: \(\Phi_m=\vec{B}\cdot\hat{n}\) is a unit vector (a vector whose its magnitude is unity) normal (perpendicular) to that surface. In this example, the area and its direction is fixed so the only factor changes is the magnitude of the magnetic field. Thus, the change in the flux is written as below: \(\begin{align*}\Delta \Phi_m&=A\Delta B\\&=\left(200\times 10^{-4}\right)(-0.08)\\&=-16\times 10^{-4}\quad {\rm Wb}\end{align*}\) Next, use Faraday's law formula to find the magnitude of the average induced emf \(\begin{align*}\mathcal{E}&=\left|\frac{\Delta \Phi_m}{\Delta t}\right|\\ \\ &=\left|\frac{-16\times 10^{-4}}{0.02}\right|\\ \\&=0.08\quad {\rm V}\end{align*}\) |
Also Read:
| Related Articles | ||
|---|---|---|
| Experiment Faraday Henry | Emf Formula | Magnetic Flux Formula |
| Electromagnetic Induction Important Questions | Electromagnetic Induction MCQ | Electromagnetic Induction NCERT Solutions |
Types of Inductance
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There are two main types of inductance:
- Self Inductance
- Mutual Inductance
| Self Inductance | Mutual Inductance |
|---|---|
| This method of the conductor due to which it competes with any decrease and increase or current of flux through it is known as Self Inductance. | When there is a change in the current or magnetic flux linked with two coils, an opposing electromotive force is produced across each coil, and is known as Mutual Induction. |
What is Self Inductance?
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As the name suggests, Self Induction occurs when the coils induce the EMF themselves. The change in the magnetic flux through the coil causes the current to be induced by itself. So once the current gets induced, the current tries to oppose the flux. Here NΦ ∝ I.
A conductor is said to have a self-inductance of 1 H (Henry) if a current of 1 ampere when flowing through it produced flux linkages of 1 Wb turn in it.
L= N Φ/I Henry
Where L is named as self-inductance of the coil or the coefficient of the self-inductance. The self-inductance depends on the cross-sectional field, the permeability of the number of turns of the material, turns in the coil, etc.
The video below explains this:
Self Inductance and Inductor Detailed Video Explanation:
What is Mutual Inductance?
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Mutual Inductance depends upon the proximity between two coils.
Two coils placed near each other take turns to carry the current which creates the magnetic field. The proximity of the two coils to each other causes the magnetic field to pass through from one coil to the other. So one coil causes the change in magnetic flux because of which current is induced in the other coil.
Mutual Inductance
Difference between Mutual Inductance and Self-Inductance
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Difference between Mutual Inductance and Self-Inductance is elaborated in the table below:
| Mutual Inductance | Self Inductance |
|---|---|
| Mutual inductance is the characteristic of a pair of conductors. | Self Inductance is the characteristic of the conductors themselves. |
| The induced current advanced in the neighboring coil faces the decay of the current in the coil when the main current in the coil reductions. | The induced current faces the decay of current in the coil when the main current in the coil reductions. |
| The induced current industrialized in the neighboring coil faces the growth of current in the coil when the main current in the coil grows. | The induced current opposes the development of current in the coil when the main current in the coil grows. |
Inductance Formula
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We know that at whatever point an electric flow moves through a coil, a magnetic area encompassing it is produced. Varying current outcomes in a differing magnetic area. Because of this, the magnetic flux varies and electromotive power is induced. The inductance value is of two types.
Formula for Inductance
| L=μN2A/l |
Where,
- L = inductance in henry (H)
- μ = permeability (Wb/A.m)
- N = number of turns in the coil
- A = area encircled by the coil
- l = length of the coil(m)
Solved ExamplesQues. A coil has inductance 4 H and supply frequency 50 Hz. Find out the reactance? Solution: Inductance (L) = 4 H Frequency (f) = 50Hz X = 2 π f L = 2 × 3.14× 50 × 4 X= 1256 Ω Ques. Three coils are connected in series. Each coil has an inductance of respectively 4 H, 6 H, and 8 H. Find out the equivalent inductance. Solution: L1 = 4 Henry L2 = 6 Henry L3 = 8 Henry The series inductance all sum as L = L1 + L2 + L3 = 4 + 6 + 8 = 18 H |
Derivation of Inductance
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Consider a DC source with its switch on. At the point when the switch is turned on, the current streams from zero to a specific worth with the end goal that there is a change in the pace of current streaming. Let φ be the change in flux because of the current stream. The change in flux is concerning time which is provided as:
dφ/dt
Apply Faraday’s law of electromagnetic induction,
E = N(dφ/dt)
Where,
E = -N(dφdt)
Previous Year Questions
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- If a current of 2.0A2.0A flows through the smaller loop, then the flux linked with bigger loop is…… [JEE Main 2013]
- A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B….. [JEE Main 21018]
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Things to Remember
- Induction is the magnetic flux that is relative to the rate of change of the magnetic field.
- The induced EMF across a coil is directly proportional to the rate of change of current through it.
- The proportionality constant in that relation is known as inductance.
- The SI Unit of inductance is H (henry). It is represented as L.
- Faraday’s law of electromagnetic induction is a basic law of electromagnetism which predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).
- This phenomenon is known as electromagnetic induction and is simply referred to as Faraday's law.
- Mutual inductance is the characteristic of a pair of conductors but Self Inductance is the characteristic of the conductors themselves.
Relatable Links:
Sample Questions
Ques. What is the SI unit of the inductance? (1 Mark)
Ans. The SI unit of Inductance is henry. It is symbolized with an H.
Ques. What are the factors affecting Inductance? (2 marks)
Ans. Inductance is influenced by the following factors:
- Number of turns of the coil
- Area of the conductor
- Length of the conductor
- Permeability of the core
Ques. What is the formula of inductance? (2 marks)
Ans. The formula of inductance is
L= L=μN2A/l
Ques. The field winding of a DC electromagnetic is wound with 960 turns and has a resistance of 50 Ω when the stirring voltage is 230 V. The magnetic flux linking the coil is 0.005 Wb. Compute the Self-Inductance of the conductor and the energy stored in the magnetic field. (2 marks)
Ans. The formula used:
L = Nφ/I Henry
Current through coil = 230/50 = 4.6 A
Φ= 0.00 Wb, N = 960
L = 960×0.005/4.6 = 1.0435 Henry.
Energy stored = 11.04 J
Ques. If a conductor of 150 turns is linked with a flux of 0.01 Wb when carrying a current of 10 A, compute the inductance of the coil. If this current is consistently reversed is 0.01 second computing the induced electromotive force? (2 marks)
Ans. L = Nφ/I = 150×0.01/10 =0.15 Henry
eL = L dI/dt; dI = - 10 – (-10) = 20 A
eL = 0.15×20/0.01 = 300 V
Ques. Define self-inductance of a coil. Write its S.I. unit. (All India 2010)
Ans. Self-induction is the property of a coil by virtue of which it opposes the growth or decay of the current flowing through it.
S.I. unit of self-inductance is henry (H).
Ques. Predict the directions of induced currents in metal rings 1 and 2 lying in the same plane where current I in the wire is increasing steadily.
Ans. In metal ring 1, the induced current flows in the clockwise direction.
In metal ring 2, the induced current flows in the anticlockwise direction.
Ques. Predict the direction of the induced current in the rectangular loop abed as it is moved into the region of a uniform magnetic field 
directed normal to the plane of the loop. (Comptt. All India 2012)
Ans. The direction of the induced current in the given rectangular loop is anti-clockwise, i.e., cbadc
Ques. The current through two inductors of self-inductance 12 mH and 30 mH is increasing with time at the same rate. Draw graphs showing the variation of the
(a) emf induced with the rate of change of current in each inductor
(b) energy stored in each inductor with the current flowing through it.
Compare the energy stored in the coils, if the power dissipated in the coils is the same. (Comptt. All India 2017)
Ans.
Comparison of energy stored :
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