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Define Self Inductance and Mutual Inductance

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Last updated date: 20th Feb 2024
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Introduction:

Inductance is basically a property that describes the ability of a circuit element, typically a coil or solenoid, to generate an electromotive force (EMF) in response to changes in the current flowing through it. Inductance plays a crucial role in various applications, ranging from power transmission and distribution systems to the operation of electronic devices. Have you ever wondered how an MRI machine produces detailed images of our internal organs? Well, self and mutual inductance are at play here. The powerful magnetic fields generated by the MRI machine rely on the principles of inductance to create images that aid in medical diagnoses. This real-life application of inductance showcases its importance in the healthcare field, where it enables us to peer inside the human body and diagnose ailments accurately.


Self Inductance:

Self-inductance is the ability of a component, such as a coil or a solenoid, to generate an opposing force within itself when the electric current flowing through it changes. This opposite force arises due to the interaction between the switching current and the magnetic field it produces. The magnitude of self-inductance is measured in henries (H) and depends on the geometry of the component, the number of turns of wire in the coil, and the properties of the materials used to construct the coil.


Self-inductance applications include tuning circuits, inductor relays, sensors, ion motors, and transformers.


Mutual Inductance:

Mutual inductance refers to the interaction between two separate circuits in close proximity to each other. When the current in one circuit changes, it produces a changing magnetic field. This magnetic field links with the nearby circuit, inducing a voltage within the coils. The magnitude of mutual inductance is measured in henries (H).


This phenomenon is termed as mutual inductance as it demonstrates how the changing magnetic field created by one coil influences the behaviour of the adjacent coil. By studying mutual inductance, we gain insights into the intricate relationship between magnetic fields and electrical currents, leading to a deeper understanding of electromagnetic phenomena and their applications in various fields of science and technology.


Mutual inductance applications include transformers, pacemakers, digital signal processing, electric cloth dryers, coil balancing, and metal detectors at airports.


Mathematical Form of Inductance:

As it is clear that the inductance is the property of the material so it depends only on the dimensions of the material that is the length, area of cross-section, number of turns and permeability of free space.


The Mathematical form of Self Inductance:

The self-inductance of a coil or inductor is given by the equation:


$L=\frac{{{\mu }_{\circ }}{{N}^{2}}A}{l}$


where:


L is the self-inductance in Henry (H).

$\mu _{\circ }$ is the permeability of free space (approximately $4π × 10^−7$ H/m).

N is the number of turns in the coil.

A is the cross-sectional area of the coil's core.

ℓ is the length of the coil's core.


The Mathematical form of Mutual Inductance:

The mutual inductance between two coils, typically denoted as Coil 1 and Coil 2, is expressed as


$L=\frac{{{\mu }_{\circ }}{{N}_{1}}{{N}_{2}}A}{l}$


where:


M is the mutual inductance in Henry (H).

$\mu _{\circ }$ is the permeability of free space.

N₁ is the number of turns in Coil 1.

N₂ is the number of turns in Coil 2.

A is the area shared by the two coils' magnetic fields.

ℓ is the distance between the coils.


Difference Between Self and Mutual Inductance:

Self-inductance is the property of a single component, while mutual inductance is the interaction between two separate circuits or coils. The self-inductance depends on the component's geometry and materials, while mutual inductance is influenced by the proximity and orientation of the circuits or coils.


The other difference is shown in the below table:


Self-Inductance

Mutual Inductance

Self-inductance refers to the property of an electrical component, such as a coil, to generate an opposing electromotive force (EMF) when the current passing through it changes.

Mutual inductance refers to the interaction between two separate electrical circuits, where a changing current in one circuit induces an electromotive force (EMF) in the other circuit.

Self-inductance occurs within a single component due to the interaction between the changing magnetic field produced by the current and the component's own turns of wire.

Mutual inductance occurs when the magnetic field produced by one circuit links with the other circuit.

It opposes changes in the current flowing through the component.

It transfers energy between the two circuits and can result in voltage and current changes in the secondary circuit.

Self-inductance is represented by the symbol 'L'.

Mutual inductance is represented by the symbol 'M'.

The unit of self-inductance is Henry (H).

The unit of mutual inductance is Henry.


Self and Mutual Inductance Reaction

Self-inductance and mutual inductance are phenomena observed in electrical circuits due to the presence of inductors or coils. Let's explore the reactions associated with self-inductance and mutual inductance:


Self-Inductance Reaction:

Self-inductance occurs within a single coil or inductor when the current passing through it changes. The reaction to changes in current in a self-inductor is as follows:


  • Opposition to Change: Self-inductance generates an opposing electromotive force (EMF) in response to any alteration in the current flowing through the coil.

  • Induced EMF: The self-induced EMF in a coil tends to oppose the change that caused it. This effect is described by Lenz's law, which states that the induced EMF in a coil opposes the change in current.

  • Energy Storage: Self-inductance allows for the storage of energy in the magnetic field created by the changing current. The coil resists rapid changes in current and releases the stored energy when the current decreases.


Mutual Inductance Reaction:

Mutual inductance occurs when two separate coils, referred to as the primary and secondary coils, are placed in proximity. The reaction to changes in current in the primary coil affects the secondary coil as follows:


  • Induced EMF: When the current in the primary coil changes, it generates a varying magnetic field. This changing magnetic field induces an electromotive force (EMF) in the secondary coil.

  • Transfer of Energy: Mutual inductance enables the transfer of energy between the primary and secondary coils. The changing magnetic field in the primary coil induces a corresponding voltage in the secondary coil, facilitating the transfer of electrical energy.

  • Step-Up and Step-Down: Mutual inductance is utilized in transformers to step up or step down the voltage levels of electrical energy. Transformers efficiently transfer electrical power at different voltage levels by varying the number of turns in the primary and secondary coils.


There are various examples of self-inductance and mutual inductance reactions examples. Both reactions are fundamental to understanding the behaviour of inductors and electromagnetic devices. These reactions highlight the interplay between changing currents, magnetic fields, and induced EMFs, ultimately shaping the operation of electrical circuits and facilitating energy transfer in various applications.


Summary:

Understanding what is self inductance and mutual inductance reaction is essential for students. Self-inductance refers to the tendency of a single component to resist changes in the current flowing through it. On the other hand, mutual inductance involves the interaction between two separate circuits, where changes in one circuit induce an electromotive force (EMF) in the other circuit. These principles have practical applications, such as energy storage in inductors and power transmission in transformers. By grasping the differences between self and mutual inductance, NEET students can build a strong foundation in electromagnetism and apply their knowledge to solve real-world problems in the field of electrical engineering.

FAQs on Define Self Inductance and Mutual Inductance

1. Can self-inductance and mutual inductance occur simultaneously in a circuit?

Yes, self-inductance and mutual inductance can coexist in a circuit. In complex circuits with multiple inductors, both self-inductance within individual inductors and mutual inductance between different inductors can occur.

2. Are there any practical applications where self-inductance and mutual inductance play a significant role together?

Yes, one such application is the transformer. Transformers utilize mutual inductance to transfer electrical energy from one coil to another by inducing a voltage across the secondary coil based on the changing magnetic field produced by the primary coil.

3. Can mutual inductance exist between two coils that are physically separated?

Yes, mutual inductance can exist even if the coils are physically separated. As long as there is a magnetic field generated by one coil that passes through the other coil, mutual inductance can occur.

4. Is the mutual inductance can be negative?

No, mutual inductance is always considered positive. The polarity of the induced voltage may be positive or negative, depending on the relative orientations of the coils and the direction of the changing current.