Mutual Inductance - Definition, Formula, Significance, Examples
Last Updated : 28 Jan, 2022
The topic of induction was first given by Oersted by discovering that a magnetic field is produced through an electric field. After this, different scientists started to think can the reverse is possible .i.e. can we produce electric current from a magnetic field.
Michael Faraday and Joseph Henry simultaneously established that an electric current is generated in a coil when the coil and a magnet are in relative motion. The current produced here is called induced current and e.m.f produced are called induced e.m.f. In this topic, we will see what is Electromagnetic Induction and one of its types which is Mutual induction.
Electromagnetic Induction
Electromagnetic induction is the phenomenon of changing magnetic flux or field causing an induced e.m.f. in a conductor or conducting coil. The idea of magnetic flux or field, which may be represented by magnetic field lines, is important to understand while researching electromagnetic induction. The direction of magnetic induction at any given place is determined by the tangent to the magnetic field lines.
There are two types of Electromagnetic Induction they are,
- Self Induction
- Mutual Induction
Mutual Induction
When two coils are kept near each other and current change in one coil is causing e.m.f change in other then this phenomenon is called mutual induction.
Consider the circuit given below,
As shown in the above figure, let there be two coils placed close to each other namely P and S. The coil P has a power source (E) and a key (k) and coil S has a galvanometer to detect the deflection. Here, let coil P be Primary coil and coil S be Secondary coil.
Working:
The galvanometer indicates momentary deflection in one direction and deflection in the other direction when key 'K' is closed. When the galvanometer shows that the current flowing through primary (P) is constant or zero when the key is turned open, no deflection is created in the galvanometer. However, when the current flowing through the main coil changes, a phenomenon is known as "Mutual Induction" occurs, and the secondary coil's e.m.f. is induced. We can see the induced e.m.f by checking the deflection in the galvanometer.
Magnetic Flux (φ): The number of magnetic field lines passing through a closed surface is known as magnetic flux. It calculates the total magnetic field that travels across a specific surface area.
Explanation:
The magnetic flux w.r.t coil S at any instance is related to the current flowing through the primary coil at that instance.
φs α ip
∴ φs = M×ip
Here, M is the coefficient of mutual inductance of the coil
So, we can find e.m.f. induced in the secondary coil (S) at any instant,
es = - dφs / dt
es = -d(M×ip)/dt
es = -M dip /dt
|es| = |-M dip/dt|
|es| = M dip / dt|
M = es / |dip / dt|
Coefficient of mutual induction: The coefficient of mutual induction can be defined as the ratio of e.m.f. induced in one coil to the rate of change of current in the next coil.
Mutual inductance depends on the number of turns on the coil, size of the coil, separation between each turn and the angle of the turns, and the medium where the coils are placed.
- S.I Unit of mutual inductance is Henry (H)
- Dimensions of mutual induction are [L2M1T-2I-2]
Examples of Mutual inductance
- An electric clothes dryer's heating coils can be counter-wound such that their magnetic fields cancel out, considerably lowering mutual inductance with the dryer's housing.
- The essential functioning principle of transformers, motors, generators, etc.
- All the electric components deal with a magnetic field.
Significance of Mutual Induction
- As discussed in previous examples the mutual induction is essential to all the electric equipment that uses a magnetic field so it is very significant in the modern world.
- Electric motors also use their principal and are a very important piece of equipment.
- A transformer's mutual inductance, also known as the coefficient of coupling, is a measurement of the efficiency with which power is transmitted from the primary to secondary coils.
- When two coils are placed close together, the magnetic field in one of them tends to connect with the magnetic field in the other. The second coil then generates a voltage as a result of this. Mutual inductance is the property of a coil that influences or modifies the current and voltage in a secondary coil.
- When two coils are placed close together, the magnetic field in one of them tends to connect with the magnetic field in the other. The second coil then generates a voltage as a result of this.
Eddy current and its relation to mutual induction
According to Faraday's law of induction, eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor. Within conductors, eddy currents flow in closed loops in planes perpendicular to the magnetic field.
Example of eddy current, speedometer in our vehicle.
Mutual induction is the principal cause of eddy current formation and generation in the test material. An alternating current is transmitted through a wire coil as the test material. An eddy cope device is then attached to the probe. Any conductive substance can be used for the next circuit. A magnetic field is generated in and around a coil when electricity is conducted through it. When a probe is introduced close to a conducting substance, the alternating magnetic field of the probe causes current to flow through it. These currents run in closed loops at right angles to the magnetic flux in a plane. Eddy currents are what we call them.
These eddy currents generate their magnetic field, which interacts with the coil's primary magnetic field. Analyzing the variances in the resistance and inductive reactance of the provided coil might provide information about the test material.
Coupling Coefficient: It's the open circuit to actual voltage ratio, as well as the ratio obtained if the flux is connected from one circuit to the other. It is related to mutual inductance and is a simple approach to comprehend the relationship between certain inductor orientations and arbitrary inductance.
Sample Questions
Question 1: Why is this inductance called "mutual Induction"?
Answer:
This induction is produced by two the induction produced on each other by two adjacent circuits thus it is the current produced Mutually between two circuits thus it is named mutual induction.
Question 2: What is the induced e.m.f. in a circular coil kept in a magnetic field?
Answer:
There is no variation in magnetic flux created since the coil is in a homogeneous magnetic field. As a result, the coil has no induced e.m.f.
Question 3: What are the S.I Unit and Dimensions of Mutual Induction?
Answer:
S.I Unit of mutual inductance is Henry (H) and Dimensions of mutual induction are [L2M1T-2I-2]
Question 4: What factors have an impact on mutual inductance?
Answer:
The factors that effects the mutual inductance are:
- Cross-sectional area
- Number of turns
- the amount of space between the two coils.
- Medium permeability between the two coils
- Dimensions
Question 5: What is magnetic flux?
Answer:
Magnetic Flux (φ): Magnetic flux is the number of magnetic field lines traveling through a closed surface. It determines the overall magnetic field that goes across a certain region.
Question 6: Where do we use the principle of mutual induction?
Answer:
We mostly use mutual induction in, transformers, generators, and all the electronic devices which use a magnetic field.
Question 7: Two coaxial coils are very closer to each other and their mutual inductance is 10mH. If a current (60 A) sin 600t is passed in one of the coils, then find the peak value of induced e.m.f. in the secondary coil.
Answer:
i = 60 sin 600t
e.m.f. here can be given by,
e = -M di/dt
e = -(10 × 103) d (60 sin 600t)/dt
e = -10 × 103 × 60 cos 600t ×600
e = -360 cos 600t
Thus according to the Mutual induction formula
e = M×ip
Induced e.m.f. in secondary coil is 360V
Similar Reads
Chapter One Electric Charges and Fields
Chapter Two Electrostatic Potential and Capacitance
Electric Potential Due to a Point ChargeElectric forces are responsible for almost every chemical reaction within the human body. These chemical reactions occur when the atoms and their charges collide together. In this process, some molecules are formed and some change their shape. Electric forces are experienced by charged bodies when t
7 min read
Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
11 min read
Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
9 min read
Electric Potential Of A Dipole and System Of ChargesElectric Potential is defined as the force experienced by a charge inside the electric field of any other charge. mathematically it is defined as the ratio of electric potential energy that is required to take a test charge from infinity to a point inside the electric field of any other charge with
7 min read
Potential Energy of a System of ChargesWhen an external force works to accomplish work, such as moving a body from one location to another against a force such as spring force or gravitational force, that work is collected and stored as the body's potential energy. When the external force is removed, the body moves, acquiring kinetic ene
11 min read
Potential Energy in an External FieldWhen an external force operates to conduct work, such as moving a body from one location to another against a force like spring force or gravitational force, the work is gathered and stored as potential energy in the body. When an external force is removed, the body moves, acquiring kinetic energy a
11 min read
Electrostatics of ConductorsWhen an external force is used to remove a body from a situation. Point to another in the face of a force like spring or gravitational force That work is stored in the body as potential energy. When the external environment When a force is eliminated, the body moves, gaining and losing kinetic energ
11 min read
Dielectrics and PolarisationHave you noticed how many of the insulators are made of wood, plastic, or glass? But why is that? When we utilise wood or plastic, why don't we receive electric shocks? Why do you only get severe shocks from metal wires? We'll look at dielectrics, polarisation, the dielectric constant, and more in t
10 min read
What is a Parallel Plate Capacitor?Answer: A Parallel Plate Capacitor is a capacitor with two parallel conducting plates separated by an insulating material and capable of storing electrical charge. Capacitance can be defined in Layman's terms as a physical quantity that indicates the ability of a component or circuit to collect and
8 min read
Capacitors in Series and ParallelCapacitors are special devices that can hold electric charges for instantaneous release in an electric circuit. We can easily connect various capacitors together as we connected the resistor together. The capacitor can be connected in series or parallel combinations and can be connected as a mix of
7 min read
Energy stored in a CapacitorCapacitors are used in almost every electronic device around us. From a fan to a chip, there are lots of capacitors of different sizes around us. Theoretically, the basic function of the capacitor is to store energy. Its common usage includes energy storage, voltage spike protection, and signal filt
6 min read
Chapter Three Current Electricity
Electric CurrentElectricity has become an essential part of our everyday life, changing the way we live and work. In the past, people depended on fire for light, warmth, and cooking. Today, we can easily turn on lights, heat our homes, and charge our devices with just a switch or button. This is all possible becaus
10 min read
Electric Current in ConductorsElectric current in conductors is the movement of electric charge through a substance, usually a metallic wire or other conductor. Electric current is the rate at which an electric charge flows past a certain point in a conductor, and it is measured in amperes. When a potential difference (voltage)
8 min read
Electrical Energy and PowerElectric energy is the most important form of energy and is widely used in almost all the electrical devices around us. These devices have a rating written on them. That rating is expressed in Watts and intuitively explains the amount of electricity the device will consume. Bigger devices like AC, r
9 min read
Resistors in Series and Parallel CombinationsResistors are devices that obstruct the flow of electric current in the circuit. They provide the hindrance to the path of the current which flows in the circuit. Resistors consume the current in any circuit and convert them to other forms of energy as required. Various resistors can be added to the
9 min read
Kirchhoff's LawsKirchhoff's Laws are the basic laws used in electrostatics to solve complex circuit questions. Kirchhoff's Laws were given by Gustav Robert Kirchhoff who was a famous German Physicist. He gave us two laws Kirchhoff’s Current Law and Kirchhoff’s Voltage Law which are discussed in this article.These l
8 min read
Meter Bridge - Explanation, Construction, Working, Sample ProblemsAn electric flow is a flood of charged particles, like electrons or particles, traveling through an electrical conveyor or space. It is estimated as the net pace of stream of electric charge through a surface or into a control volume. The moving particles are called charge transporters, which might
7 min read
Potentiometer - Definition, Working Principle, TypesAn electric flow is a surge of charged particles, like electrons or particles, travelling through an electrical channel or space. It is estimated as the net pace of stream of electric charge through a surface or into a control volume. The moving particles are called charge transporters, which might
15 min read
Chapter Four Moving Charges and Magnetism
Magnetic Force on a Current carrying WireWhen a charge is moving under the influence of a magnetic field. It experiences forces, which are perpendicular to its movement. This property of charge is exploited in a lot of fields, for example, this phenomenon is used in the making of motors which in turn are useful for producing mechanical for
5 min read
Motion of a Charged Particle in a Magnetic FieldThis has been already learned about the interaction of electric and magnetic fields, as well as the motion of charged particles in the presence of both electric and magnetic fields. We have also deduced the relationship of the force acting on the charged particle, which is given by the Lorentz force
9 min read
Motion of a Charged Particle in a Magnetic FieldThis has been already learned about the interaction of electric and magnetic fields, as well as the motion of charged particles in the presence of both electric and magnetic fields. We have also deduced the relationship of the force acting on the charged particle, which is given by the Lorentz force
9 min read
Biot-Savart LawThe Biot-Savart equation expresses the magnetic field created by a current-carrying wire. This conductor or wire is represented as a vector quantity called the current element. Lets take a look at the law and formula of biot-savart law in detail, Biot-Savart Law The magnitude of magnetic induction a
7 min read
Magnetic Field on the Axis of a Circular Current LoopMoving charges is an electric current that passes through a fixed point in a fixed period of time. Moving charges are responsible for establishing the magnetic field. The magnetic field is established due to the force exerted by the flow of moving charges. As the magnetic field is established moving
7 min read
Ampere's Circuital Law and Problems on ItAndré-Marie Ampere, a French physicist, proposed Ampere's Circuital Law. Ampere was born in Lyon, France, on January 20, 1775. His father educated him at home, and he showed an affinity for mathematics at a young age. Ampere was a mathematician and physicist best known for his work on electrodynamic
5 min read
Chapter Five Magnetism and Matter
Bar Magnet as an Equivalent SolenoidA permanent magnet is a bar magnet, but an electromagnet is a solenoid that operates as a magnet only when an electric current is supplied through it. When a bar magnet is split in half, both parts behave like magnets with the same magnetic characteristics, however, when a solenoid is sliced in half
7 min read
Dipole in a Uniform Magnetic FieldThe magnetic field lines produced by the magnet are represented by the pattern of iron filings. We may get a rough estimate of the magnetic field B by looking at these magnetic field lines. However, we are frequently called upon to precisely measure the magnitude of the magnetic field B. We do this
11 min read
Gauss's LawGauss's law is defined as the total flux out of the closed surface is equal to the flux enclosed by the surface divided by the permittivity. The Gauss Law, which analyses electric charge, a surface, and the issue of electric flux, is analyzed. Let us learn more about the law and how it functions so
15+ min read
Earth's Magnetic Field - Definition, Causes, ComponentsIf you've ever used a compass (either a classic mechanical one or one incorporated into your smartphone), you'll know that it always points north. If you hang a refrigerator magnet from the ceiling, it will also point north. This implies that the ground beneath your feet generates a magnetic field a
7 min read
Magnetization and Magnetic IntensityWe've all had fun with magnets as kids. Some of us are now even playing with them! What makes them magnetic though? Why aren't there magnetic fields in all materials and substances? Have you ever given it any thought? The subjects of magnetization and magnetic intensity will be covered in this chapt
6 min read
Diamagnetic Materials - Definition, Properties, ApplicationsThe genesis of magnetism is due to the spin motion of electrons and their interactions with one another. Describing how materials respond to magnetism is the greatest approach to present different sorts of magnetic materials. You might be surprised to learn that all matter is magnetic. The main dist
6 min read
Ferromagnetism - Definition, Causes, Properties, HysteresisThere are several types of magnetism, with ferromagnetism being the most powerful. Ferromagnetic materials have a spontaneous net magnetization at the atomic level, even when no external magnetic field is present. When ferromagnetic materials are exposed to an external magnetic field, they become hi
7 min read
Chapter Six Electromagnetic Induction
Experiments of Faraday and HenryFor a long time, electricity and magnetism were thought to be separate and unrelated phenomena. Experiments on electric current by Oersted, Ampere and a few others in the early decades of the nineteenth century established the fact that electricity and magnetism are inter-related. They discovered th
5 min read
Magnetic FluxMagnetic Flux is defined as the surface integral of the normal component of the Magnetic Field(B) propagating through that surface. It is indicated by φ or φB. Its SI unit is Weber(Wb). The study of Magnetic Flux is done in Electromagnetism which is a branch of physics that deals with the relation b
6 min read
Faraday’s Laws of Electromagnetic InductionFaraday's Law of Electromagnetic Induction is the basic law of electromagnetism that is used to explain the working of various equipment that includes an electric motor, electric generator, etc. Faraday's law was given by an English scientist Michael Faraday in 1831. According to Faraday's Law of El
10 min read
Lenz's LawLenz law was given by the German scientist Emil Lenz in 1834 this law is based on the principle of conservation of energy and is in accordance with Newton's third law. Lenz law is used to give the direction of induced current in the circuit. In this article, let's learn about Lenz law its formula, e
7 min read
Motional Electromotive ForceThe process of induction occurs when a change in magnetic flux causes an emf to oppose that change. One of the main reasons for the induction process in motion. We can say, for example, that a magnet moving toward a coil generates an emf, and that a coil moving toward a magnet creates a comparable e
14 min read
Problems on Motional EMFElectromagnetic or magnetic induction is the generation of an electromotive force across an electrical conductor in a changing magnetic field. Michael Faraday discovered induction in 1831, and James Clerk Maxwell mathematically defined it as Faraday's law of induction. Lenz's law describes the direc
9 min read
What are Eddy Currents?Eddy currents are whirling currents produced in a conductor by a changing magnetic field. They are a fundamental phenomenon in electromagnetism, resulting from Faraday's law of electromagnetic induction, which states that a changing magnetic field generates an electromotive force (EMF) and, eventual
9 min read
Mutual Inductance - Definition, Formula, Significance, ExamplesThe topic of induction was first given by Oersted by discovering that a magnetic field is produced through an electric field. After this, different scientists started to think can the reverse is possible .i.e. can we produce electric current from a magnetic field. Michael Faraday and Joseph Henry si
7 min read
Self Inductance - Definition, Coefficient, Factors Affecting, ApplicationsWhen a coil made of copper wire is placed inside a magnetic field, the magnetic flux gets added to the coil. Faraday found that when the magnetic flux attached to the coil is charged, an electric current is introduced into the coil, provided that the coil is closed. If the coil is open, then an elec
7 min read
AC Generator - Principle, Construction, Working, ApplicationsA changing magnetic flux produces a voltage or current in a conductor, which is known as electromagnetic induction. It can happen when a solenoid's magnetic flux is changed by moving a magnet. There will be no generated voltage (electrostatic potential difference) across an electrical wire if the ma
7 min read
Chapter Seven Alternating Current
AC Voltage Applied to a ResistorAlternating Currents are used almost as a standard by electricity distribution companies. In India, 50 Hz Alternating Current is used for domestic and industrial power supply. Many of our devices are in fact nothing but resistances. These resistances cause some voltage drop but since the voltage thi
5 min read
AC Voltage Applied to an InductorAlternating Currents and Voltages vary and change their directions with time. They are widely used in modern-day devices and electrical systems because of their numerous advantages. Circuits in everyday life consist of resistances, capacitors, and inductances. Inductors are devices that store energy
5 min read
AC Voltage Applied to a CapacitorAlternating Currents and Voltages vary and change their directions with time. They are widely used in modern-day devices and electrical systems because of their numerous advantages. Circuits in everyday life consist of resistances, capacitors, and inductance. Capacitors are the devices that accumula
6 min read
Series LCR CircuitsIn contrast to direct current (DC), which travels solely in one direction, Alternating Current (AC) is an electric current that occasionally reverses direction and alters its magnitude constantly over time. Alternating current is the type of electricity that is delivered to companies and homes, and
8 min read
Power in AC CircuitAlternating Current and Voltages change their magnitude and direction with time. This changes the way calculations for power and other quantities are done in circuits. Furthermore, with the introduction of capacitors and inductances, many other effects come into play which alters the power calculati
6 min read
LC OscillationsThe Difference between the Direct and Alternating current is that the direct current (DC), travels only in one direction while the alternating current (AC) is an electric current that alternates direction on occasion and alters its amplitude continuously over time. Alternating current is the type of
9 min read
TransformerA transformer is the simplest device that is used to transfer electrical energy from one alternating-current circuit to another circuit or multiple circuits, through the process of electromagnetic induction. A transformer works on the principle of electromagnetic induction to step up or step down th
15+ min read
Chapter Eight Electromagnetic Waves
Chapter Nine Ray Optics and Optical Instruments
Refraction of LightRefraction is an important term used in the Ray Optics branch of Physics. Refraction of light is defined as the change in direction or the bending of a wave passing from one medium to another due to the change in speed of the wave. Some natural phenomena occurring in nature where refraction of light
11 min read
Total Internal ReflectionIn Physics, total internal reflection is the complete reflection of a light ray within the medium (air, water glass, etc). For example, the total internal reflection of rays of light takes place in a Diamond. Since Dimond has multiple reflecting surfaces through which the Total internal reflection t
8 min read
Refraction of Light at Curved SurfacesWhen the medium changes, the velocity and wavelength vary, but the frequency remains constant. The velocity of light remains constant in a particular medium. Light seems to travel along a straight-line path in a transparent medium. But what happens when it travels from one transparent medium to anot
9 min read
Dispersion of Light through a PrismDispersion of Light happens when white light is split into its constituent hues due to refraction. Dispersion of Light can be achieved through various means but the most common way to achieve dispersion of light is through Prism. Dispersion of light by a prism results in the breaking of white light
6 min read
Scattering of LightScattering of Light is a fascinating phenomenon that occurs when light travel through different mediums and is scattered by the particles of the medium or other irregularities. Light is nothing but energy which can be either considered waves or particles (dual nature of light) and travels in a strai
11 min read
Resolving Power of a Microscope and TelescopeWave optics, also known as Physical optics, deals with the study of various phenomena such as diffraction, polarization, interference, resolution, and other occurrences. Wave optics is the segment of optics that focuses on the study and behavior of light and its wave characteristics. Wave optics par
10 min read
Chapter Ten Wave Optics
Huygen's Wave TheoryChristiaan Huygens proposed the Huygens principle. In 1678, he changed the way we think about light and its properties. You've probably heard of the rectilinear theory of light, which states that light travels in straight lines. One of the most important ways for examining various optical phenomena
8 min read
Diffraction of lightDiffraction is a phenomenon shown by light. When the wave of light interacts with the particle in the atmosphere it bends at the corners and scatters in the area to illuminate the whole area, this phenomenon is called the Diffraction of light. It is a property of light which is used to explain vario
8 min read
Problems on Diffraction - Class 12 PhysicsThe bending of light at the edges of an obstacle whose size is comparable to the wavelength of light is called diffraction. To put it another way, it is the spreading of waves when they go through or around a barrier. Diffraction of light, as it is used to describe light, occurs more explicitly when
7 min read
Polarization of LightPolarization of Light: If you were to leave your house on a hot, sunny day, you would undoubtedly wear sunglasses. This is because the light emitted by the sun is unpolarized light and the sunglasses we wear transform the unpolarized light. Polarized light is light in which the electric field vector
9 min read
Polarisation by Scattering and ReflectionPhysical optics, frequently known as wave optics, is a discipline of optics that looks at obstruction, diffraction, polarization, and different peculiarities for which the mathematical optics beam estimate isn't material. The connection between waves and light beams is very much portrayed by wave op
11 min read