Electromagnetic Induction — Class 12 Physics Notes

Electromagnetic Induction · Class 12 Physics · 8 topics.

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Topics covered in Electromagnetic Induction

  1. 1.Introduction of Electromagnetic Induction

    Short Answer

    Electromagnetic induction is the process where a change in magnetic field causes the generation of an electric current in a conductor. It's used in generators and transformers, impacting our daily life by powering our homes and gadgets.

    Long Answer

    Electromagnetic induction is a fundamental principle of physics discovered by Michael Faraday. It occurs when a conductor moves through a magnetic field or when a magnetic field changes around a conductor. This change in the magnetic field induces an electromotive force (EMF) and, consequently, an electric current in the conductor. Here are the key points:

    1. Faraday's Law of Electromagnetic Induction: It states that the induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.


    2. Applications:

      • Generators: Convert mechanical energy into electrical energy using electromagnetic induction.
      • Transformers: Change the voltage of alternating current (AC) electricity, stepping it up or down for various uses.
      • Electric Motors: Use induction for converting electrical energy to mechanical energy.


    3. Real-life Examples:

      • Charging a smartphone using a wireless charger.
      • Electricity generation in hydroelectric plants.
      • The functioning of an MRI machine in hospitals.


    4. Careers and Industries:

      • Electrical engineering: Designing and developing electrical systems.
      • Renewable energy: Working with wind turbines and solar panels.
      • Healthcare: Developing medical imaging devices.

    Activity to Understand Electromagnetic Induction:

    Try moving a magnet back and forth through a coil of wire connected to a light bulb. When the magnet is in motion, you'll see the bulb light up due to the induced current!

  2. 2.The Experiments Of Faraday And Henry

    There are 3 experiments:- Short Answer

    Experiment 1 demonstrates the induction of current in a coil when a magnet is moved towards or away from it. Experiment 2 shows current induction in one coil due to the motion of another nearby current-carrying coil. Experiment 3 is a setup to show that relative motion between a coil and a magnetic field induces current.

    Long Answer

    Let's delve deeper into the experiments, which are classic demonstrations of electromagnetic induction:

    Experiment 1: Moving Magnet and Coil

    • Setup: A coil C1 is connected to a galvanometer G. A bar magnet is moved towards and away from the coil.
    • Observation: As the magnet approaches or retreats from the coil, the galvanometer needle deflects, indicating current flow.
    • Principle Demonstrated: This is a direct demonstration of Faraday's Law of Electromagnetic Induction. The relative motion between the magnet and the coil changes the magnetic flux through the coil, inducing an electromotive force (EMF), and as a result, an electric current flows through the coil.
    • Step-by-Step Process:
      1. The bar magnet is moved toward the coil.
      2. The magnetic field lines intersecting the coil change.
      3. The changing magnetic field (magnetic flux) through the coil generates an EMF.
      4. This EMF produces a current in the coil, detected by the galvanometer.

    Experiment 2: Induction by a Changing Current in a Nearby Coil

    • Setup: Two coils, C1 and C2, are placed close to each other. Coil C2 is connected to a battery through a switch, and coil C1 is connected to a galvanometer.
    • Observation: When the switch in the circuit with coil C2 is closed, creating a current, the galvanometer in the circuit with coil C1 deflects momentarily.
    • Principle Demonstrated: This experiment illustrates the induction of an electric current in a nearby coil (C1) due to a change in current in another coil (C2). This is due to the fact that a changing current in C2 creates a changing magnetic field, which extends into the space around it, including where C1 is located, thus inducing a current in C1.

    Experiment 3: Induction by Relative Motion between a Coil and a Circuit

    • Setup: A coil C1 is connected to a galvanometer, and a switch K is included in a separate circuit with a coil C2.
    • Observation: When the switch K is toggled, altering the current in coil C2, an induced current is observed in coil C1.
    • Principle Demonstrated: The principle here is the same as in experiment 2, but this setup can demonstrate both the effect of a moving magnetic field on a stationary coil and the effect of moving the coil in a stationary magnetic field.

    Real-life Applications:

    • Generators: Convert mechanical energy into electrical energy using the principles from Experiment 1.
    • Transformers: Use principles from Experiment 2 to transfer energy between two circuits through electromagnetic induction.
    • Electric Vehicles: Utilize induction for charging without wires, similar to the principles observed in the experiments.

    Activity to Try at Home: You can create a simple version of Experiment 1 using household items:

    1. Wrap some wire around a cardboard tube to make a coil.
    2. Connect the ends of the coil to a small light bulb or LED.
    3. Move a strong magnet in and out of the coil and watch the bulb light up as you generate electricity.

    Careers and Industries:

    • Engineering: Designing electrical machines and power systems.
    • Energy: Working with renewable resources and power generation.
    • Automotive: Developing electric and hybrid vehicles with regenerative braking systems, which use similar principles to generate electricity while braking.

    This detailed exploration of the experiments shows how the basic principles of electromagnetic induction manifest in various applications, from household electronics to large-scale power generation and cutting-edge technology.

  3. 3.Magnetic Flux

    Short Answer

    Magnetic flux refers to the total magnetic field which passes through a given area. It's measured in Weber (Wb) and is a measure of the strength of the magnetic field as it relates to the area it passes through.

    Long Answer

    Magnetic flux, symbolized by the Greek letter Phi (Φ), is a key concept in electromagnetism. It quantifies the number of magnetic field lines (also known as flux lines) that pass through a specified area. Here's a more detailed explanation:

    1. Definition: Magnetic flux through a surface is the surface integral of the normal component of the magnetic field passing through that surface.

    2. Mathematical Expression: Φ = B · A · cos(θ), where:

      • Φ is the magnetic flux.
      • B is the magnetic field strength.
      • A is the area through which the field lines pass.
      • θ is the angle between the field lines and the normal (perpendicular) to the surface.

    3. Units: The SI unit of magnetic flux is the Weber (Wb). One Weber is equal to one Tesla meter squared (1 Wb = 1 T·m²).

    4. Applications: Magnetic flux is critical in Faraday's law of electromagnetic induction, where a change in flux over time induces an electromotive force (EMF). It's used in designing electric motors, generators, inductors, and transformers.

    5. Real-life Examples:

      • The operation of a metal detector is based on changes in magnetic flux.
      • Magnetic resonance imaging (MRI) uses changes in magnetic flux to generate images of the body.

    Activity to Understand Magnetic Flux:

    You can demonstrate magnetic flux by placing a piece of paper over a magnet and sprinkling iron filings on it. The pattern formed by the filings represents the magnetic field lines and flux through the paper.

  4. 4.Faraday’s Law Of Induction

    Short Answer

    Faraday's law of induction states that the voltage induced in a circuit is directly proportional to the rate of change of magnetic flux through the circuit. The formula is =−ΔΦΔEMF=−NΔtΔΦ​, where EMF is the induced voltage, N is the number of turns in the coil, ΔΦΔΦ is the change in magnetic flux, and ΔΔt is the time it takes for the flux to change.

    Long Answer

    Faraday's Law of Induction Explained:

    Faraday's law of electromagnetic induction is a fundamental principle of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon known as electromagnetic induction. It's a basic law of electromagnetism linking electricity and magnetism.

    Mathematical Expression:

    The mathematical formula for Faraday's law of induction is expressed as:

    =−ΔΦΔEMF=−NΔtΔΦ​

    where:

    • EMF is the electromotive force in volts.
    • N is the number of turns in the coil.
    • ΔΦΔΦ is the change in magnetic flux in webers.
    • ΔΔt is the time in seconds over which the flux changes.

    Derivation:

    1. Magnetic Flux (ΦΦ): The magnetic flux through a loop is defined as the product of the magnetic field (B), the area of the loop (A), and the cosine of the angle (θ) between the magnetic field and the normal to the loop: Φ=⋅⋅cos⁡Φ=B⋅A⋅cos(θ).

    2. Change in Magnetic Flux: If the magnetic flux changes, either by changing the magnetic field strength, the area of the loop, or the angle, there is a change in magnetic flux ΔΦΔΦ over time ΔΔt.

    3. Induced EMF: According to Faraday's law, this change in magnetic flux over time induces an electromotive force (EMF) in the loop. The negative sign in the equation indicates the direction of the induced EMF opposes the change in magnetic flux, according to Lenz's law.

    Real-Life Applications and Careers:

    Faraday's law is used in various applications such as electric generators, transformers, and induction motors, which are fundamental to the electrical industry. Understanding this principle is crucial for careers in electrical engineering, renewable energy, and any field involving electromechanical systems.

  5. 5.Lenz’s Law And Conservation Of Energy

    Short Answer

    Lenz's law states that the direction of the current induced by a change in magnetic flux is such that it creates a magnetic field opposing the change. This law preserves the conservation of energy. In the diagrams (a) and (b), the direction of the induced current in the loop is shown by the arrows inside the loop, which generate a magnetic field that opposes the movement of the magnet, as indicated by the outward and inward facing curved arrows around the loop.

    Long Answer

    Lenz's Law Explained:

    Heinrich Friedrich Lenz formulated a law in 1834 that describes the direction of an induced current in a conductor due to a changing magnetic field. Lenz's law is a manifestation of the conservation of energy, stating that the induced electromotive force (EMF) always generates a current whose magnetic field opposes the original change in magnetic flux.

    Illustration with the Diagram:

    1. In diagram (a), when the north pole of a magnet approaches a loop of wire, the changing magnetic field induces a current.

    2. According to Lenz's law, the induced current will flow in such a direction that the magnetic field it creates will oppose the motion of the magnet. In this case, the current flows counterclockwise, creating a north pole on the nearest side, which repels the approaching north pole of the magnet.

    3. In diagram (b), when the north pole is moved away from the loop, the induced current will flow in a direction that tries to keep the magnetic field inside the loop the same. Therefore, the current flows clockwise, creating a south pole on the nearest side, which tries to attract the retreating north pole of the magnet.

    Real-Life Applications and Careers:

    Lenz's law is fundamental in designing electrical systems like transformers, inductors, and many types of electric motors and generators. This principle is crucial for careers in electrical engineering, power generation, and any field that involves the design and manufacture of electrical devices.

  6. 6.Motional Electromotive Force

    Short Answer: Motional EMF is the voltage generated when a part of a circuit moves through a magnetic field. This movement changes the area of the loop within the magnetic field, leading to a change in magnetic flux, which in turn induces an EMF.

    Long Answer with Derivation:

    1. Conceptual Setup:

      • Consider a straight conductor PQ moving within a magnetic field, which is part of the loop PQRS. The conductor PQ moves with velocity v to the left, decreasing the area of the rectangular loop.

    2. Magnetic Flux (ΦΦB​):

      • The magnetic flux through the loop is given by Φ=×ΦB​=B×A, where B is the magnetic field strength and A is the area of the loop.

    3. Change in Flux with Movement:

      • As the conductor moves, the area A changes because one side of the loop is moving. If the length RS of the loop is l and the length RQ is x, the area =×A=l×x.

    4. Faraday's Law of Induction:

      • According to Faraday's Law, the induced EMF (ϵ) is equal to the negative rate of change of the magnetic flux, =−Φϵ=−dtdΦB​​.

    5. Deriving the EMF:

      • Substituting the expression for ΦΦB​, we have =−(××)ϵ=−dtd(B×l×x)​.
      • Because B and l are constants, the derivative simplifies to =−××ϵ=−B×l×dtdx​.
      • The rate of change of x with respect to time (dtdx​) is the velocity v, hence =−××ϵ=−B×l×v.

    6. Direction of EMF:

      • The negative sign indicates that the direction of the induced EMF is such that it opposes the change in the magnetic flux through the loop, according to Lenz's Law.

    Numerical Example: Let's calculate the motional EMF given the following values:

    • Magnetic field strength, =0.3B=0.3 Tesla
    • Length of the loop, =0.4l=0.4 meters
    • Velocity of the conductor, =5v=5 meters/second

    Using the derived formula, =−××ϵ=−B×l×v, we plug in our values:

    =−0.3×0.4×5ϵ=−0.3×0.4×5 =−0.6 Vϵ=−0.6 V

    The negative sign indicates the direction of EMF, so the magnitude of the motional EMF is 0.6 volts.

    In real life, this phenomenon is used in the operation of generators and motors. In a generator, motion is used to create electricity, while in a motor, electricity is used to create motion.

  7. 7.Inductance

    Short Answer: Inductance is the property of a conductor by which a change in current in the conductor induces an electromotive force (emf) in both the conductor itself (self-inductance) and in any nearby conductors (mutual inductance).

    Long Answer:

    Inductance is a fundamental concept in electromagnetism. There are two types of inductance: self-inductance and mutual inductance.

    • Self-Inductance: This is the phenomenon where a changing current in a coil produces a changing magnetic field, which in turn induces an emf in the same coil.

    • Mutual Inductance: This occurs when a changing current in one coil induces an emf in a nearby coil.

    Using the Diagram for Derivation:

    In the diagram, we see two coils labeled 1S1​ and 2S2​, each with a number of turns 1N1​ and 2N2​, respectively. The radius of the coils is 1r1​ and 2r2​, and they are positioned such that the magnetic field created by 1S1​ passes through 2S2​.

    1. Mutual Inductance Derivation:

      • When a current 1I1​ flows through 1S1​, it produces a magnetic field.
      • According to Ampere's Law, the magnetic field B at a distance r from a long straight conductor is given by =02B=2πrμ0​I​, where 0μ0​ is the permeability of free space.
      • For a coil of 1N1​ turns, the magnetic field inside the coil is =01121B=μ0​2πr1​N1​I1​​.
      • This magnetic field links with 2S2​ and the flux (ΦΦ) linking 2S2​ is Φ=⋅Φ=B⋅A, where A is the cross-sectional area of 2S2​.
      • Therefore, Φ=01121⋅22Φ=μ0​2πr1​N1​I1​​⋅πr22​.
      • The mutual inductance M is then defined by the ratio of the magnetic flux through 2S2​ to the current in 1S1​: =2Φ1M=I1​N2​Φ​.
      • Substituting for ΦΦ, we get =0122221M=μ0​2πr1​N1​N2​πr22​​.

    2. Self-Inductance Derivation:

      • Consider now the coil 1S1​ itself. When the current 1I1​ changes, the magnetic field inside the coil changes.
      • This changing magnetic field induces an emf in 1S1​ itself according to Faraday's Law of electromagnetic induction.
      • The induced emf E is proportional to the rate of change of the magnetic flux ΦΦ and the number of turns 1N1​: =−1ΦE=−N1​dtdΦ​.
      • The self-inductance L is defined by the ratio of the magnetic flux through the coil to the current in the coil: =1Φ1L=I1​N1​Φ​.
      • Substituting for ΦΦ, we get =0121221L=μ0​2πr1​N12​πr12​​.

    Real-life Examples and Applications:

    • Self-inductance is used in transformers where coils are used to step up or step down voltage levels.
    • Mutual inductance is the principle behind wireless charging, where a changing current in a transmitter coil induces a current in a receiver coil in your device.

    Careers and Industries:

    • Electrical engineering: designing electrical circuits and components like inductors and transformers.
    • Communications industry: for creating components in radio and wireless technology.
    • Automotive industry: in the design of ignition systems and RFID systems.

  8. 8.AC Generator

    Short Answer:

    An AC generator is a device that converts mechanical energy into electrical energy using electromagnetic induction. The mechanical energy, usually provided by a rotating motion, moves a conductor within a magnetic field to produce alternating current (AC).

    Long Answer:

    Working Principle: The AC generator works on the principle of electromagnetic induction, discovered by Michael Faraday. When a coil rotates within a magnetic field, the magnetic flux linkage with the coil changes, inducing an electromotive force (emf).

    Components:

    • Magnetic Field: Created by permanent magnets or electromagnets labeled as N (North) and S (South).
    • Coil: A loop of wire that rotates within the magnetic field.
    • Axle: Attached to the coil, it helps in rotating the coil.
    • Slip Rings: They are connected to the ends of the coil and rotate with it, maintaining a continuous connection with the brushes.
    • Brushes: Typically made of carbon, they are stationary and transfer the current from the slip rings to the external circuit.
    • Alternating EMF: The electrical output which changes direction as the coil rotates.

    Working:

    1. As the coil rotates, the magnetic flux linkage changes.
    2. According to Faraday's law of electromagnetic induction, a change in magnetic flux induces an emf.
    3. The direction of the induced emf changes with every half rotation due to the change in the direction of the magnetic field relative to the coil, producing AC.

    Mathematical Expression: The emf (ε) can be expressed as: =−Φε=−NdtdΦ​ where:

    • ε is the induced emf,
    • N is the number of turns in the coil,
    • ΦΦ is the magnetic flux.

    Derivation: The flux ΦΦ through the coil is given by: Φ=cos⁡Φ=BAcos(θ) where:

    • B is the magnetic field strength,
    • A is the area of the coil,
    • θ is the angle between the magnetic field and the normal to the coil, =θ=ωt (where ω is the angular velocity and t is the time).

    Differentiating ΦΦ with respect to t, we get the induced emf as: =−(cos⁡)=sin⁡ε=−Ndtd(BAcos(ωt))​=NBAωsin(ωt)

    Applications:

    • Power Generation: AC generators are used in power plants to generate electricity.
    • Transport: They are used in locomotives for electric traction.
    • Industries: They serve as power sources for many industrial machines.

    Real-Life Example: Think of a hand-cranked flashlight. When you turn the handle, you are acting like the axle in the generator, and this mechanical action creates electricity that powers the light.

    Career or Industry: Learning about AC generators can be very useful if you are interested in careers in electrical engineering, energy production, industrial machinery, or any field that deals with electricity.

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