Faraday’s Law of Induction

  • Key concept in electromagnetism
  • Describes the relationship between a changing magnetic field and induced electromotive force (emf)
  • Proposed by Michael Faraday in 1831
  • Two main phenomena associated with Faraday’s law:
    • Mutual induction
    • Self-induction

Mutual Induction

  • Occurs when the magnetic field produced by a changing current in one coil induces an emf in another coil
  • Based on the principle of magnetic flux linkage
  • Formula for mutual induction:
    • emf = -N2(dΦ1/dt)
      • emf: Electromotive force induced in the second coil
      • N2: Number of turns in the second coil
      • Φ1: Magnetic flux linked with the first coil
      • dt: Time interval

Mutual Induction (contd.)

  • Applications of mutual induction:
    • Transformers: Step-up and step-down transformers are based on mutual induction
    • Inductive coupling: Used in wireless power transfer and data communication systems
  • Example: Step-up transformer
    • Converts low voltage and high current into high voltage and low current
    • Primary coil has fewer turns than the secondary coil

Self-Induction

  • Occurs when a changing current in a coil induces an emf in the same coil
  • Based on the principle of magnetic field self-linkage
  • Formula for self-induction:
    • emf = -L(dI/dt)
      • emf: Electromotive force induced in the same coil
      • L: Self-inductance of the coil
      • dI/dt: Rate of change of current

Self-Induction (contd.)

  • Applications of self-induction:
    • Choke coil: Used to impede alternating current flow in electronic circuits
    • Inductor: Component used in electronic circuits to store energy in magnetic fields
  • Example: Choke coil
    • In fluorescent lights, choke coil restricts alternating current flow and allows high voltage across the tube

Oscillating Copper Plate Experiment

  • Demonstrates Faraday’s law of induction
  • Consists of a copper plate and a magnet
  • When the magnet is moved towards the plate, the magnetic field changes, inducing a current in the plate
  • The copper plate experiences eddy currents that oppose the change in magnetic field
  • Result: The copper plate starts oscillating due to the repulsion between the plate and the magnet

Eddy Currents

  • Circulating currents induced in a conducting material by a changing magnetic field
  • Result of Faraday’s law of induction
  • Eddy currents produce strong opposing magnetic fields, leading to various effects such as heating and damping
  • Applications of eddy currents:
    • Induction heating: Used in cooktops and industrial processes
    • Eddy current brakes: Used in high-speed trains to provide efficient braking

Lenz’s Law

  • Formulated by Heinrich Lenz in 1834
  • States that the direction of the induced current is always such as to oppose the change producing it
  • Consequence of the law of conservation of energy
  • Lenz’s law helps determine the direction of induced currents in various situations

Faraday’s Law of Induction:

Faraday’s law of induction describes the relationship between a changing magnetic field and induced electromotive force (emf). It is a key concept in electromagnetism.

  • Proposed by Michael Faraday in 1831
  • Two main phenomena associated with Faraday’s law:
    • Mutual induction
    • Self-induction

Mutual Induction:

Mutual induction occurs when the magnetic field produced by a changing current in one coil induces an emf in another coil.

  • Based on the principle of magnetic flux linkage
  • Formula for mutual induction:
    • emf = -N2(dΦ1/dt)
  • Applications of mutual induction:
    • Transformers
    • Inductive coupling

Mutual Induction - Example: Step-up Transformer:

A step-up transformer converts low voltage and high current into high voltage and low current.

  • Primary coil has fewer turns than the secondary coil
  • Used in power distribution systems to increase voltage for long-distance transmission

Self-Induction:

Self-induction occurs when a changing current in a coil induces an emf in the same coil.

  • Based on the principle of magnetic field self-linkage
  • Formula for self-induction:
    • emf = -L(dI/dt)
  • Applications of self-induction:
    • Choke coil
    • Inductor in electronic circuits

Self-Induction - Example: Choke Coil:

A choke coil is used to impede alternating current flow in electronic circuits.

  • Restricts the flow of AC current
  • Allows high voltage across the tube in fluorescent lights

Oscillating Copper Plate Experiment:

The oscillating copper plate experiment demonstrates Faraday’s law of induction.

  • Consists of a copper plate and a magnet
  • Moving the magnet induces current in the plate
  • Eddy currents in the plate cause repulsion and oscillation

Eddy Currents:

Eddy currents are circulating currents induced in a conducting material by a changing magnetic field.

  • Result of Faraday’s law of induction
  • Oppose the change in the magnetic field
  • Effects of eddy currents:
    • Heating
    • Damping

Applications of Eddy Currents:

Eddy currents have various applications in different fields.

  • Induction heating:
    • Used in cooktops and industrial processes
  • Eddy current brakes:
    • Used in high-speed trains for efficient braking

Lenz’s Law:

Lenz’s law states that the direction of the induced current is always such as to oppose the change producing it.

  • Proposed by Heinrich Lenz in 1834
  • Consequence of the law of conservation of energy
  • Determines the direction of induced currents

Slide s 21 to 30 on “Faraday’s Law of Induction - Mutual and Self-Inductance - Oscillating Copper Plate”:

  1. Faraday’s Law of Induction (contd.)
  • In Faraday’s law of induction, the induced electromotive force (emf) is directly proportional to the rate of change of magnetic flux.
  • Formula for Faraday’s law of induction:
    • emf = -dΦ/dt
      • emf: Electromotive force induced
      • Φ: Magnetic flux linked with the coil
      • dt: Time interval
  1. Induced emf with a Straight Conductor
  • If a straight conductor moves in a constant magnetic field, the induced emf can be calculated using the formula:
    • emf = Bvl
      • B: Magnetic field strength
      • v: Velocity of the conductor
      • l: Length of the conductor
  1. Lenz’s Law (contd.)
  • Lenz’s law helps us determine the direction of induced current in electromagnetic phenomena.
  • It states that the induced current will flow in a direction such that it opposes the change producing it.
  1. Mutual Inductance (contd.)
  • The mutual inductance between two coils depends on the number of turns and the geometry of the coils.
  • When two coils are wound around a magnetic core, the mutual inductance can be calculated using the formula:
    • M = k√(L1L2)
      • M: Mutual inductance
      • L1, L2: Self-inductances of the individual coils
      • k: Coefficient of coupling between the two coils
  1. Self-Inductance (contd.)
  • Self-inductance is a measure of the ability of a coil to create an induced emf within itself.
  • The self-inductance of a coil depends on its number of turns and the geometry of the coil.
  • The formula for self-inductance of a coil is:
    • L = (μ₀N²A)/l
      • L: Self-inductance
      • μ₀: Permeability of free space
      • N: Number of turns in the coil
      • A: Cross-sectional area of the coil
      • l: Length of the coil
  1. Inductors in Circuits
  • Inductors are electronic components used in circuits to store energy in magnetic fields and oppose the change in current.
  • They are used in various applications such as filters, tuning circuits, and energy storage devices.
  1. RL Circuits
  • An RL circuit consists of a resistor (R) and an inductor (L) connected in series.
  • When a voltage is applied to the circuit, the inductor opposes the change in current, causing a delay in the rise or fall of current.
  1. RL Circuits (contd.)
  • The time constant (τ) of an RL circuit is given by the formula:
    • τ = L/R
      • τ: Time constant
      • L: Inductance of the inductor
      • R: Resistance of the resistor
  1. Oscillating Copper Plate Experiment (contd.)
  • In the oscillating copper plate experiment, the changing magnetic field induces eddy currents in the copper plate.
  • The interaction between the eddy currents and the magnetic field causes the plate to oscillate.
  • This phenomenon is an example of the repulsive force between the induced currents and the original magnetic field.
  1. Oscillating Copper Plate Experiment (contd.)
  • The oscillating copper plate experiment demonstrates the principle of magnetic damping.
  • The eddy currents created in the copper plate dissipate energy as heat, leading to a decrease in the oscillation amplitude over time.
  • This concept is applied in electromagnetic damping mechanisms used in various devices.