Electromagnetic Induction

• Introduction to the topic of Electromagnetic Induction
• Definition: the production of an electromotive force (emf) or voltage across a conductor when it is exposed to a changing magnetic field
• Discovered by Michael Faraday in the early 19th century
• Key concept in understanding electricity and magnetism
• Plays an important role in various applications such as generators, transformers, and induction cooktops

Observations from the Experiment

• Faraday’s experiment: a coil of wire connected to a galvanometer is moved in and out of a magnetic field
• Key observations from the experiment:
  • The needle of the galvanometer deflects when the coil is moved in or out of the magnetic field
  • The deflection of the galvanometer is greater when the coil is moved faster or the magnetic field is stronger
  • No deflection when the coil is held stationary or when there is no magnetic field present
  • If the direction of motion or the magnetic field is reversed, the direction of deflection also reverses

Faraday’s Law

• Faraday’s first law of electromagnetic induction:
  • The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux through a circuit coil
  • Mathematically expressed as:
    • ε = -N(dΦ/dt)
    • ε: induced emf
    • N: number of turns in the coil
    • dΦ/dt: rate of change of magnetic flux

Lenz’s Law

• Lenz’s law:
  • The direction of the induced emf is such that it opposes the change producing it
  • This law is consistent with the principle of conservation of energy
  • The negative sign in Faraday’s law represents Lenz’s law

Magnetic Flux

• Magnetic flux (Φ):
  • A measure of the total magnetic field passing through a given area
  • Mathematically expressed as:
    • Φ = B⋅A⋅cosθ
    • B: magnetic field strength
    • A: area
    • θ: angle between the magnetic field and the normal to the area
• The unit of magnetic flux is Weber (Wb)

Induced Emf in a Straight Conductor

• Consider a straight conductor moving through a uniform magnetic field at a constant velocity
• The induced emf can be calculated using:
  • ε = B⋅l⋅v⋅sinθ
  • B: magnetic field strength
  • l: length of the conductor
  • v: velocity of the conductor
  • θ: angle between the magnetic field and the direction of motion

Induced Emf in a Coil

• The induced emf in a coil is directly proportional to:
  • The number of turns in the coil
  • The rate of change of magnetic flux passing through the coil
• Induced emf in a coil can be calculated using Faraday’s law:
  • ε = -N(dΦ/dt)

Mutual Induction

• Mutual induction:
  • The process by which a changing magnetic field in one coil induces an emf in a nearby coil
  • Two coils in close proximity are required for mutual induction to occur
• The induced emf in the second coil can be calculated using:
  • ε₂ = -M(dI₁/dt)
  • ε₂: induced emf in the second coil
  • M: mutual inductance
  • dI₁/dt: rate of change of current in the first coil

Self-Induction

• Self-induction:
  • The process by which a changing current in a coil induces an emf in the same coil
• The induced emf in the coil can be calculated using:
  • ε = -L(dI/dt)
  • ε: induced emf in the coil
  • L: self-inductance
  • dI/dt: rate of change of current in the coil

Applications of Electromagnetic Induction

• Generators:
  • Convert mechanical energy into electrical energy through electromagnetic induction
• Transformers:
  • Use electromagnetic induction to step up or step down AC voltages
• Induction Cooktops:
  • Utilize electromagnetic induction to heat cooking utensils directly by generating eddy currents

Electromagnetic Induction

• Electromagnetic Induction
  • The phenomenon of inducing an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field
• Observations from the experiment
  • The needle of the galvanometer deflects when the coil is moved in or out of the magnetic field
  • The deflection increases with the speed of motion or the strength of the magnetic field
  • No deflection when the coil is stationary or there is no magnetic field present
  • The direction of deflection changes with the direction of motion or the magnetic field

Faraday’s Law

• Faraday’s First Law of Electromagnetic Induction
  • The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux through a circuit coil
  • ε = -N(dΦ/dt)
    • ε: induced emf
    • N: number of turns in the coil
    • dΦ/dt: rate of change of magnetic flux
• Magnetic Flux
  • Magnetic flux (Φ) is the total magnetic field passing through a given area
  • Φ = B⋅A⋅cosθ
    • B: magnetic field strength
    • A: area
    • θ: angle between the magnetic field and the normal to the area

Lenz’s Law

• Lenz’s Law
  • The direction of the induced emf is such that it opposes the change producing it
  • It follows the principle of conservation of energy
  • The negative sign in Faraday’s law represents Lenz’s law
• Example:
  • When a magnet moves towards a coil, an induced current is produced in the coil which opposes the motion of the magnet

Induced EMF in a Straight Conductor

• Consider a straight conductor moving through a uniform magnetic field
• Induced emf in a straight conductor:
  • ε = B⋅l⋅v⋅sinθ
    • B: magnetic field strength
    • l: length of the conductor
    • v: velocity of the conductor
    • θ: angle between the magnetic field and the direction of motion
• Examples:
  • Moving a wire through a magnetic field
  • Rotating a loop of wire in a magnetic field

Induced EMF in a Coil

• Induced emf in a coil:
  • In a coil, induced emf is directly proportional to the number of turns and the rate of change of magnetic flux
  • ε = -N(dΦ/dt)
    • N: number of turns in the coil
    • dΦ/dt: rate of change of magnetic flux
• Examples:
  • Generator coils
  • Primary coil in a transformer

Mutual Induction

• Mutual Induction
  • The process where a changing magnetic field in one coil induces an emf in a nearby coil
• Induced emf in the second coil:
  • ε₂ = -M(dI₁/dt)
    • ε₂: induced emf in the second coil
    • M: mutual inductance
    • dI₁/dt: rate of change of current in the first coil
• Example:
  • Transforming electrical energy between two coils in a transformer

Self-Induction

• Self-Induction
  • The process where a changing current in a coil induces an emf in the same coil
• Induced emf in the coil:
  • ε = -L(dI/dt)
    • ε: induced emf in the coil
    • L: self-inductance
    • dI/dt: rate of change of current in the coil
• Example:
  • Electric spark produced in a vehicle’s ignition coil

Applications of Electromagnetic Induction

• Generators
  • Converts mechanical energy into electrical energy through electromagnetic induction
• Transformers
  • Step up or step down AC voltages using electromagnetic induction
• Induction Cooktops
  • Heats cooking utensils through electromagnetic induction by generating eddy currents

Example: Generator

• Generators use electromagnetic induction to generate electricity
• A rotating coil in a magnetic field
  • The coil is attached to a shaft that is rotated mechanically
  • The magnetic field can be produced by permanent magnets or electromagnets
• As the coil rotates, the magnetic field lines passing through it change, leading to the generation of an induced emf
• This emf can be utilized to power electrical devices and supply electricity to homes, industries, etc.

Example: Transformer

• Transformers utilize electromagnetic induction to change the voltage of an alternating current (AC)
• Consists of primary and secondary coils wrapped around a common iron core
• The alternating current in the primary coil creates a changing magnetic field in the core
• This changing magnetic field induces an emf in the secondary coil, allowing for the stepping up or stepping down of voltage
• Transformers are used in power transmission, distribution, and equipment such as chargers and adapters

Electromagnetic Induction

• Electromagnetic Induction
  • The process of generating an electromotive force (emf) or voltage in a conductor by changing the magnetic field around it
• Observations from the experiment
  • The galvanometer deflects when the coil is moved in or out of the magnetic field
  • The deflection increases with the speed or the strength of the magnetic field
  • No deflection when the coil is stationary or when there is no magnetic field
  • The direction of deflection depends on the direction of motion or the magnetic field

Faraday’s Law

• Faraday’s First Law of Electromagnetic Induction
  • The induced emf is directly proportional to the rate of change of magnetic flux through a circuit coil.
  • Mathematically expressed as: ε = -N(dΦ/dt)
    • ε: induced emf
    • N: number of turns in the coil
    • dΦ/dt: rate of change of magnetic flux
• Faraday’s Second Law of Electromagnetic Induction (Lenz’s Law)
  • The induced emf produces a current that opposes the change in magnetic field causing it

Magnetic Flux

• Magnetic Flux (Φ)
  • The measure of the total magnetic field passing through a given area
  • Formula: Φ = B⋅A⋅cosθ
    • B: magnetic field strength
    • A: area
    • θ: angle between the magnetic field and the normal to the area

Induced EMF in a Straight Conductor

• For a straight conductor moving through a magnetic field, the induced emf can be calculated using:
  • ε = B⋅l⋅v⋅sinθ
    • B: magnetic field strength
    • l: length of the conductor
    • v: velocity of the conductor
    • θ: angle between the magnetic field and the direction of motion
• Examples:
  • Moving a wire through a magnetic field
  • Rotating a loop of wire in a magnetic field

Induced EMF in a Coil

• In a coil, the induced emf is directly proportional to:
  • The number of turns in the coil
  • The rate of change of magnetic flux passing through the coil
• Formula: ε = -N(dΦ/dt)
  • ε: induced emf
  • N: number of turns in the coil
  • dΦ/dt: rate of change of magnetic flux
• Examples:
  • Generator coils
  • Primary coil in a transformer

Mutual Induction

• Mutual induction occurs when a changing magnetic field in one coil induces an emf in a nearby coil
• The induced emf in the second coil can be calculated using:
  • ε₂ = -M(dI₁/dt)
    • ε₂: induced emf in the second coil
    • M: mutual inductance
    • dI₁/dt: rate of change of current in the first coil
• Example:
  • Transformer with primary and secondary coils

Self-Induction

• Self-induction occurs when a changing current in a coil induces an emf in the same coil
• The induced emf in the coil can be calculated using:
  • ε = -L(dI/dt)
    • ε: induced emf in the coil
    • L: self-inductance
    • dI/dt: rate of change of current in the coil
• Example:
  • Ignition coil in a vehicle

Applications of Electromagnetic Induction

• Generators
  • Convert mechanical energy into electrical energy through electromagnetic induction
  • Examples: hydroelectric power plants, wind turbines
• Transformers
  • Transform voltage levels in AC circuits using electromagnetic induction
  • Examples: power distribution, step-up or step-down transformers
• Induction Cooktops
  • Use electromagnetic induction to heat cooking utensils directly
  • Examples: induction stoves, cookers

Example: Generator

• Generators use electromagnetic induction to generate electricity
• A rotating coil in a magnetic field
  • The coil is attached to a shaft that is rotated mechanically
  • Permanent magnets or electromagnets create the magnetic field
• As the coil rotates, the magnetic field passing through it changes, inducing an emf
• This emf can be utilized to power electrical devices and supply electricity to homes, industries, etc.

Example: Transformer

• Transformers utilize electromagnetic induction to change the voltage of an AC current
• Consisting of primary and secondary coils wrapped around a common iron core
• The alternating current in the primary coil generates a changing magnetic field in the core
• This changing magnetic field induces an emf in the secondary coil, allowing voltage transformation
• Transformers are used in power transmission, distribution, and various electrical devices.