Electromagnetic Induction

• Introduction & Basic Concepts

  • Definition: Production of induced emf and induced current due to changing magnetic flux.
  • Historical context: Experiments by Faraday and Henry.
  • Key requirement: Relative motion between conductor and magnetic field.

• Magnetic Flux ($\Phi_B$)

  • Definition: Number of magnetic field lines passing normally through a given area.
  • Formula: $\Phi_B = B \cdot A = BA \cos\theta$
  • SI Unit: Weber (Wb) or $T \cdot m^2$
  • Nature: Scalar quantity.

• Faraday's Law of Electromagnetic Induction

  • First Law: Whenever magnetic flux linked with a circuit changes, an emf is induced.
  • Second Law: Magnitude of induced emf is directly proportional to the rate of change of magnetic flux.
  • Mathematical Form: $\varepsilon = -N \frac{d\Phi_B}{dt}$

• Lenz's Law & Conservation of Energy

  • Statement: The polarity of induced emf is such that it opposes the very cause that produces it.
  • Formula: $\varepsilon = -\frac{d\Phi_B}{dt}$ (Negative sign signifies opposition).
  • Principle: Follows the Law of Conservation of Energy.
  • Right-Hand Rule applications.

• Motional Electromotive Force (Emf)

  • Concept: Emf induced across a conductor moving in a uniform magnetic field.
  • Formula: $\varepsilon = Blv$ ($B$: Magnetic field, $l$: Length, $v$: Velocity).
  • Derivation via Lorentz force.
  • Energy consideration: Mechanical energy converted to electrical energy.

• Eddy Currents

  • Definition: Induced circulating currents set up in bulk pieces of conductors when magnetic flux changes.
  • Disadvantages: Energy loss as heat, damping, machinery damage.
  • Applications:
    • Magnetic braking in trains.
    • Induction furnace.
    • Speedometer.
    • Electrostatic damping.
  • Minimization technique: Laminated iron cores.

• Inductance

  • Self-Inductance ($L$)
    • Definition: Induction of emf in a coil due to change in its own current.
    • Magnetic Flux linkage: $N\Phi = LI$
    • Induced Emf: $\varepsilon = -L \frac{di}{dt}$
    • Formula for Solenoid: $L = \mu_0 n^2 A l$
    • SI Unit: Henry (H)
  • Mutual Induction ($M$)
    • Definition: Induction of emf in a secondary coil due to change of current in the primary coil.
    • Magnetic Flux linkage: $N_2\Phi_2 = M I_1$
    • Induced Emf: $\varepsilon_2 = -M \frac{di_1}{dt}$
    • Formula for coaxial solenoids: $M = \mu_0 n_1 n_2 A l$
    • Coupling coefficient.

• AC Generator (Alternator)

  • Principle: Based on Electromagnetic Induction (rotating a coil in a magnetic field).
  • Main Parts:
    • Armature coil
    • Strong field magnet
    • Slip rings
    • Brushes
  • Working & Mathematical Expression: $\varepsilon = NBA\omega \sin(\omega t)$
  • Output: Alternating Current (AC).