Toppers’ Detailed Notes: Faraday’s Law of Induction and Mutual and Self-Inductance

1. Faraday’s Law of Induction

• NCERT: Chapter 6 - “Magnetic Effects of Electric Current” (Class 12)

• Basics of Electromagnetic Induction:

• Induced emf arises due to a change in magnetic flux.

• Right-hand rule determines the direction of induced emf.

• Lenz’s Law:

• Opposes the change in magnetic flux through the coil.

• Induces an emf that creates a current to oppose the change.

• Motional emf:

• A conductor’s motion in a magnetic field generates emf.

• Applications include generators and dynamos.

2. Mutual Inductance

• NCERT: Chapter 7 - “Alternating Current” (Class 12)

• Definition:

• The phenomenon of emf induction in one coil due to a changing current in a nearby coil.

• Calculation:

• Formula for mutual inductance (M) between two coils: M = μ₀ * N₁ * N₂ * A * l / d where:

  • μ₀ = Permeability of free space (4π × 10⁻⁷ T·m/A)
  • N₁, N₂ = Number of turns in the respective coils
  • A = Cross-sectional area for both coils
  • l = Length of the coils
  • d = Distance between the coils

• Applications:

• Transformers, where mutual induction allows voltage transformation.

• Coupled circuits that exhibit inductive coupling effects.

3. Self-Inductance

• NCERT: Chapter 7 - “Alternating Current” (Class 12)

• Definition:

• The property of a coil to oppose changes in current flow due to its own magnetic field.

• Calculation:

• Self-inductance (L) of a solenoid: L = μ₀ * N² * A * l / d where:

  • μ₀ = Permeability of free space (4π × 10⁻⁷ T·m/A)
  • N = Number of turns in the coil
  • A = Cross-sectional area of the coil
  • l = Length of the coil

• Applications:

• Inductors control current flow, store energy, and exhibit inductive reactance in AC circuits.

4. Inductance and Inductors in Circuits

• NCERT: Chapter 7 - “Alternating Current” (Class 12)

• Behavior in DC and AC Circuits:

• Inductors oppose rapid changes in DC current, causing growth or decay.

• In AC circuits, inductors exhibit inductive reactance, affecting current and voltage.

• Inductive Circuits:

• Time constant (τ) determines the rate of current growth/decay in an inductive circuit: τ = L/R where:

  • L = Self-inductance
  • R = Resistance

• Transient currents occur when circuits are switched on/off.

• RL Circuits:

• Analysis involves solving differential equations for current and voltage.

• Energy considerations examine energy storage and dissipation.

5. Applications of Faraday’s Law and Inductance

• NCERT: Chapter 7 - “Alternating Current” (Class 12)

• Generators and Motors:

• Generators use Faraday’s Law to convert mechanical energy into electrical energy.

• Back emf in motors opposes the applied voltage and limits motor speed.

• Transformers:

• Faraday’s Law enables voltage transformation through mutual inductance.

• Ideal transformers have turns ratios directly related to voltage ratios.

• Inductors in Electronic Devices:

• Inductors in filters smooth out voltage/current variations.

• Inductors in oscillators generate AC signals and control circuit behavior.

6. Energy Considerations and Power Loss

• NCERT: Chapter 7 - “Alternating Current” (Class 12)

• Energy Stored in Magnetic Fields:

• Magnetic field energy is stored in inductors: U = ½ LI² where:

  • L = Self-inductance
  • I = Current

• Hysteresis and Eddy Currents:

• Hysteresis causes energy loss in magnetic materials during magnetization/demagnetization.

• Eddy currents are induced circular currents that create heat loss in inductors, transformers, etc.