Notes from Toppers
Toppers’ Detailed Notes: Faraday’s Law of Induction and Mutual and Self-Inductance
1. Faraday’s Law of Induction
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NCERT: Chapter 6 - “Magnetic Effects of Electric Current” (Class 12)
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Basics of Electromagnetic Induction:
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Induced emf arises due to a change in magnetic flux.
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Right-hand rule determines the direction of induced emf.
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Lenz’s Law:
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Opposes the change in magnetic flux through the coil.
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Induces an emf that creates a current to oppose the change.
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Motional emf:
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A conductor’s motion in a magnetic field generates emf.
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Applications include generators and dynamos.
2. Mutual Inductance
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NCERT: Chapter 7 - “Alternating Current” (Class 12)
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Definition:
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The phenomenon of emf induction in one coil due to a changing current in a nearby coil.
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Calculation:
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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
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Applications:
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Transformers, where mutual induction allows voltage transformation.
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Coupled circuits that exhibit inductive coupling effects.
3. Self-Inductance
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NCERT: Chapter 7 - “Alternating Current” (Class 12)
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Definition:
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The property of a coil to oppose changes in current flow due to its own magnetic field.
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Calculation:
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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
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Applications:
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Inductors control current flow, store energy, and exhibit inductive reactance in AC circuits.
4. Inductance and Inductors in Circuits
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NCERT: Chapter 7 - “Alternating Current” (Class 12)
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Behavior in DC and AC Circuits:
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Inductors oppose rapid changes in DC current, causing growth or decay.
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In AC circuits, inductors exhibit inductive reactance, affecting current and voltage.
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Inductive Circuits:
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Time constant (τ) determines the rate of current growth/decay in an inductive circuit: τ = L/R where:
- L = Self-inductance
- R = Resistance
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Transient currents occur when circuits are switched on/off.
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RL Circuits:
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Analysis involves solving differential equations for current and voltage.
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Energy considerations examine energy storage and dissipation.
5. Applications of Faraday’s Law and Inductance
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NCERT: Chapter 7 - “Alternating Current” (Class 12)
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Generators and Motors:
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Generators use Faraday’s Law to convert mechanical energy into electrical energy.
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Back emf in motors opposes the applied voltage and limits motor speed.
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Transformers:
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Faraday’s Law enables voltage transformation through mutual inductance.
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Ideal transformers have turns ratios directly related to voltage ratios.
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Inductors in Electronic Devices:
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Inductors in filters smooth out voltage/current variations.
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Inductors in oscillators generate AC signals and control circuit behavior.
6. Energy Considerations and Power Loss
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NCERT: Chapter 7 - “Alternating Current” (Class 12)
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Energy Stored in Magnetic Fields:
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Magnetic field energy is stored in inductors: U = ½ LI² where:
- L = Self-inductance
- I = Current
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Hysteresis and Eddy Currents:
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Hysteresis causes energy loss in magnetic materials during magnetization/demagnetization.
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Eddy currents are induced circular currents that create heat loss in inductors, transformers, etc.