Questions
3–5 questions per board paper
Difficulty
Medium-Hard
Importance
Core — high conceptual weightage
Overview
Electromagnetic Induction describes the generation of electromotive force due to changing magnetic flux linked with a circuit. It is a cornerstone of Class 12 Physics, serving as the underlying principle for generators, transformers, and inductors, and frequently appears in board exams as both conceptual and numerical problems.
Faraday's Law of Induction
Faraday's Law states that the induced EMF in a circuit is directly proportional to the time rate of change of magnetic flux linked with it. This law quantifies the induction process and establishes the relationship between time-varying magnetic fields and electric potential.
- Magnetic Flux formula: Φ = B · A · cos(θ)
- Faraday's Law: ε = -dΦ/dt
- For a coil with N turns: ε = -N · (dΦ/dt)
- Flux unit: Weber (Wb)
- EMF unit: Volts (V)
Lenz's Law
Lenz's Law provides the physical direction of the induced current by stating that it always opposes the change in magnetic flux that produced it. It is a direct consequence of the Law of Conservation of Energy in electromagnetism.
- Direction rule: Opposes the cause
- Consistency with Energy Conservation: Principle behind the negative sign in ε = -dΦ/dt
- Application: Used to determine current direction in loops entering/exiting magnetic fields
- Work done against magnetic force is converted into electrical energy
Self and Mutual Inductance
Inductance measures a coil's opposition to changes in current. Self-inductance occurs within a single coil due to its own changing current, while mutual inductance occurs between two adjacent coils due to flux linkage between them.
- Self-induced EMF: ε = -L · (di/dt)
- Mutual EMF in coil 2: ε₂ = -M · (di₁/dt)
- Self-inductance of solenoid: L = (μ₀ · N² · A) / l
- Coupling coefficient: M = k · sqrt(L₁ · L₂)
- Units: Henry (H)
Formula Sheet
Φ = B · A · cos(θ)
ε = -dΦ/dt
ε = -N · (dΦ/dt)
ε = -L · (di/dt)
ε₂ = -M · (di₁/dt)
L = (μ₀ · N² · A) / l
Energy stored in inductor: U = 0.5 · L · I²
M = k · sqrt(L₁ · L₂)
Exam Tip
Always verify if the magnetic field, the area, or the angle between them is the changing parameter before applying the dΦ/dt derivative.
Common Mistakes
- Forgetting the negative sign in Faraday's Law, which represents Lenz's Law and the opposition to change.
- Confusing the cross-sectional area A with the effective area A·cos(θ) when calculating flux.
- Treating self-inductance and mutual inductance as constants regardless of the physical geometry of the coils.
More Revision Notes
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