Electromagnetic Induction Overview

Overview

This lecture covers Chapter 6, "Electromagnetic Induction," focusing on key concepts, laws, calculations, applications, and illustrative examples as per the CBSE/NCERT Class 12 syllabus.

Magnetic Flux

• Magnetic flux (Φ) measures how many magnetic field lines pass perpendicularly through a surface.
• Mathematically, Φ = B ⋅ A = BA cosθ, where B is magnetic field, A is area, θ is the angle between them.
• SI unit of magnetic flux is Weber (Wb); 1 Wb = 1 Tesla·m².

Faraday’s Experiments & Laws

• Faraday’s first experiment: Relative motion between a magnet and coil induces current (no battery needed).
• Faraday’s Law: Induced emf (E) in a coil is proportional to the rate of change of magnetic flux; E = –dΦ/dt.
• Induced current I = E/R, and induced charge Q = ΔΦ/R.
• Direction of induced current is found using Lenz’s law (see below).
• Change in magnetic field, area, or angle can induce emf.

Lenz’s Law

• Direction of induced current always opposes the change causing it.
• Expressed by the negative sign in Faraday’s law: E = –dΦ/dt.
• Demonstrates energy conservation: induced current opposes flux change, preventing violation of energy conservation.

Motional and Rotational EMF

• Moving a conductor of length l with velocity v in a magnetic field B gives induced emf: E = Bvl.
• For a rotating rod/disk of length/radius l with angular speed ω: E = (1/2)Bωl².
• Direction determined by Fleming’s right-hand rule or v × B.

Self and Mutual Inductance

• Self-inductance (L): Ability of a coil to oppose change in its own current; Φ = L·I.
• Induced emf in coil: E = –L(dI/dt).
• Mutual inductance (M): When a changing current in one coil induces emf in a nearby coil; E₂ = –M(dI₁/dt).
• For solenoids: L ∝ μ₀n²Al/ℓ and M ∝ μ₀n₁n₂A₂/ℓ.

Energy in Inductors

• Energy stored: U = (1/2)LI².
• Energy density in magnetic field: u = B²/(2μ₀).

AC Generator and Alternating Current (AC)

• Rotating a coil within a magnetic field produces alternating emf: E = E₀ sin(ωt), E₀ = NABω.
• AC current: I = I₀ sin(ωt), changing direction and magnitude periodically.
• Applications: Power plants, windmills, hydroelectric generators.

Key Terms & Definitions

• Magnetic Flux (Φ) — Number of magnetic field lines passing through a surface, Φ = B ⋅ A.
• Electromagnetic Induction — Production of emf due to changing magnetic flux.
• Faraday’s Law — Induced emf equals negative rate of change of magnetic flux.
• Lenz’s Law — Induced current opposes the change in magnetic flux.
• Self-Inductance (L) — Property of a coil to oppose its own current change.
• Mutual Inductance (M) — Induced emf in one coil due to current change in another.
• Motional EMF — Emf generated by moving a conductor in a magnetic field.
• AC Generator — Device converting mechanical to electrical energy using electromagnetic induction.

Action Items / Next Steps

• Practice NCERT solved examples and exercises, especially numerical problems.
• Memorize key formulas: Φ = BA cosθ, E = –dΦ/dt, E = Bvl, E = (1/2)Bωl², U = (1/2)LI².
• Complete homework: Solve the NEET and CBSE example questions assigned in the lecture.
• Prepare short notes for key derivations (Faraday’s Law, Lenz’s Law, Motional/Rotational EMF, Self/Mutual Inductance).
• Review the distinctions between self-inductance and mutual inductance for short-answer questions.