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Electromagnetic Induction - Quick Reference Guide
Magnetic Flux
Φ_B = B·A = BA cos θ
θ = angle between B and area vector A
SI Unit: Weber (Wb) = T·m²
Scalar quantity
For N turns: Total flux linkage = NΦ_B
Faraday's Law of Induction
ε = -N(dΦ_B/dt)
Induced emf = negative rate of change of flux
Negative sign: Lenz's law (opposes change)
If circuit closed: I = ε/R
Lenz's Law
Induced current opposes the change in flux
Based on conservation of energy
If flux increases: Induced current creates opposing field
If flux decreases: Induced current creates field in same direction
Motional EMF
ε = Blv
For conductor moving perpendicular to B
Due to Lorentz force F = qvB on charges
Rotating rod: ε = ½Bωl²
Self-Inductance
L = NΦ/I (flux linkage per unit current)
ε = -L(dI/dt)
SI Unit: Henry (H) = Wb/A = V·s/A
For solenoid: L = μ₀n²Al
n = turns/length, A = area, l = length
Mutual Inductance
M = N₂Φ₁₂/I₁
ε₂ = -M(dI₁/dt)
Reciprocity: M₁₂ = M₂₁ = M
SI Unit: Henry (H)
Energy in Inductor
U = ½LI²
Energy stored in magnetic field
Analogous to ½mv² (kinetic) or ½CV² (capacitor)
AC Generator
ε = NBAω sin(ωt)
Peak emf: ε₀ = NBAω = NBA(2πν)
Converts mechanical → electrical energy
India: ν = 50 Hz | USA: ν = 60 Hz
Important Constants
μ₀
4π×10⁻⁷ H/m
1 Wb
1 T·m² = 1 V·s
1 H
1 Wb/A = 1 V·s/A
India AC
50 Hz, 230 V
⚡ Quick Problem-Solving Tips
Flux Φ = BA cos θ is maximum when θ = 0° (perpendicular), zero when θ = 90° (parallel)
Induced emf depends on RATE of change of flux, not flux itself
Use Lenz's law: induced effects ALWAYS oppose the cause
For motional emf, use ε = Blv when motion ⊥ to both l and B
Self-inductance L depends on geometry (N², A, l), NOT on current
Back emf in inductor opposes current change (Lenz's law)
In AC generator: emf is max when flux passes through zero (fastest change)
Essential Formula Sheet
Φ_B = BA cos θ
ε = -N(dΦ_B/dt)
ε = Blv
L = NΦ/I
ε = -L(dI/dt)
M = N₂Φ₁₂/I₁
U = ½LI²
L = μ₀n²Al
ε₀ = NBAω
❌ Common Mistakes to Avoid
Wrong: Using BA when θ ≠ 0°
Wrong: ε = -dΦ/dt (forgot N turns)
Wrong: Induced current aids flux change
Correct: Φ = BA cos θ always
Correct: ε = -N(dΦ/dt) for N turns
Correct: Induced current opposes (Lenz)
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