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Use this the night before your exam. Every formula, every concept one-liner, and flashcards — compressed for rapid recall.
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📋 One-Page Chapter Summary
⚡ Key Laws & Their Essence
Faraday's 1st Law: Any change in magnetic flux through a circuit → induces EMF
Faraday's 2nd Law: |ε| = N|dΦ/dt|. Faster change = larger EMF.
Lenz's Law: Induced current opposes the change in flux. Consequence of energy conservation.
Motional EMF: Moving conductor in B → Lorentz force separates charges → potential difference.
Self-Induction: Coil's own changing current induces back-EMF in itself. L = NΦ/I.
Mutual Induction: Primary's changing current induces EMF in secondary. M = N₂Φ₂₁/I₁.
Eddy Currents: Bulk currents in solid conductors. Cause heating. Reduced by lamination.
📋 Critical One-Liners
Static magnet: No change in flux → EMF = 0 (even if strong magnet inside coil)
Flux max position: EMF = 0 (plane ⊥ B). EMF max position: Flux = 0 (plane ∥ B)
Induced charge: q = NΔΦ/R — independent of time. Only depends on total flux change.
Terminal velocity: v_T = FR/(B²L²) when electromagnetic braking = applied force
L ∝ N² (solenoid): Doubling turns → 4× inductance. L ∝ μᵣ, A, 1/l.
Energy analogy: ½LI² (inductor) ↔ ½mv² (mechanics). L↔m, I↔v.
LC oscillation: ω = 1/√(LC). Energy alternates: ½LI²_max = Q₀²/2C = total energy
🔢 Complete Formula Dump
Magnetic Flux
Φ = BA cosθ
θ with normal; unit = Wb = T·m²
Faraday's Law
ε = −N dΦ/dt
−ve sign = Lenz's Law; average: ε = −NΔΦ/Δt
Motional EMF
ε = BLv
For v ⊥ B; general: ε = BLv sinα
Current (Rail)
I = BLv/R
R = total resistance including rod
Opposing Force
F = B²L²v/R
Acts opposite to velocity (Lenz's Law)
Power Dissipated
P = B²L²v²/R
= Fv = ε²/R; equals input power at terminal v
Rotating Rod EMF
ε = ½BωL²
Pivot at one end; B perpendicular to plane
Self-Inductance (L)
ε = −L dI/dt
L = NΦ/I; unit = Henry (H) = V·s/A
Solenoid Inductance
L = μ₀N²A/l
= μ₀n²Al where n = N/l; with core: L = μ₀μᵣN²A/l
Mutual Inductance
ε₂ = −M dI₁/dt
M = N₂Φ₂₁/I₁; symmetric: M₁₂ = M₂₁
Coaxial Solenoid M
M = μ₀N₁N₂A/l
A = smaller solenoid area; l = length of primary
Energy in Inductor
U = ½LI²
Stored in magnetic field; analogy to ½mv²
Magnetic Energy Density
u_B = B²/2μ₀
J/m³; compare u_E = ε₀E²/2
Induced Charge
q = NΔΦ/R
Independent of time! Ballistic galvanometer principle
AC Generator EMF
ε = NBAω sin(ωt)
ε₀ = NBAω; derived from Φ = NBAcos(ωt)
Transformer
V₂/V₁ = N₂/N₁ = I₁/I₂
Ideal transformer; V₁I₁ = V₂I₂ (power conservation)
LC Oscillation
ω = 1/√(LC)
T = 2π√(LC); I_max = Q₀/√(LC)
Series Inductors (M)
L_eff = L₁+L₂±2M
+ for aiding, − for opposing mutual coupling
🧠 Concept Flashcards (Click to Flip)
Faraday's 2nd Law
Click to reveal the formula
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ε = −N · dΦ/dt
Magnitude: |ε| = N × |rate of flux change|
Negative sign → Lenz's Law
Magnitude: |ε| = N × |rate of flux change|
Negative sign → Lenz's Law
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🧩 Memory Tricks
Lenz's Law — "OPPOSE the CHANGE"
Lenz's Law = Electromagnetic Inertia. Like Newton's first law resists change in motion, Lenz's law resists change in flux. Whatever the flux is doing — the induced current fights it.
L = μ₀N²A/l — "N Squared Always"
The N² is the key differentiator. Wind 100 turns vs 200 turns → 4× inductance. If a question changes N, L changes by N² ratio. This is where most students make factor errors.
EMF Zero When Flux is Maximum
"If the bucket is full, nothing flows in." Maximum flux = no change = no EMF. The coil perpendicular to B has maximum flux but zero EMF. The coil parallel to B has zero flux but maximum EMF rate of change.
Induced Charge = Flux Change / Resistance
Think of it as: total "electromagnetic impulse" ÷ resistance. Time doesn't matter — only total flux change. This is why ballistic galvanometers work — they measure total charge (flux change) regardless of how fast the magnet moves through.
Rail Problem: "Don't Forget the Rod's R"
In EVERY rail problem: check if the rod itself has resistance. If yes → total R = R_external + R_rod (series). This is the most common error in JEE Main. Make it a habit to write R_total first.
Flux Angle: "Normal, Not Surface"
Φ = BAcosθ where θ = angle with NORMAL. If B makes angle α with the surface, then θ with normal = 90° − α. Draw a quick sketch in the exam to avoid confusion. This mistake costs marks in NEET every year.
Motional EMF Direction: Right Hand Rule
Point fingers of right hand in direction of velocity (v). Curl toward B. Thumb points in direction of conventional current in the rod. The end where thumb points = high potential end (+ve terminal).
Time Constant in Rail Dynamics
τ = mR/B²L² (time constant for rod approaching terminal velocity). Bigger mass → slower approach. Bigger B or L → faster approach. Analogous to RC circuit: τ = RC. Velocity follows: v(t) = v_T(1 − e^(−t/τ)).
📊 Exam Quick Reference
CBSE — Must Know
| Derivation 1 | L = μ₀N²A/l (solenoid) |
| Derivation 2 | ε = NBAω sinωt (AC generator) |
| Derivation 3 | M = μ₀N₁N₂A/l (coaxial solenoids) |
| Diagram | AC generator (labeled, with slip rings) |
| Application Q | Eddy currents — 3 uses, lamination reason |
| Numerical type | ε = NΔΦ/Δt, q = NΔΦ/R, U = ½LI² |
NEET — Focus Points
| Annual pattern | Lenz's Law direction problem |
| Common trap | Static magnet → EMF = 0 |
| Must formula | q = NΔΦ/R (no time) |
| Applications | Eddy: induction heater, EM brake, galvanometer |
| Speed | Max 90 sec per EMI question |
| Negative mark | Eliminate 2 options before guessing |
JEE Main — Must Know
| High frequency | ε = ½BωL² (rotating rod) |
| High frequency | Rail problem (full: ε, I, F, P) |
| Graph type | Φ = f(t) → differentiate for EMF |
| Terminal v | v_T = FR/(B²L²) |
| Series L | L₁+L₂±2M (aiding/opposing) |
| Speed | 3 min per EMI question max |
JEE Advanced — Key Skills
| ODE solving | ma = mg − B²L²v/R → v(t) = v_T(1−e^(−t/τ)) |
| Energy method | Heat = Initial KE − Final KE |
| Two rods | Momentum conservation → v_f = v₀/2 |
| Geometry | B not ⊥ incline → resolve B components |
| LC circuits | Q(t), I(t), energy distribution at any t |
| Rotating rod | EMF from center to end = 3BωL²/8 |
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