Class 12 Physics Formula Sheet

1. Magnetic Flux & Faraday’s Laws

• Magnetic Flux (Φ [Phi]): Φ = B · A = BA cos(θ [θ = angle between B and normal vector to area A]) (Unit: Weber [Wb] or Tesla·m²)
• Faraday’s Law of Induction: e = -N × (dΦ / dt) (Where e = induced EMF, N = number of turns, dΦ/dt = rate of change of magnetic flux. Negative sign indicates Lenz's law)
• Induced Current (I) & Charge Flow (q): I = e / R (R = circuit resistance) and q = ΔΦ / R (Charge flown is independent of time)

2. Motional Electromotive Force (EMF)

• Motional EMF in a Straight Conductor: e = BvL (Where B = magnetic field, v = velocity, L = length of conductor moving perpendicular to B)
• Motional EMF of a Rotating Rod (about one end): e = (1 / 2) × B ω L² (ω = angular velocity)
• Power Required & Force: F = (B² v L²) / R (Magnetic force opposing motion) and P = (B² v² L²) / R

3. Inductance (Self & Mutual Induction)

• Self-Inductance (L): NΦ = LI → e = -L × (dI / dt) (Unit: Henry [H] or Wb/A)
• Self-Inductance of a Long Solenoid: L = (μ₀ μ_r N² A) / l (Where N = total turns, A = area, l = length, μ_r = relative permeability)
• Mutual Induction (M): N₂Φ₂ = M I₁ → e₂ = -M × (dI₁ / dt) (Mutual inductance between two coils)
• Energy Stored in an Inductor: U = (1 / 2) × L I² (Magnetic Energy Density u_B = B² / (2 μ₀))

4. AC Generator (Alternator)

• Induced EMF in AC Generator: e = e₀ sin(ωt) (Where peak EMF e₀ = NBAω, ω = angular frequency)