NSEP cheat sheet

Physics (CBSE Class 12 syllabus): formulas, laws and decision rules

• Electrostatics: Coulomb force F = (1/4πε₀)|q₁q₂|/r² with 1/4πε₀ = 9×10⁹ N·m²/C²; field of a point charge E = kq/r²; uniform field between plates E = V/d.

• Gauss's law: ∮E·dA = q_enclosed/ε₀. Use it for spherical, cylindrical and infinite-plane symmetry: E = λ/(2πε₀r) for a line charge, E = σ/(2ε₀) for a conductor surface, E = σ/ε₀ outside an infinite sheet.

• Capacitance: C = Q/V; parallel plate C = ε₀A/d (κ multiplies it with a dielectric); series 1/C = Σ1/Cᵢ; parallel C = ΣCᵢ; energy U = ½CV² = Q²/2C; energy density u = ½ε₀E².

• Current electricity: drift velocity v_d = I/(nAe); R = ρL/A; series/parallel resistor rules; Kirchhoff's junction (ΣI = 0) and loop (ΣΔV = 0) laws; Wheatstone balance P/Q = R/S; potentiometer compares EMFs as l₁/l₂.

• Moving charges: F = qv×B, radius r = mv/(qB), cyclotron frequency f = qB/(2πm); force on a wire F = BIL sinθ; parallel wires attract when currents are in the same direction; torque on a current loop τ = NIAB sinθ.

• Magnetic fields: Biot–Savart dB = (μ₀/4π)(I dl×r̂)/r²; long wire B = μ₀I/(2πr); centre of a loop B = μ₀I/2R; solenoid B = μ₀nI; Ampere's law ∮B·dl = μ₀I_enclosed.

• Electromagnetic induction: ε = −dΦ/dt; motional EMF ε = BvL; self-inductance ε = −L dI/dt, energy U = ½LI²; mutual inductance; transformer V_s/V_p = N_s/N_p with ideal power equality.

• Alternating current: RMS values I_rms = I₀/√2; impedance Z = √(R² + (X_L − X_C)²) with X_L = ωL, X_C = 1/ωC; resonance at ω = 1/√(LC); power P = V_rms I_rms cosφ; power factor cosφ = R/Z.

• Optics and modern physics: mirror 1/f = 1/v + 1/u, lens 1/f = 1/v − 1/u, lens maker (n−1)(1/R₁ − 1/R₂); Young's fringes β = λD/d; photoelectric hν = φ₀ + K_max, stopping potential eV₀ = hν − φ₀; de Broglie λ = h/p; Bohr E_n = −13.6/n² eV and r_n ∝ n².