Chapter 1–2: Electrostatics — Key Formulas
Coulomb's Law
F = kq₁q₂/r² where k = 1/4πε₀ = 9×10⁹ N·m²/C²
Force between two point charges. Note: This is a vector force — direction is along the line joining the charges.
Electric Field
E = F/q = kQ/r² (Point charge)
E (infinite line charge) = λ/2πε₀r
E (infinite plane) = σ/2ε₀
E (infinite line charge) = λ/2πε₀r
E (infinite plane) = σ/2ε₀
Gauss's Law
∮E·dA = Q_enclosed/ε₀
Total electric flux through any closed surface = enclosed charge/ε₀
Electric Potential
V = kQ/r = Work done per unit charge
E = -dV/dr (relation to field)
V_sphere (inside) = kQ/R (constant)
E = -dV/dr (relation to field)
V_sphere (inside) = kQ/R (constant)
Capacitance
C = Q/V
C_parallel_plate = ε₀A/d (without dielectric)
C_parallel_plate = Kε₀A/d (with dielectric K)
Energy = ½CV² = Q²/2C
C_parallel_plate = ε₀A/d (without dielectric)
C_parallel_plate = Kε₀A/d (with dielectric K)
Energy = ½CV² = Q²/2C
Chapter 3: Current Electricity — Key Formulas
V = IR (Ohm's Law)
R = ρL/A (Resistivity)
ρ = ρ₀(1 + α·ΔT) (Temperature dependence)
P = VI = I²R = V²/R (Power)
R = ρL/A (Resistivity)
ρ = ρ₀(1 + α·ΔT) (Temperature dependence)
P = VI = I²R = V²/R (Power)
Kirchhoff's Laws
KCL: ΣI_in = ΣI_out (at junction)
KVL: ΣV = 0 (in closed loop)
KVL: ΣV = 0 (in closed loop)
Wheatstone Bridge (Balanced)
P/Q = R/S → Ig = 0 (balanced condition)
Chapter 4–5: Magnetic Effects of Current
F = q(v × B) (Lorentz force)
F = BIL sinθ (force on current-carrying conductor)
B (infinite wire) = μ₀I/2πr (Ampere's Law)
B (solenoid) = μ₀nI
μ₀ = 4π×10⁻⁷ T·m/A
F = BIL sinθ (force on current-carrying conductor)
B (infinite wire) = μ₀I/2πr (Ampere's Law)
B (solenoid) = μ₀nI
μ₀ = 4π×10⁻⁷ T·m/A
Chapter 6–8: EMI, Faraday's Law & AC
EMF = -dΦ/dt (Faraday's Law)
Φ = BA cosθ (Magnetic flux)
V_rms = V₀/√2, I_rms = I₀/√2
Z = √(R² + (X_L - X_C)²) (Impedance)
Resonance: f = 1/(2π√LC)
Φ = BA cosθ (Magnetic flux)
V_rms = V₀/√2, I_rms = I₀/√2
Z = √(R² + (X_L - X_C)²) (Impedance)
Resonance: f = 1/(2π√LC)
Chapter 9: Ray Optics
1/f = 1/v - 1/u (Mirror formula)
1/f = 1/v - 1/u (Lens formula)
m = -v/u (magnification)
n₁sinθ₁ = n₂sinθ₂ (Snell's Law)
n = c/v (refractive index)
1/f = (n-1)(1/R₁ - 1/R₂) (Lens Maker's Equation)
1/f = 1/v - 1/u (Lens formula)
m = -v/u (magnification)
n₁sinθ₁ = n₂sinθ₂ (Snell's Law)
n = c/v (refractive index)
1/f = (n-1)(1/R₁ - 1/R₂) (Lens Maker's Equation)
Chapter 10: Wave Optics
Path difference for bright: Δ = nλ
Path difference for dark: Δ = (2n-1)λ/2
Fringe width β = λD/d (YDSE)
Resolving power = 1.22λ/(2μsinθ)
Path difference for dark: Δ = (2n-1)λ/2
Fringe width β = λD/d (YDSE)
Resolving power = 1.22λ/(2μsinθ)
Chapter 11: Dual Nature of Matter
E = hν (Photon energy)
KE_max = hν - φ (Photoelectric effect)
λ = h/mv = h/p (de Broglie wavelength)
h = 6.626×10⁻³⁴ J·s (Planck's constant)
KE_max = hν - φ (Photoelectric effect)
λ = h/mv = h/p (de Broglie wavelength)
h = 6.626×10⁻³⁴ J·s (Planck's constant)
Chapter 12: Atoms — Bohr's Model
r_n = 0.529n² Å (Bohr radius)
v_n = 2.18×10⁶/n m/s
E_n = -13.6/n² eV
ν = R(1/n₁² - 1/n₂²) (Rydberg formula)
v_n = 2.18×10⁶/n m/s
E_n = -13.6/n² eV
ν = R(1/n₁² - 1/n₂²) (Rydberg formula)
Chapter 13: Nuclei
R = R₀A^(1/3) (Nuclear radius, R₀=1.2 fm)
Binding energy = [ZM_p + NM_n - M_nucleus]c²
N = N₀e^(-λt) (Radioactive decay)
T₁/₂ = 0.693/λ (Half-life)
Binding energy = [ZM_p + NM_n - M_nucleus]c²
N = N₀e^(-λt) (Radioactive decay)
T₁/₂ = 0.693/λ (Half-life)
Chapter 14: Semiconductor Electronics
Forward bias: I = I₀(e^(V/V_T) - 1)
Transistor: I_E = I_B + I_C
β = I_C/I_B (current gain)
α = I_C/I_E = β/(1+β)
Transistor: I_E = I_B + I_C
β = I_C/I_B (current gain)
α = I_C/I_E = β/(1+β)
Important Constants to Memorise
ε₀ = 8.85×10⁻¹² C²/N·m²
μ₀ = 4π×10⁻⁷ T·m/A
c = 3×10⁸ m/s
h = 6.626×10⁻³⁴ J·s
e = 1.6×10⁻¹⁹ C
m_e = 9.11×10⁻³¹ kg
m_p = 1.67×10⁻²⁷ kg
k = 9×10⁹ N·m²/C²
μ₀ = 4π×10⁻⁷ T·m/A
c = 3×10⁸ m/s
h = 6.626×10⁻³⁴ J·s
e = 1.6×10⁻¹⁹ C
m_e = 9.11×10⁻³¹ kg
m_p = 1.67×10⁻²⁷ kg
k = 9×10⁹ N·m²/C²
How to Use This Formula Sheet Effectively
Don't just read this sheet — interact with it:
- For every formula: write the derivation in 3–5 steps in your notebook
- Identify which formulas require memorisation vs which you can derive quickly
- Practice dimensional analysis for each formula — this catches errors in exams
- Note the limiting conditions: when does each formula apply? When does it break down?
🎯 Remember: Formulas are the final output of understanding. If you can derive every formula on this sheet, you'll never forget it — and you'll know exactly when to apply it. Get personalised Class 12 Physics coaching →