Class 12 Physics Derivations List — Board Exam Must Know 2027
Complete list of 25+ must-know Class 12 Physics derivations for board exams 2027. Organized by chapter: Electrostatics, Current Electricity, Magnetism, EMI, Optics, Modern Physics, Semiconductors. Starting point, final result, and typical marks for each.
In short: This page lists every derivation you need for Class 12 Physics board exams 2027. For each one: the name, chapter, starting formula, final result, and how many marks it typically carries. Bookmark this page and check off derivations as you master them. No theory — just the complete derivation checklist.
How to Use This List
Step
Action
1
Read through the full list once to see the scope
2
Mark derivations you already know with a tick
3
Practice unknown ones from NCERT — write fully, step by step
4
Revise 3-4 derivations daily from this list
5
In the last week, do one full "derivation dump" — write all from memory
Electrostatics (Chapter 1-2) — 6 Derivations
#
Derivation Name
Starting Point
Final Result
Typical Marks
1
Electric field due to a dipole (axial point)
Coulomb's law for two charges
E = (1/4πε₀) × (2p/r³)
3
2
Electric field due to a dipole (equatorial point)
Superposition of fields
E = (1/4πε₀) × (p/r³)
3
3
Torque on a dipole in uniform electric field
Force on each charge
τ = pE sinθ or τ = p × E
3
4
Electric field due to infinite plane sheet of charge
Gauss's law with cylindrical Gaussian surface
E = σ/2ε₀
5
5
Electric field due to uniformly charged spherical shell
Gauss's law with spherical Gaussian surface
E = (1/4πε₀)(Q/r²) outside, E = 0 inside
5
6
Capacitance of a parallel plate capacitor
C = Q/V, using E = σ/ε₀
C = ε₀A/d
3
Electrostatics — Key Formulas Reference
Formula
Expression
Unit
Coulomb's Law
F = (1/4πε₀)(q₁q₂/r²)
Newton (N)
Electric field
E = F/q₀
N/C or V/m
Electric potential
V = (1/4πε₀)(q/r)
Volt (V)
Capacitance
C = Q/V
Farad (F)
Energy in capacitor
U = ½CV² = ½QV = Q²/2C
Joule (J)
With dielectric
C' = KC = Kε₀A/d
Farad (F)
ε₀ value
8.854 × 10⁻¹² C²N⁻¹m⁻²
—
Current Electricity (Chapter 3) — 3 Derivations
#
Derivation Name
Starting Point
Final Result
Typical Marks
7
Drift velocity and current relation
I = nAv_d
v_d = eE/m × τ (relaxation time)
3
8
Ohm's Law from drift velocity
J = σE, using v_d expression
R = ρl/A where ρ = m/(ne²τ)
3
9
Wheatstone Bridge condition
Kirchhoff's laws on bridge circuit
P/Q = R/S (balanced condition)
3
Current Electricity — Key Formulas
Formula
Expression
Current
I = Q/t = nAv_d × e
Drift velocity
v_d = eEτ/m
Resistivity
ρ = m/(ne²τ)
Conductivity
σ = ne²τ/m
EMF of cell
ε = V + Ir (internal resistance)
Cells in series
ε_total = nε, r_total = nr
Cells in parallel
ε_total = ε, r_total = r/n
Meter bridge
R = S × l/(100 - l)
Potentiometer
ε₁/ε₂ = l₁/l₂
Magnetism and Moving Charges (Chapter 4-5) — 3 Derivations
#
Derivation Name
Starting Point
Final Result
Typical Marks
10
Magnetic field on axis of a circular current loop
Biot-Savart law, integrate
B = μ₀IR²/2(R² + x²)^(3/2), at centre: B = μ₀I/2R
5
11
Force between two parallel current-carrying conductors
B from one wire, F = BIL on other
F/L = μ₀I₁I₂/2πd
3
12
Torque on a current loop in magnetic field
Force on each arm
τ = NIAB sinθ or τ = m × B
3
Magnetism — Key Formulas
Formula
Expression
Biot-Savart Law
dB = (μ₀/4π)(Idl × r̂)/r²
Ampere's Circuital Law
∮B·dl = μ₀I_enclosed
Solenoid field
B = μ₀nI
Toroid field
B = μ₀NI/2πr
Force on moving charge
F = qv × B
Cyclotron frequency
f = qB/2πm
Magnetic moment
m = NIA
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Optics — Ray and Wave (Chapters 9-10) — 5 Derivations
#
Derivation Name
Starting Point
Final Result
Typical Marks
17
Refraction at a spherical surface
Snell's law at curved surface
n₁/u + n₂/v = (n₂ - n₁)/R
5
18
Lens Maker's formula
Refraction at two surfaces
1/f = (n-1)(1/R₁ - 1/R₂)
5
19
Prism — deviation and refractive index
Geometry + Snell's law
n = sin[(A+D_m)/2] / sin(A/2)
3
20
Young's double slit — fringe width
Path difference = nλ
β = λD/d
5
21
Diffraction at single slit (central max width)
Path difference analysis
Width of central max = 2λD/a
3
Optics — Key Formulas
Formula
Expression
Mirror formula
1/f = 1/v + 1/u
Lens formula
1/f = 1/v - 1/u
Power of lens
P = 1/f (metres), unit: Dioptre
Magnifying power (Simple microscope)
m = 1 + D/f
Magnifying power (Compound microscope)
m = (L/f_o)(D/f_e)
Telescope magnification
m = f_o/f_e
Resolving power (microscope)
1/d_min = 2n sinθ/λ
Fringe width (YDSE)
β = λD/d
Malus's Law
I = I₀ cos²θ
Brewster's angle
tan i_B = n
Modern Physics (Chapters 11-13) — 3 Derivations
#
Derivation Name
Starting Point
Final Result
Typical Marks
22
de Broglie wavelength
E = hν, p = mv
λ = h/mv = h/p
2
23
Bohr's model — radius and energy of H-atom
Centripetal force = Electrostatic force + quantization
rₙ = n²a₀, Eₙ = -13.6/n² eV
5
24
Radioactive decay law
dN/dt = -λN
N = N₀e^(-λt), T₁/₂ = 0.693/λ
3
Modern Physics — Key Formulas
Formula
Expression
Einstein's photoelectric equation
KE_max = hν - φ = h(ν - ν₀)
Threshold frequency
ν₀ = φ/h
Stopping potential
eV₀ = hν - φ
de Broglie wavelength
λ = h/mv = h/√(2mKE)
Bohr radius
rₙ = 0.529 × n²/Z Angstrom
Bohr energy
Eₙ = -13.6 × Z²/n² eV
Mass-energy
E = mc²
Binding energy
BE = [Zm_p + (A-Z)m_n - M] × 931.5 MeV
Half-life
T₁/₂ = 0.693/λ
Activity
A = λN = A₀e^(-λt)
Hydrogen spectrum
1/λ = R(1/n₁² - 1/n₂²)
Semiconductors (Chapter 14) — 2 Derivations
#
Derivation Name
Starting Point
Final Result
Typical Marks
25
p-n junction diode — forward and reverse bias
Energy band diagram, depletion layer
I-V characteristics, barrier potential ~0.7V (Si)
3
26
Logic gates — truth tables and Boolean expressions
AND, OR, NOT, NAND, NOR
Universal gates: NAND, NOR can make any gate
2
Semiconductor Devices — Quick Reference
Device
Key Property
Application
p-n junction diode
Allows current in one direction
Rectifier
Zener diode
Operates in reverse breakdown
Voltage regulator
LED
Emits light in forward bias
Displays, lighting
Photodiode
Current increases with light (reverse bias)
Light sensors
Solar cell
Converts light to electricity
Power generation
Transistor (npn/pnp)
Current amplification: I_C = βI_B
Amplifier, Switch
Derivation Mastery Tracker
Chapter Group
Total Derivations
High Priority (5 marks)
Medium Priority (3 marks)
Quick (2 marks)
Electrostatics
6
2 (Gauss's law applications)
4
0
Current Electricity
3
0
3
0
Magnetism
3
1 (Biot-Savart on axis)
2
0
EMI & AC
3
0
2
1
EM Waves
1
0
0
1
Optics
5
3 (Lens maker, YDSE, Refraction)
2
0
Modern Physics
3
1 (Bohr model)
1
1
Semiconductors
2
0
1
1
Total
26
7
15
4
Important Constants for Class 12 Physics
Constant
Symbol
Value
Speed of light
c
3 × 10⁸ m/s
Planck's constant
h
6.63 × 10⁻³⁴ J·s
Electron charge
e
1.6 × 10⁻¹⁹ C
Electron mass
mₑ
9.1 × 10⁻³¹ kg
Proton mass
mₚ
1.67 × 10⁻²⁷ kg
Permittivity of free space
ε₀
8.854 × 10⁻¹² C²N⁻¹m⁻²
Permeability of free space
μ₀
4π × 10⁻⁷ T·m/A
Boltzmann constant
k_B
1.38 × 10⁻²³ J/K
Rydberg constant
R
1.097 × 10⁷ m⁻¹
Bohr radius
a₀
0.529 × 10⁻¹⁰ m
1 eV
—
1.6 × 10⁻¹⁹ J
1 AMU
u
931.5 MeV/c²
Frequently Asked Questions
Q1. How many derivations are asked in the Class 12 Physics board exam?
Typically 2-3 derivations appear as 5-mark or 3-mark questions. That accounts for 10-15 marks out of 70. Mastering all 26 derivations listed here covers every possibility.
Q2. Which derivations are repeated most often?
Lens Maker's formula, Young's double slit fringe width, Gauss's law for spherical shell, Bohr model energy levels, and magnetic field on axis of circular loop are the top 5 most repeated derivations across boards.
Q3. Should I memorize derivations or understand them?
Understand first, then practice writing them. Examiners check logical flow — each step should follow from the previous one. Skipping steps loses marks even if the final answer is correct.
Q4. How long does it take to write a full derivation in the exam?
A 5-mark derivation takes about 8-10 minutes if you write clearly with diagrams. A 3-mark derivation takes about 5-6 minutes. Budget your time accordingly.
Q5. Are these derivations the same for CBSE and State Boards?
The core derivations (Gauss's law, Lens Maker's, YDSE, Bohr model) are common across all boards. Some State Boards may add or skip 1-2 derivations. Cross-check with your specific board syllabus.
