Class 12 Physics: Important Derivations, Chapter by Chapter (CBSE)

Ask any Class 12 student which part of the Physics board paper feels most predictable, and most will say derivations. The steps are fixed, the diagrams are standard, and the marking scheme rewards each correct step.

Yet many students lose marks here. They learn derivations by reading them, not writing them, and then miss a step, a diagram or a sign in the exam.

This guide gives you a chapter-wise list based on the current rationalised NCERT textbook, two worked derivations, and a method for writing them for full marks.

Check before you study. NCERT rationalised the Class 12 Physics textbook, and some topics (for example the potentiometer, the cyclotron and parts of semiconductor electronics) were removed. Always match this list against the CBSE curriculum for your session on cbseacademic.nic.in.

How derivations are marked

The CBSE Class 12 Physics theory paper is worth 70 marks, with 30 marks for practicals. Derivations usually appear as 3-mark or 5-mark questions, sometimes as part of a longer question.

Marks are typically awarded for:

1. A labelled diagram where one applies
2. The starting principle or law (for example Gauss's law or Kirchhoff's rule)
3. The key intermediate steps
4. The final result, clearly shown

A correct final formula with missing steps rarely gets full marks.

Chapter-wise list of important derivations

Unit I: Electrostatics

Ch 1. Electric Charges and Fields

• Electric field of a dipole on the axial line and on the equatorial line
• Torque on an electric dipole in a uniform electric field
• Field due to an infinitely long straight charged wire (Gauss's law)
• Field due to a uniformly charged infinite plane sheet
• Field due to a uniformly charged thin spherical shell, outside and inside

Ch 2. Electrostatic Potential and Capacitance

• Potential due to a point charge and due to an electric dipole
• Potential energy of a dipole in a uniform electric field
• Capacitance of a parallel plate capacitor, with and without a dielectric
• Equivalent capacitance in series and in parallel
• Energy stored in a capacitor and energy density of the electric field

Unit II: Current Electricity

Ch 3. Current Electricity

• Relation between current and drift velocity, I = neAv_d
• Ohm's law from drift velocity, and the expression for resistivity
• Equivalent emf and internal resistance of cells in series and in parallel
• Balance condition of the Wheatstone bridge using Kirchhoff's rules

Unit III: Magnetic Effects of Current and Magnetism

Ch 4. Moving Charges and Magnetism

• Magnetic field on the axis of a circular current loop (Biot–Savart law)
• Field due to a long straight wire and inside a long solenoid (Ampère's law)
• Force between two parallel current-carrying conductors; definition of the ampere
• Torque on a rectangular current loop in a uniform magnetic field
• Radius of the circular path of a charge moving perpendicular to a magnetic field

Ch 5. Magnetism and Matter

• Bar magnet as an equivalent solenoid
• Torque and potential energy of a magnetic dipole in a uniform field

Unit IV: Electromagnetic Induction and Alternating Currents

Ch 6. Electromagnetic Induction

• Motional emf in a rod moving in a magnetic field, ε = Blv
• Self-inductance of a long solenoid
• Mutual inductance of two long coaxial solenoids
• Energy stored in an inductor
• Emf of an AC generator, ε = NBAω sin ωt

Ch 7. Alternating Current

• Current and phase in pure resistive, inductive and capacitive circuits
• Impedance of a series LCR circuit using a phasor diagram; resonance
• Average power in an AC circuit and power factor
• Ideal transformer: voltage and current ratios

Unit V: Electromagnetic Waves

Ch 8. Electromagnetic Waves is mostly conceptual. Know displacement current and the properties and spectrum of EM waves rather than long derivations.

Unit VI: Optics

Ch 9. Ray Optics and Optical Instruments

• Mirror formula
• Refraction at a spherical surface
• Lens maker's formula and the thin lens formula
• Equivalent focal length of two thin lenses in contact
• Refractive index of a prism in terms of A and the angle of minimum deviation
• Magnifying power of a compound microscope and an astronomical telescope

Ch 10. Wave Optics

• Laws of reflection and refraction using Huygens' principle
• Fringe width in Young's double-slit experiment
• Conditions for the minima in single-slit diffraction

Unit VII: Dual Nature of Radiation and Matter

Ch 11. Dual Nature of Radiation and Matter

• Einstein's photoelectric equation
• de Broglie wavelength of an electron accelerated through a potential V

Unit VIII: Atoms and Nuclei

Ch 12. Atoms

• Distance of closest approach in alpha-particle scattering
• Radius and energy of the nth Bohr orbit for hydrogen
• Wavelengths of spectral lines (Rydberg formula from Bohr's model)

Ch 13. Nuclei

• Mass defect and binding energy
• Nuclear density is independent of mass number (R = R₀A^(1/3))

Unit IX: Electronic Devices

Ch 14. Semiconductor Electronics asks mainly for explanations and circuit diagrams: the formation of the p–n junction, and the working of half-wave and full-wave rectifiers, with input and output waveforms.

Worked derivation 1: field of a dipole on the axial line

An electric dipole has charges −q and +q separated by 2a. Find the field at a point P on its axis, at distance r from the centre, on the side of +q.

Diagram: draw −q at A and +q at B, centre O, and P on the extended line beyond B, with OP = r.

Distance of P from +q = r − a. Distance from −q = r + a.

Field due to +q (directed away from +q, along the dipole moment p):

E₊ = (1/4πε₀) · q / (r − a)²

Field due to −q (directed towards −q, opposite to p):

E₋ = (1/4πε₀) · q / (r + a)²

E₊ is larger, so the net field points along p:

E = (q/4πε₀) [1/(r − a)² − 1/(r + a)²] = (q/4πε₀) · 4ar / (r² − a²)²

Using p = q × 2a:

E = (1/4πε₀) · 2pr / (r² − a²)²

For a short dipole (r ≫ a): E = (1/4πε₀) · 2p / r³, along p.

(On the equatorial line the result is E = (1/4πε₀) · p / (r² + a²)^(3/2), opposite to p, which becomes p / 4πε₀r³ for r ≫ a. So the axial field is twice the equatorial field at the same large distance.)

Worked derivation 2: de Broglie wavelength of an electron

An electron of mass m and charge e is accelerated from rest through a potential difference V. Find its de Broglie wavelength.

Kinetic energy gained = work done by the field:

K = eV

Since K = p² / 2m, the momentum is:

p = √(2meV)

de Broglie wavelength λ = h / p:

λ = h / √(2meV)

Substituting h = 6.63 × 10⁻³⁴ J s, m = 9.11 × 10⁻³¹ kg and e = 1.60 × 10⁻¹⁹ C:

λ ≈ 1.227 / √V nm

For V = 100 V, λ ≈ 0.123 nm, which is comparable to the spacing between atoms in a crystal. That is why electron beams show diffraction.

How to practise derivations

• Write, don't read. Close the book and write the derivation from memory. Then compare line by line.
• One diagram, every time. Even when the question doesn't ask for one, a labelled diagram earns credit and helps you avoid sign errors.
• Make a one-page sheet per unit with the starting law and the final result of each derivation.
• Revise in rounds. Write every derivation once a month until January, then twice in the final weeks.
• Link to numericals. After each derivation, solve two NCERT numericals that use the result.

Plan your Physics year

If derivations in Electrostatics or Optics still feel shaky, start there; together they carry a large share of the paper. Our Class 12 Physics for Boards and JEE Main programme covers the NCERT syllabus with weekly tests, written derivation practice and full mock papers. For a short, intense revision before the boards, see the Board Exam Crash Course. You can also watch chapter lectures on our YouTube channel, youtube.com/@alphaacademyofphysics.

Next step: read what to look for in Physics coaching in Karnal, or take ASCAT, our scholarship-cum-admission test.