12th Physics Derivations List: Every Derivation You Should Know
Physics differs from Maths in one useful way: a fairly fixed list of derivations reappears in the public exam every year. Once you know that list, the five-mark section stops being unpredictable.
Below are the derivations worth knowing cold, unit by unit.
Unit 1: Electrostatics
- Electric field due to a dipole at a point on the axial line and on the equatorial line
- Torque experienced by a dipole in a uniform electric field
- Electric field due to an infinitely long charged wire using Gauss law
- Electric field due to a charged infinite plane sheet
- Electric field due to a uniformly charged spherical shell, inside and outside
- Capacitance of a parallel plate capacitor, with and without a dielectric
- Energy stored in a capacitor and energy density
Unit 2: Current Electricity
- Expression for drift velocity and the relation between current and drift velocity
- Wheatstone bridge balance condition using Kirchhoff laws
- Metre bridge and potentiometer principle
- Comparison of emf of two cells using a potentiometer
Unit 3: Magnetism and Magnetic Effects of Electric Current
- Magnetic field at a point on the axis of a circular current loop
- Magnetic field due to a long straight conductor using Ampere circuital law
- Magnetic field inside a solenoid and inside a toroid
- Force between two long parallel current carrying conductors
- Torque on a current loop in a uniform magnetic field
- Theory of the moving coil galvanometer
- Conversion of a galvanometer into an ammeter and a voltmeter
Unit 4: Electromagnetic Induction and Alternating Current
- Self inductance of a long solenoid
- Mutual inductance of two coaxial solenoids
- Energy stored in an inductor
- Principle and working of an AC generator
- Impedance of a series LCR circuit and the resonance condition
- Power in an AC circuit and the power factor
- Working of a transformer and its energy losses
Unit 5: Electromagnetic Waves
- Properties of electromagnetic waves and the origin of displacement current
Unit 6: Optics
- Mirror equation for a spherical mirror
- Refraction at a single spherical surface
- Lens maker formula
- Equivalent focal length of two thin lenses in contact
- Angle of minimum deviation for a prism
- Young double slit experiment and the expression for fringe width
- Condition for constructive and destructive interference
- Resolving power of a microscope and a telescope
- Brewster law and Malus law
Optics carries the largest number of derivations of any unit. If you are choosing where to invest, invest here.
Unit 7: Dual Nature of Radiation and Matter
- Einstein photoelectric equation and its explanation of experimental observations
- de Broglie wavelength of a particle, including for an accelerated electron
Unit 8: Atomic and Nuclear Physics
- Radius, velocity and energy of an electron in the nth Bohr orbit
- Expression for the wavelength of spectral lines and the Rydberg formula
- Radioactive decay law and the relation between half life and decay constant
- Mass defect and binding energy per nucleon
Unit 9: Semiconductor Electronics
- Working of a p-n junction diode under forward and reverse bias
- Half wave and full wave rectifier with waveforms
- Transistor characteristics in common emitter configuration
- Transistor as an amplifier and as a switch
- De Morgan theorems
How to actually retain a derivation
Reading a derivation five times produces the feeling of knowing it and very little of the ability to write it. Use this instead:
- Read it once for the logic. Ask what the starting point is and what the target is. Most derivations are three or four moves, not twenty.
- Write down only the skeleton. The starting law, the two or three key substitutions, the final result. Four lines, not the whole page.
- Reproduce it from the skeleton the next day, on blank paper, without looking.
- Repeat after three days, then after a week. Spaced repetition is what moves a derivation from recognition to recall.
Always draw the diagram. In several of these, the diagram itself carries marks, and an examiner reading a derivation without one has less to award against.
A practical order
If exams are close, work in this order: Optics, then Electrostatics, then Magnetism and Electromagnetic Induction, then Atomic and Nuclear Physics, then Semiconductor Electronics. That sequence front-loads the units with the most derivation-heavy marks.
Chapter-wise Class 12 practice material is available on the Class 12 section.