Class 12 Physics Derivations

Continuous scrolling PDF of all essential Class 12 derivations required for CBSE, HP Board subjective exams, and competitive conceptual building.

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Why Derivations Are Not Just "Proofs"—They Are Your Solution Manual

A massive misconception among Class 12 students preparing for CBSE, HP Board, JEE, or NEET is that derivations are just long blocks of math to memorize for 3-mark board questions. This couldn't be further from the truth.

A derivation is actually the step-by-step logical algorithm for solving a numerical. When an examiner twists a question, your final memorized formula will fail. But if you know the steps of the derivation, you can apply that exact same logic to solve the twisted problem.

Example: Electric Field of a Dipole (Equatorial Line)

Most students simply memorize the final formula: $$ E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3} $$

But what happens if a JEE question asks for the field when a third charge is placed nearby, or if the dipole charges are unequal? The standard formula becomes useless. However, if you know the derivation steps:

  1. Calculate the individual electric field vectors $E_{+q}$ and $E_{-q}$.
  2. Resolve these vectors into horizontal ($E \cos\theta$) and vertical ($E \sin\theta$) components.
  3. Observe that vertical components cancel out, and add the horizontal components together.

You simply repeat these exact three vector-resolution steps for the twisted question, and you arrive at the correct answer safely. Derivations teach you how to think like a physicist.

Top Lengthy & Important Derivations (Board Exam Favorites)

Examiners in the CBSE and HP Board love testing your endurance, sign-convention accuracy, and mathematical precision. These are the lengthy derivations that almost always appear as 5-mark long-answer questions:

1. Lens Maker's Formula

Ray Optics

Proving the relation between focal length, refractive index, and radii of curvature. Requires setting up refraction equations for two separate spherical surfaces and combining them.

$$ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) $$
2. Impedance of LCR Circuit

Alternating Current

Involves drawing the phasor diagram for voltage and current across an Inductor, Capacitor, and Resistor, and using vector addition to find the net impedance.

$$ Z = \sqrt{R^2 + (X_L - X_C)^2} $$
3. Magnetic Field on Axis of Loop

Moving Charges and Magnetism

Deriving the magnetic field using the Biot-Savart Law. Involves resolving magnetic field vectors ($dB$) and integrating the effective components over the entire circular loop.

$$ B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}} $$

Categorizing the Complexity

The "Easy" Derivations

Short, algebra-based proofs that are highly scoring.

  • Drift Velocity relation ($I = neAv_d$).
  • Equivalent Capacitance/Resistance in Series and Parallel.
  • De Broglie Wavelength relation ($\lambda = \frac{h}{\sqrt{2mK}}$).
The "Hard" Derivations

Conceptually dense, relies heavily on complex ray diagrams or 3D vector calculus.

  • Magnifying power of a Compound Microscope / Astronomical Telescope.
  • Applications of Gauss's Law (e.g., Electric field of a uniformly charged solid sphere).
  • Force between two parallel current-carrying conductors.