Physics Formula Sheet: What to Memorise vs What to Derive for Classes 11-12

Physics in Classes 11 and 12 under the updated NCERT/NCF-SE, CBSE, ICSE, and state board frameworks is not a test of memory. Yet, students often sit down to create formula sheets spanning fifty pages, trying to commit every single expression to rote storage. When the exam paper arrives, numbers change, contexts shift, and memorised equations fail.

Success in board exams, JEE, and NEET requires a clear distinction between core results you must have on instant recall and foundational relations you should be able to derive within seconds.

The Core Memorisation List

Some formulas appear so frequently that stopping to derive them wastes critical minutes during a high-stakes exam. Memorise these definitions and fundamental constants, ensuring you know the exact conditions under which each applies.

Mechanics (Class 11)

• Equations of motion under constant acceleration: $v = u + at$, $s = ut + \frac{1}{2}at^2$, $v^2 = u^2 + 2as$.
• Centripetal acceleration and force: $a_c = \frac{v^2}{r}$ and $F_c = \frac{mv^2}{r}$.
• Universal law of gravitation and gravitational potential energy: $F = \frac{Gm_1m_2}{r^2}$ and $U = -\frac{GMm}{r}$.
• Simple harmonic motion displacement and time period: $x(T) = A \sin(\omega t + \phi)$ and $T = 2\pi\sqrt{\frac{m}{k}}$.

Electrodynamics and Modern Physics (Class 12)

• Coulomb's Law and Electric Field due to a point charge: $F = \frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^2}$ and $E = \frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}$.
• Magnetic force on a moving charge and a current-carrying wire: $\vec{F} = q(\vec{v} \times \vec{B})$ and $\vec{F} = I(\vec{L} \times \vec{B})$.
• Lens maker's formula and Snell's Law: $\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ and $n_1 \sin i = n_2 \sin r$.
• Einstein's photoelectric equation: $K_{\max} = h\nu - \phi$.

| Topic | Must-Memorise Formula | Key Condition / Limitation | | :--- | :--- | :--- | | Current Electricity | $R = \rho \frac{l}{A}$ | Uniform cross-section, constant temperature | | Capacitance | $C = \frac{\varepsilon_0 A}{d}$ | Parallel plate capacitor, vacuum medium | | Wave Optics | $\beta = \frac{\lambda D}{d}$ | Young's Double Slit Experiment, $d \ll D$ | | Thermodynamics | $PV = nRT$ | Ideal gas assumptions |

What to Derive On-the-Spot

If you try to memorise every variation of a formula, your brain will overload. Instead, memorise the foundational law and practice deriving the specific case during your revision sessions until it takes less than thirty seconds.

1. Variations of Work-Energy and Impulse

Do not memorise separate formulas for every type of collision or inclined plane problem. Start from the Work-Energy Theorem: $W_{\text{net}} = \Delta K$ From here, integrate force with respect to displacement to find work done by variable forces, or use impulse-momentum relations ($J = \Delta p = \int F dt$).

2. Field and Potential Derivations in Electrostatics

Memorising the electric field and potential for every geometry (infinite sheet, spherical shell, coaxial cable) is inefficient. Memorise Gauss's Law: $\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\varepsilon_0}$ For symmetric distributions, you can reconstruct the electric field formula in three lines. For potential, integrate the field: $V = -\int \vec{E} \cdot d\vec{r}$

3. Induced EMF and Circuit Formulas

Do not memorise specialized formulas for motional EMF in odd shapes. Start from Faraday's Law and Lenz's Law: $\mathcal{E} = -\frac{d\Phi_B}{dt}$ Substitute $\Phi_B = B A \cos\theta$ and differentiate based on what is changing—area, magnetic field, or orientation.

Strategic Application for JEE and NEET

Competitive exams test boundary conditions. In NEET, saving time means recognizing when a standard derivation yields a shortcut formula. In JEE Advanced, questions often alter the standard setup (e.g., a non-uniform magnetic field or a dielectric partially filled in a capacitor), rendering memorised shortcut formulas completely useless. Knowing how a formula is built lets you modify it mid-exam when the examiner throws a curveball.

Quick Checklist

• [ ] Can I state the assumptions behind every memorised formula?
• [ ] Do I derive Gauss's Law applications and Biot-Savart law consequences weekly?
• [ ] Am I avoiding long lists of derived "shortcut" formulas that only apply to one textbook question?
• [ ] Do my notes clearly separate fundamental definitions from derived results?