JEE Main Physics Formula Sheet: High-Yield Equations, Modern Physics & Mechanics Shortcuts

In JEE Main, Physics carries 100 marks (25 questions). Over recent NTA exam trends, Physics has emerged as the most scoring paper when students master direct formula substitution, dimensional analysis, and standard shortcut theorems.

This cheat-sheet compiles the highest-yield formula templates across Modern Physics, Mechanics, Electrodynamics, and Heat & Thermodynamics.

1. High-Yield Modern Physics & Nuclear Physics (12–16 Marks)

Modern Physics consistently yields 3 to 4 direct questions requiring minimal calculation time:

A. Photoelectric Effect & de Broglie Wavelength

• Einstein's Equation: $K_{\max} = h\nu - \phi = eV_0$ (where $V_0$ is stopping potential).
• de Broglie Wavelength of electron: $\lambda = \frac{h}{\sqrt{2mE}} = \frac{12.27}{\sqrt{V}} \text{ \AA}$.
• For particle with charge $q$ accelerated by voltage $V$: $\lambda = \frac{h}{\sqrt{2mqV}}$.

B. Bohr's Model for Hydrogen-like Atoms

• Radius: $r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$.
• Velocity: $v_n = 2.18 \times 10^6 \times \frac{Z}{n} \text{ m/s}$.
• Total Energy: $E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV}$.
• Rydberg Formula: $\frac{1}{\lambda} = R Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ where $R \approx 1.097 \times 10^7 \text{ m}^{-1}$.

C. Radioactivity & Binding Energy

• Half-life: $T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$.
• Mean life: $\tau = \frac{1}{\lambda} = 1.44 T_{1/2}$.
• Mass defect: $\Delta m = [Z m_p + (A - Z) m_n] - M_{\text{nucleus}}$.
• Binding Energy: $BE = \Delta m \times 931.5 \text{ MeV}$.

2. Electrodynamics & Current Electricity (16–20 Marks)

• Drift Velocity & Current: $I = n e A v_d$, where $v_d = \frac{e E \tau}{m}$.
• Temperature Dependence of Resistance: $R_T = R_0 (1 + \alpha \Delta T)$.
• Wheatstone Bridge Balance Condition: $\frac{P}{Q} = \frac{R}{S}$ (Galvanometer current = 0).
• Biot-Savart Law (Axis of circular loop): $B = \frac{\mu_0 I R^2}{2 (R^2 + x^2)^{3/2}}$. At center: $B = \frac{\mu_0 I}{2R}$.
• Self-Inductance of Solenoid: $L = \mu_0 n^2 A l$.
• LC Oscillations Frequency: $\omega = \frac{1}{\sqrt{LC}}$, $f = \frac{1}{2\pi \sqrt{LC}}$.

3. Mechanics & Rotational Motion Shortcuts

• Work-Energy Theorem: $W_{\text{all forces}} = \Delta K = K_f - K_i$.
• Moment of Inertia Core Catalog:
  • Ring (central axis): $MR^2$; Disc: $\frac{1}{2} M R^2$.
  • Solid Sphere: $\frac{2}{5} M R^2$; Hollow Sphere: $\frac{2}{3} M R^2$.
  • Solid Cylinder: $\frac{1}{2} M R^2$; Hollow Cylinder: $M R^2$.
• Parallel Axis Theorem: $I = I_{cm} + M d^2$.
• Rolling Motion Acceleration on Incline: $a = \frac{g \sin \theta}{1 + \frac{k^2}{R^2}}$.

4. Cross-Study Resources & Preparation Links

• Predict your admission chances with our JEE Main Percentile to Rank Predictor.
• Download authentic past 10-year question papers on the Competitive Exam PYQ Archive.
• Explore the complete engineering preparation ecosystem on the JEE Main Portal.
• Practice full-length computerized CBT tests on the Student CBT Mock Engine.

Frequently Asked Questions (FAQ)

Q1: How many questions in JEE Main Physics are purely formula-based?

Historically, between 14 and 16 out of 25 questions in the Section A (MCQ) can be solved within 90 seconds if the standard formula and unit conversion are readily recalled.

Q2: What chapters should I master to score 60+ marks in JEE Physics?

Modern Physics, Current Electricity, Semiconductor Devices, Thermal Physics (Thermodynamics & KTG), and Gravitation together account for 50 to 60 marks.