JEE Mains Physics 2026

Cheatsheet Content

### Kinematics - **Displacement ($\vec{s}$)**: Change in position. - **Velocity ($\vec{v}$)**: Rate of change of displacement. $\vec{v} = \frac{d\vec{s}}{dt}$. - **Acceleration ($\vec{a}$)**: Rate of change of velocity. $\vec{a} = \frac{d\vec{v}}{dt} = \frac{d^2\vec{s}}{dt^2}$. - **Equations of Motion (Constant Acceleration)**: 1. $v = u + at$ 2. $s = ut + \frac{1}{2}at^2$ 3. $v^2 = u^2 + 2as$ 4. $s_n = u + \frac{a}{2}(2n-1)$ (Displacement in $n$-th second) - **Relative Velocity**: $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$. - **Projectile Motion**: - Horizontal range $R = \frac{u^2 \sin(2\theta)}{g}$ - Max height $H = \frac{u^2 \sin^2\theta}{2g}$ - Time of flight $T = \frac{2u \sin\theta}{g}$ ### Laws of Motion - **Newton's First Law**: Inertia. - **Newton's Second Law**: $\vec{F} = m\vec{a}$. Impulse $\vec{J} = \Delta\vec{p} = \vec{F}_{avg} \Delta t$. - **Newton's Third Law**: Action-reaction pairs. - **Conservation of Momentum**: In absence of external force, $\sum \vec{p}_{initial} = \sum \vec{p}_{final}$. - **Friction**: - Static friction $f_s \le \mu_s N$ - Kinetic friction $f_k = \mu_k N$ - **Circular Motion**: - Centripetal acceleration $a_c = \frac{v^2}{r} = \omega^2 r$ - Centripetal force $F_c = \frac{mv^2}{r} = m\omega^2 r$ ### Work, Energy and Power - **Work Done**: $W = \vec{F} \cdot \vec{s} = Fs \cos\theta$. For variable force, $W = \int \vec{F} \cdot d\vec{s}$. - **Kinetic Energy**: $KE = \frac{1}{2}mv^2$. - **Potential Energy**: - Gravitational $PE = mgh$ - Spring $PE = \frac{1}{2}kx^2$ - **Work-Energy Theorem**: $W_{net} = \Delta KE$. - **Conservation of Mechanical Energy**: For conservative forces, $KE_i + PE_i = KE_f + PE_f$. - **Power**: Rate of doing work. $P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}$. ### Mechanical Properties of Solids and Fluids #### Solids - **Stress**: Force per unit area ($\sigma = F/A$). - **Strain**: Change in dimension per original dimension ($\epsilon = \Delta L/L$, $\Delta V/V$, $\phi$). - **Young's Modulus (Y)**: $\frac{\text{Tensile Stress}}{\text{Tensile Strain}} = \frac{FL}{A\Delta L}$. - **Bulk Modulus (B)**: $\frac{\text{Volume Stress}}{\text{Volume Strain}} = \frac{\Delta P}{\Delta V/V}$. - **Shear Modulus (G)**: $\frac{\text{Shear Stress}}{\text{Shear Strain}} = \frac{F/A}{\phi}$. - **Poisson's Ratio ($\nu$)**: $\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$. #### Fluids - **Pressure**: $P = F/A$. - **Pascal's Law**: Pressure applied to an enclosed fluid is transmitted undiminished. - **Archimedes' Principle**: Buoyant force $F_B = \rho_{fluid} V_{submerged} g$. - **Equation of Continuity**: $A_1v_1 = A_2v_2$ (for incompressible fluid). - **Bernoulli's Principle**: $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$. - **Viscosity**: $\vec{F} = -\eta A \frac{dv}{dy}$ (Newton's Law of Viscosity). - **Stokes' Law**: Viscous drag force $F = 6\pi\eta rv$. Terminal velocity $v_T = \frac{2r^2(\rho-\sigma)g}{9\eta}$. - **Surface Tension**: $T = F/L$. Surface energy $E = T \cdot A$. - **Capillary Rise**: $h = \frac{2T \cos\theta}{\rho rg}$. ### Thermal Properties of Matter - **Thermal Expansion**: - Linear: $\Delta L = L_0 \alpha \Delta T$ - Area: $\Delta A = A_0 \beta \Delta T$ ($\beta = 2\alpha$) - Volume: $\Delta V = V_0 \gamma \Delta T$ ($\gamma = 3\alpha$) - **Heat Capacity**: $C = \frac{\Delta Q}{\Delta T}$. Specific heat capacity $c = \frac{C}{m}$. - **Latent Heat**: $Q = mL$ (for phase change). - **Heat Transfer**: - **Conduction**: $\frac{dQ}{dt} = -KA\frac{dT}{dx}$. Thermal resistance $R_{th} = \frac{L}{KA}$. - **Convection**: Transfer by mass movement of fluid. - **Radiation**: Stefan-Boltzmann Law: $P = \epsilon \sigma A T^4$. Wien's Displacement Law: $\lambda_m T = b$. - Newton's Law of Cooling: $\frac{dT}{dt} = -k(T-T_0)$. ### Kinetic Theory of Gases & Thermodynamics #### Kinetic Theory of Gases (KTG) - **Assumptions**: Point particles, random motion, elastic collisions, no intermolecular forces. - **Pressure**: $P = \frac{1}{3}\frac{mN}{V}v_{rms}^2$. - **Average Kinetic Energy per molecule**: $KE_{avg} = \frac{3}{2}kT$. - **Root Mean Square Speed**: $v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3kT}{m}}$. - **Degrees of Freedom ($f$)**: - Monatomic: 3 - Diatomic: 5 (at normal temp) - Polyatomic: 6 - **Internal Energy of ideal gas**: $U = \frac{f}{2}nRT$. - **Molar Heat Capacities**: - $C_V = \frac{f}{2}R$ - $C_P = C_V + R$ (Mayer's relation) - $\gamma = C_P/C_V = 1 + \frac{2}{f}$. #### Thermodynamics - **First Law of Thermodynamics**: $\Delta U = Q - W$. - **Thermodynamic Processes**: - **Isothermal**: $T=$ constant, $\Delta U = 0$, $Q=W=nRT \ln(V_f/V_i)$. - **Adiabatic**: $Q=0$, $\Delta U = -W$. $PV^\gamma = \text{constant}$, $T V^{\gamma-1} = \text{constant}$, $T^\gamma P^{1-\gamma} = \text{constant}$. $W = \frac{nR(T_i-T_f)}{\gamma-1}$. - **Isobaric**: $P=$ constant, $W = P\Delta V$. - **Isochoric**: $V=$ constant, $W=0$, $\Delta U = Q = nC_V\Delta T$. - **Heat Engine Efficiency**: $\eta = 1 - \frac{Q_C}{Q_H} = 1 - \frac{T_C}{T_H}$ (Carnot engine). - **Coefficient of Performance (COP) for Refrigerator**: $COP = \frac{Q_C}{W} = \frac{T_C}{T_H - T_C}$. ### Electrostatics - **Coulomb's Law**: $F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}$. - **Electric Field**: $\vec{E} = \frac{\vec{F}}{q_0}$. For point charge, $E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$. - **Electric Potential**: $V = \frac{W}{q_0}$. For point charge, $V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$. - **Relation between E and V**: $\vec{E} = -\vec{\nabla}V$, i.e., $E_x = -\frac{\partial V}{\partial x}$. - **Electric Dipole**: - Dipole moment $\vec{p} = q(2\vec{a})$. - Field on axial line: $E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}$. - Field on equatorial line: $E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$. - Torque on dipole in uniform E-field: $\vec{\tau} = \vec{p} \times \vec{E}$. - Potential energy of dipole: $U = -\vec{p} \cdot \vec{E}$. - **Gauss's Law**: $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$. ### Capacitance - **Capacitance**: $C = Q/V$. Unit: Farad (F). - **Parallel Plate Capacitor**: $C = \frac{\epsilon_0 A}{d}$. With dielectric $C = \frac{K\epsilon_0 A}{d}$. - **Capacitors in Series**: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ...$ ($Q$ same, $V$ divides). - **Capacitors in Parallel**: $C_{eq} = C_1 + C_2 + ...$ ($V$ same, $Q$ divides). - **Energy Stored in a Capacitor**: $U = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{1}{2}QV$. - **Energy Density**: $u = \frac{1}{2}\epsilon_0 E^2$. ### Current Electricity - **Electric Current**: $I = \frac{dQ}{dt} = nAve$. - **Ohm's Law**: $V = IR$. Resistance $R = \rho \frac{L}{A}$. - **Drift Velocity**: $v_d = \frac{eE\tau}{m}$. - **Resistors in Series**: $R_{eq} = R_1 + R_2 + ...$ ($I$ same, $V$ divides). - **Resistors in Parallel**: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$ ($V$ same, $I$ divides). - **Kirchhoff's Laws**: - **Junction Rule**: $\sum I = 0$ at a junction. - **Loop Rule**: $\sum \Delta V = 0$ in a closed loop. - **Electrical Power**: $P = VI = I^2R = \frac{V^2}{R}$. - **Cells**: - EMF ($\epsilon$), Internal Resistance ($r$). - Terminal Voltage $V = \epsilon - Ir$. - Cells in series: $\epsilon_{eq} = \sum \epsilon_i$, $r_{eq} = \sum r_i$. - Cells in parallel: $\frac{1}{\epsilon_{eq}} = \sum \frac{1}{\epsilon_i}$, $\frac{1}{r_{eq}} = \sum \frac{1}{r_i}$ (if same $\epsilon$, then $\epsilon_{eq}=\epsilon$). - **Wheatstone Bridge**: Balanced condition $\frac{R_1}{R_2} = \frac{R_3}{R_4}$. ### Electromagnetic Waves - **Characteristics**: Transverse waves, do not require medium. - **Speed in vacuum**: $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8 \text{ m/s}$. - **Speed in medium**: $v = \frac{1}{\sqrt{\mu \epsilon}}$. $n = \frac{c}{v}$. - **Relation between E and B field**: $E = cB$. - **Energy Density**: $u = u_E + u_B = \frac{1}{2}\epsilon_0 E^2 + \frac{1}{2\mu_0} B^2 = \epsilon_0 E^2 = \frac{B^2}{\mu_0}$. - **Poynting Vector**: $\vec{S} = \frac{1}{\mu_0}(\vec{E} \times \vec{B})$. Represents energy flux. - **EM Spectrum**: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma ray (increasing freq/energy, decreasing wavelength). ### Ray Optics - **Reflection**: Angle of incidence = Angle of reflection. - Mirror Formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$. - Magnification: $m = -\frac{v}{u} = \frac{h_i}{h_o}$. - For spherical mirrors: $f = R/2$. - **Refraction**: Snell's Law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$. - Absolute refractive index $n = c/v$. - Apparent Depth: $d_{app} = d_{real}/n$. - Critical Angle: $\sin C = n_2/n_1$ (for $n_1 > n_2$). - **Lenses**: - Lens Maker's Formula: $\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$. - Lens Formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$. - Magnification: $m = \frac{v}{u} = \frac{h_i}{h_o}$. - Power of a lens: $P = 1/f$ (in diopters if f in meters). - Lenses in contact: $P_{eq} = P_1 + P_2$, $\frac{1}{f_{eq}} = \frac{1}{f_1} + \frac{1}{f_2}$. - **Prism**: - Angle of deviation $\delta = (n-1)A$ (for small angle prism). - For minimum deviation: $n = \frac{\sin((A+\delta_m)/2)}{\sin(A/2)}$. ### Modern Physics - **Photoelectric Effect**: - Einstein's Equation: $E = h\nu = \phi_0 + KE_{max}$. - Work function $\phi_0 = h\nu_0$. - $KE_{max} = eV_s$. - **Dual Nature of Matter and Radiation**: - De Broglie wavelength: $\lambda = h/p = h/mv$. - For electron accelerated through V volts: $\lambda = \frac{12.27}{\sqrt{V}} \text{ Å}$. - **Atomic Structure (Bohr Model)**: - Radius of $n$-th orbit: $r_n = 0.529 \frac{n^2}{Z} \text{ Å}$. - Energy of $n$-th orbit: $E_n = -13.6 \frac{Z^2}{n^2} \text{ eV}$. - Wavelength of emitted photon: $\frac{1}{\lambda} = RZ^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$. - **X-rays**: - Continuous X-rays (Bremsstrahlung) minimum wavelength: $\lambda_{min} = \frac{hc}{eV} = \frac{12400}{V} \text{ Å}$. - Characteristic X-rays (Moseley's Law): $\sqrt{\nu} = a(Z-b)$. - **Nuclear Physics**: - Mass defect: $\Delta m = (Zm_p + (A-Z)m_n) - M_{nucleus}$. - Binding Energy: $BE = \Delta m c^2$. - Radioactivity: $N = N_0 e^{-\lambda t}$. - Half-life: $T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$. - Average life: $\tau = 1/\lambda$. - Activity: $A = \lambda N$. - Nuclear Fission & Fusion. - **Semiconductors**: - Intrinsic semiconductors (Si, Ge). - Extrinsic semiconductors (n-type, p-type). - p-n junction diode: Forward bias, Reverse bias. - Rectifiers (half-wave, full-wave). - Zener diode (voltage regulator). - Transistors (BJT): $I_E = I_B + I_C$, $\alpha = I_C/I_E$, $\beta = I_C/I_B$. $\beta = \frac{\alpha}{1-\alpha}$. - Logic Gates (AND, OR, NOT, NAND, NOR).