JEE Physics

Cheatsheet Content

### Mechanics #### 1. Kinematics - **Equations of Motion (Constant Acceleration):** - $v = u + at$ - $s = ut + \frac{1}{2}at^2$ - $v^2 = u^2 + 2as$ - $s_n = u + \frac{a}{2}(2n-1)$ (Displacement in n-th second) - **Projectile Motion:** - Time of Flight: $T = \frac{2u \sin\theta}{g}$ - Max Height: $H = \frac{u^2 \sin^2\theta}{2g}$ - Range: $R = \frac{u^2 \sin(2\theta)}{g}$ #### 2. Newton's Laws of Motion - **First Law:** Inertia - **Second Law:** $F = ma$ - **Third Law:** Action-Reaction - **Impulse:** $J = F \Delta t = \Delta p$ - **Conservation of Momentum:** $\sum p_{initial} = \sum p_{final}$ #### 3. Work, Energy & Power - **Work Done:** $W = F \cdot s = Fs \cos\theta$ - **Kinetic Energy:** $KE = \frac{1}{2}mv^2$ - **Potential Energy (Gravity):** $PE = mgh$ - **Work-Energy Theorem:** $W_{net} = \Delta KE$ - **Power:** $P = \frac{W}{t} = F \cdot v$ #### 4. Rotational Motion - **Angular Displacement:** $\theta$ - **Angular Velocity:** $\omega = \frac{d\theta}{dt}$ - **Angular Acceleration:** $\alpha = \frac{d\omega}{dt}$ - **Torque:** $\tau = r \times F = I\alpha$ - **Moment of Inertia:** $I = \sum mr^2$ - **Rotational KE:** $KE_{rot} = \frac{1}{2}I\omega^2$ - **Angular Momentum:** $L = I\omega = r \times p$ #### 5. Gravitation - **Newton's Law of Gravitation:** $F = \frac{Gm_1m_2}{r^2}$ - **Gravitational Potential Energy:** $U = -\frac{Gm_1m_2}{r}$ - **Escape Velocity:** $v_e = \sqrt{\frac{2GM}{R}}$ - **Orbital Velocity:** $v_o = \sqrt{\frac{GM}{r}}$ ### Thermodynamics #### 1. Heat & Temperature - **Heat Transfer:** - Conduction: $\frac{dQ}{dt} = -KA\frac{dT}{dx}$ - Convection - Radiation: $P = \epsilon \sigma A T^4$ (Stefan-Boltzmann Law) - **Specific Heat Capacity:** $Q = mc\Delta T$ - **Latent Heat:** $Q = mL$ #### 2. Laws of Thermodynamics - **Zeroth Law:** Thermal Equilibrium - **First Law:** $\Delta U = Q - W$ - **Second Law:** Entropy always increases for an isolated system. - Efficiency of Heat Engine: $\eta = 1 - \frac{T_C}{T_H}$ - **Third Law:** Entropy of a perfect crystal at absolute zero is zero. #### 3. Kinetic Theory of Gases - **Ideal Gas Equation:** $PV = nRT = Nk_BT$ - **Average KE per molecule:** $KE_{avg} = \frac{3}{2}k_BT$ - **RMS Speed:** $v_{rms} = \sqrt{\frac{3RT}{M}}$ - **Degrees of Freedom (f):** - Monatomic: f=3 - Diatomic: f=5 (at normal temp) - Polyatomic: f=6 - **Internal Energy:** $U = \frac{f}{2}nRT$ ### Waves and Optics #### 1. Wave Motion - **Wave Equation:** $y(x,t) = A \sin(kx - \omega t + \phi)$ - **Wave Speed:** $v = f\lambda = \frac{\omega}{k}$ - **Speed of Sound:** $v = \sqrt{\frac{B}{\rho}}$ (Solids/Liquids), $v = \sqrt{\frac{\gamma P}{\rho}}$ (Gases) - **Standing Waves:** - String (fixed ends): $L = \frac{n\lambda}{2}$, $f_n = \frac{nv}{2L}$ - Open Organ Pipe: $L = \frac{n\lambda}{2}$, $f_n = \frac{nv}{2L}$ - Closed Organ Pipe: $L = \frac{(2n-1)\lambda}{4}$, $f_n = \frac{(2n-1)v}{4L}$ - **Doppler Effect:** $f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right)$ #### 2. Ray Optics - **Reflection:** Angle of incidence = Angle of reflection - **Refraction (Snell's Law):** $n_1 \sin\theta_1 = n_2 \sin\theta_2$ - **Lens/Mirror Formula:** $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ - **Magnification:** $m = -\frac{v}{u} = \frac{h_i}{h_o}$ - **Power of Lens:** $P = \frac{1}{f}$ (in diopters, f in meters) - **Total Internal Reflection:** $\sin C = \frac{n_2}{n_1}$ #### 3. Wave Optics - **Young's Double Slit Experiment (YDSE):** - Path Difference: $\Delta x = d \sin\theta$ - Bright Fringes (Constructive): $\Delta x = n\lambda$ - Dark Fringes (Destructive): $\Delta x = (n + \frac{1}{2})\lambda$ - Fringe Width: $\beta = \frac{\lambda D}{d}$ - **Diffraction (Single Slit):** - Minima: $a \sin\theta = n\lambda$ - **Polarization (Brewster's Law):** $\tan \theta_p = \frac{n_2}{n_1}$ ### Electrostatics & Current Electricity #### 1. Electrostatics - **Coulomb's Law:** $F = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2}$ - **Electric Field:** $E = \frac{F}{q_0} = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$ - **Electric Potential:** $V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$ - **Electric Potential Energy:** $U = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r}$ - **Capacitance:** $C = \frac{Q}{V}$ - Parallel Plate Capacitor: $C = \frac{\epsilon_0 A}{d}$ - Energy Stored: $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C}$ #### 2. Current Electricity - **Ohm's Law:** $V = IR$ - **Resistance:** $R = \rho \frac{L}{A}$ - **Series Combination:** $R_{eq} = R_1 + R_2 + ...$ - **Parallel Combination:** $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$ - **Joule's Law of Heating:** $H = I^2Rt = VIt = \frac{V^2}{R}t$ - **Kirchhoff's Laws:** - Junction Rule: $\sum I = 0$ - Loop Rule: $\sum V = 0$ ### Magnetism & Electromagnetic Induction #### 1. Magnetism - **Biot-Savart Law:** $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \vec{r}}{r^3}$ - **Magnetic Field due to Long Straight Wire:** $B = \frac{\mu_0 I}{2\pi r}$ - **Magnetic Field at center of Circular Loop:** $B = \frac{\mu_0 I}{2R}$ - **Magnetic Force on Moving Charge:** $\vec{F} = q(\vec{v} \times \vec{B})$ - **Magnetic Force on Current-Carrying Wire:** $\vec{F} = I(\vec{L} \times \vec{B})$ - **Ampere's Circuital Law:** $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$ - **Torque on Current Loop:** $\tau = NIAB \sin\theta = \vec{M} \times \vec{B}$ #### 2. Electromagnetic Induction (EMI) - **Magnetic Flux:** $\Phi_B = \int \vec{B} \cdot d\vec{A} = BA \cos\theta$ - **Faraday's Law of EMI:** $\mathcal{E} = -\frac{d\Phi_B}{dt}$ - **Motional EMF:** $\mathcal{E} = (Blv)$ - **Lenz's Law:** Induced current opposes the change in magnetic flux. - **Inductance:** $L = \frac{\Phi_B}{I}$ - Energy Stored in Inductor: $U = \frac{1}{2}LI^2$ #### 3. Alternating Current (AC) - **RMS Values:** $V_{rms} = \frac{V_0}{\sqrt{2}}$, $I_{rms} = \frac{I_0}{\sqrt{2}}$ - **Reactance:** - Inductive: $X_L = \omega L$ - Capacitive: $X_C = \frac{1}{\omega C}$ - **Impedance (RLC Series Circuit):** $Z = \sqrt{R^2 + (X_L - X_C)^2}$ - **Phase Angle:** $\tan\phi = \frac{X_L - X_C}{R}$ - **Power in AC Circuit:** $P = V_{rms}I_{rms}\cos\phi$ (Power Factor $\cos\phi$) - **Resonance:** $X_L = X_C \implies \omega_0 = \frac{1}{\sqrt{LC}}$ ### Modern Physics #### 1. Dual Nature of Radiation and Matter - **Planck's Quantum Theory:** $E = h\nu = \frac{hc}{\lambda}$ - **Photoelectric Effect:** $KE_{max} = h\nu - \phi_0$ (Work Function $\phi_0$) - **De Broglie Wavelength:** $\lambda = \frac{h}{p} = \frac{h}{mv}$ #### 2. Atomic Structure - **Bohr's Model:** - Quantized Orbits: $L = n\frac{h}{2\pi}$ - Energy Levels: $E_n = -\frac{13.6}{n^2}$ eV (for Hydrogen) - Radius of Orbit: $r_n = 0.529 n^2$ Å - **Rydberg Formula:** $\frac{1}{\lambda} = RZ^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ #### 3. Nuclear Physics - **Mass Defect:** $\Delta m = (Zm_p + Nm_n) - M_{nucleus}$ - **Binding Energy:** $BE = \Delta m c^2$ - **Radioactive Decay Law:** $N = N_0 e^{-\lambda t}$ - **Half-Life:** $T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$ - **Activity:** $A = \lambda N$ #### 4. Semiconductors - **Types:** Intrinsic (pure), Extrinsic (doped - N-type, P-type) - **p-n Junction Diode:** Forward and Reverse Bias characteristics - **Rectifiers:** Half-wave, Full-wave - **Transistors:** Basic working (common emitter configuration) - **Logic Gates:** AND, OR, NOT, NAND, NOR, XOR, XNOR