Class 12 Physics Formula Cheat Sheet PDF

# Physics Formula Cheat Sheet ## Class 12 ### Electric Charges & Fields * **Coulomb's Law** * $F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}$ for vacuum * $F = \frac{1}{4\pi\epsilon r} \frac{q_1 q_2}{r^2}$ for medium * **Electric Field Intensity** * $\overrightarrow{E}...

# Physics Formula Cheat Sheet ## Class 12 ### Electric Charges & Fields * **Coulomb's Law** * $F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}$ for vacuum * $F = \frac{1}{4\pi\epsilon r} \frac{q_1 q_2}{r^2}$ for medium * **Electric Field Intensity** * $\overrightarrow{E} = \frac{\overrightarrow{F}}{q_0}$ * $\overrightarrow{E} = k \frac{q}{r^2} \hat{r}$ * $q$ = Source charge * $q_0$ = Test charge * **Electric Flux** * $\phi = \overrightarrow{E} \cdot \overrightarrow{A} = EA \cos\theta$ for uniform electric field * $\phi = \int \overrightarrow{E} \cdot d\overrightarrow{A}$ for non-uniform * $\oint \overrightarrow{E} \cdot d\overrightarrow{A} = \frac{q_{in}}{\epsilon_0}$ for a closed surface * **Gauss's Law** * $\phi = \oint \overrightarrow{E} \cdot d\overrightarrow{A} = \frac{q_{net}}{\epsilon_0}$ Net charge enclosed by the closed surface * **Dipole Moment** ($\overrightarrow{p}$) * $p = q \cdot 2a$ * **Dipole placed in U-E-F** * Torque $\overrightarrow{\tau} = \overrightarrow{p} \times \overrightarrow{E}$ * Net force = 0 * **Work done in rotation of dipole from $\theta_1$ to $\theta_2$** * $U = pE (\cos\theta_1 - \cos\theta_2)$ * **Electrostatic potential energy** * $U = -p \cdot E$ * **Charge density** * Linear = $\lambda = \frac{q}{l}$ * Surface = $\sigma = \frac{q}{A}$ * Volume = $\rho= \frac{q}{V}$ * **Electric field due to dipole** * At an axial point: $E = \frac{2kp}{r^3}$ * On the equatorial line: $E = \frac{kp}{r^3}$ * At any general point: $E = \frac{kp}{r^3} \sqrt{1 + 3\cos^2\theta}$ * **Electric Field due to:** * Infinite Sheet of Charge = $E = \frac{\sigma}{2\epsilon_0} \hat{n}$ * Infinite long charged wire = $E = \frac{\lambda}{2\pi \epsilon_0 r}$ * **Potential due to uniformly charged Sphere** * $V = \frac{q}{4\pi\epsilon_0 r}$ Outside ($r > R$) * $V = \frac{q}{4\pi\epsilon_0 R}$ on the shell ($r = R$) * $V = \frac{q}{4\pi\epsilon_0 R}$ inside ($r < R$) $k=\frac{1}{4 \pi \varepsilon_{0}}$ $ \varepsilon_{0} = 8.854 \times 10^{-12} \frac{C^2}{N-m^2}$ * **Potential due to Non Conducting Uniformly Charged Sphere** * $V = \frac{q}{4\pi\epsilon_0 r}$ * $V = \frac{q}{4\pi\epsilon_0 R}$ * $V = \frac{q}{4\pi\epsilon_0 R^3} (3R^2 - r^2)$ * **Energy Stored in a Capacitor** * $U = \frac{1}{2}CV^2 = \frac{1}{2}QV = \frac{1}{2} \frac{Q^2}{C}$ * **Force Between Plates of capacitor** * $F = \frac{Q^2}{2A\epsilon_0}$ * **Common Potential after connecting two Capacitors** * $V = \frac{q_1 + q_2}{C_1 + C_2} = \frac{C_1V_1 + C_2V_2}{C_1 + C_2}$ * **Energy density** * $U = \frac{1}{2} \epsilon_0 E^2$ * **Energy loss** * $\Delta U = \frac{1}{2} \frac{C_1C_2}{C_1 + C_2} (V_1 - V_2)^2$ * **Electric Potential & Capacitance** * $V = \frac{q}{4\pi \epsilon_0 r}$ * *Potential* * Axial = $V = \frac{P \cos\theta}{4\pi \epsilon r^2}$ * Equatorial = $V = 0$ * At any point = $V = \frac{P \cos\theta}{4\pi \epsilon r^2}$ * Electric Potential Energy * $U = \frac{q_1q_2}{4\pi \epsilon_0 r}$ for two charges * **Capacitance** * $C = \frac{q}{v}$ * Series Combination $$\frac{1}{C_{eq}}= \frac{1}{c_1}+\frac{1}{c_2}$$ * Parallel Combination $$C_{eq} ={c_1}+{c_2}$$ * Relation between $\overrightarrow{E}$ & $V$: $E = -\frac{dv}{dr}$ or $V = -\int{\overrightarrow{E} \cdot \overrightarrow{dr}}$ * **Capacitance of Parallel Plate Capacitor** * Air filled= $C = \frac{\epsilon_0 A}{d}$ * Partially filled with dielectric= $C = \frac{\epsilon_0 A}{d-t(1-\frac{1}{k})}$ * Completely air filled capacitor: $$C= \frac{K \epsilon_0 A}{d}$$. * **Spherical Capacitor** * $C = 4\pi\epsilon_0 \frac{ab}{b-a}$ where a and b are radius of big and small sphere respectively within capacitor * **If inner grounded** * $C = 4\pi \epsilon_0 a$ *Capacitance of Isolated Sphere C=4πε0r where r is sphere's radius ### Current Electricity * **Electric Current (Average)** * $i = \frac{q}{t}$ * **Instantaneous** * $i = \frac{dq}{dt}$ * **Current Density** * $J = \frac{i}{A}$ * **Drift Velocity** * $V_d = \frac{e\tau E}{m} = \frac{i}{neA}$ * **Mobility** * $\mu = \frac{|V_d|}{E}= \frac{e \tau}{m}$ * **Resistivity** $$P=\frac{m}{ne^2 \tau}$$ * **Ohm's Law** * $V = IR$ * $R = \rho \frac{L}{A}$ Relation between $J$ & $\sigma$ are missing * **EMF of cell** * $E = V + Ir$ * **Terminal Potential Difference** * $V = E - Ir$ * **Relation b/w I&Vd**: I=AneVd Relation b/w J&E: $$J=\sigma E=1/AE=\sqrt{AR}$$ * **Power** * $P = VI = i^2R = \frac{V^2}{R}$ * **Energy** * $W = Vq = Vit = i^2Rt = \frac{V^2}{R}t$ * **Principle of Wheatstone Bridge** * $\frac{P}{Q} = \frac{R}{S}$ * **Temperature Coefficient** * $\alpha = \frac{R - R_0}{R_0(T - T_0)}$ * **Principle of Potentiometer** * $\frac{K}{V} = \frac{l}{L}$ * **Principle of Meter Bridge** * $R = \frac{l}{100 - l}S$ * **Combination of Identical Cell** * **Series** - ne/R + Nr * Current =ne/(R+nr) * Parallel * $$\frac{me}{mR+r}$$ * **Mixed** - mne/(mR+Nr) * **Joule's Law** $$H=I^2 R_t Joules$$ * Conversion between Joule and Calorie *$$H=\frac{I^2 R_t}{ 4.18} Calorie$$ ### Moving Charges and Magnetism * **Magnetic Force** * $\overrightarrow{F} = q(\overrightarrow{V} \times \overrightarrow{B})$ * Pitch (P) = \frac{2\pi mv \cos\theta }{qB} $$\mu_0=4\pi \times 10^{-7} \frac{T-M}{A} $$, * M=u(1+Xm) * Relation between B, H B= μH μ=μ0(1+xm) \*Gauss's Law for magnetism $$\oint B-dS= 0$$ #### Motion of Charge in Uniform Transverse Magnetic Field * $F_m = qVB = \frac{mv^2}{r}$ * **Radius of Circular Path** * $r = \frac{mv}{qB} = \frac{p}{qB} = \frac{\sqrt{2mK}}{qB} = \frac{\sqrt{2mqV}}{qB}$ Time period Time Period =$$T= \frac{2\pi r }{V}= \frac{2\pi m}{qB}$$ * **Magnetic Force on a Current Carrying Conductor** * $\overrightarrow{F} = I (\overrightarrow{l} \times \overrightarrow{B})$ * **Biot-Savart Law** * $dB = \frac{\mu_0}{4\pi} \frac{Idl \sin\theta}{r^2}$ **Magnetic field due to a Circular coil** *m.f at center of center circular coil,$$B=\frac{\mu_0 I}{2a}$$ * **Force between two Current Carrying parallel straight Conductor.** * $F = \frac{\mu_0}{4\pi} \frac{2I_1I_2}{r} l$ * **mf at axis of current carrying coil . $$ B=\frac{\mu_02\pi \alpha^2 }{ 4\pi (a^2+x^2)}$$ * **Ampere's Circuital law** $$\oint{B}=μ_0 $$ * Magnetic field due to an infinitely long straight wire of radius, a carrying current i at a point $$ B=\frac{\mu_0 r}{ 2\pi a} < a ,$$ $$B= μ0 /2\piα r = a $$ and $$ B=\frac{\mu_0 i}{ 2\pi r}> a`$$ * **Torque on a Current Carrying Coil placed in a Uniform magnetic Field.** $$I= \frac{NA Bsinθ }{CR}$$ OR $I= Kθ$ K=galvanometer Constant K=NAB/CI * **Galvanometer conversion and formula is as following ** *Conversion into Ammeter *Shunt resistance $$R = R_G/ I/l_g-I$$ \*Conversion into voltmeter R= V-Ig/Ig **Current senitivity (CS) and formulas** $$\frac{I α}{v} = N/k AB , Vs=\frac{(CS = Vs/R) }{(V/R) }$$ * Magnetic field to a current carrying solenoid Magnetic field strength due to core/ solenoid Bs = μoni = (μ • Ni)/l ,where n= number of turns per unit length ### Magnetism and Matter * Bar magnet as an equivalent solenoid * Magnet filed for bar magnet $$ B= \frac{μ_0 2M}{4πr^3,} $$ Q=2nI(πσ²) Potential energy of magnetic dipoles and magnet is given as :- * P=-MB cosθ * P = - M.B m = μ(1+ xm) μ=permeability v= volume and xm=suspectibility ### Alternating Current * RMS value of current & voltage $$v_r. m. s /i r.m.s =1.414 , v r.m.s or i r.m.s /2=0.70$$ * Average value of current & voltage * Average vale of current & voltage $$VorI = \frac {2 \to } π =0.6 37$$ * Alternating law V= Vosint I= Iosint $$X_L= wL= inductive reactance and X_c = {1\over Wc}$$ ### Ray Optics * Mirror formula $$1/f = 1/v+ 1/4 $$ and refractive index μ= Sini/ Sinr * For lenses equation $$1/ = 1/4 + 1/$$+Magnification , $$P=h^1/h2/ = V/4sin (A-m / 2 )$$ * Lens Marker Sin(A/2) $$M=\frac{(U-1)+( 1 / (P=2)} P=U/4$$ #### Refraction at spherical surfaces R & actual and apparent D u=Real depth App=App depth P = U-1/ R U= P/1-M ### Combination of Lenses * P = P1 +P2 - d P P1 #### Simple Microscope * M0 - final image at D- #### Wave Optics *Interference of light I(Max)=(a+b)^2 where I = a² and I α wave length from transition N₂->N₁ 1/ =(μ-I)(1+1) (a=0, 82x 10² ) 1/1=(1/ μ0 -1)/ L A =Angular from secondary Maxima 2 =2 /a