Science—Physics 2 Equations Calculus Version

Electric Forces

$LaTeX: F_e=k_e\displaystyle{\frac{|q_1||q_2|}{r^2}}$ $F_e=k_e\displaystyle{\frac{|q_1||q_2|}{r^2}}$ (Coulomb's Law)

$LaTeX: k_e=\displaystyle{\frac{1}{4\pi \epsilon_0}}$ $k_e=\displaystyle{\frac{1}{4\pi \epsilon_0}}$ (Coulomb's Constant)

$LaTeX: \overset{\rightharpoonup}{F}_e=q_0\overset{\rightharpoonup}{E}$ $\overset{\rightharpoonup}{F}_e=q_0\overset{\rightharpoonup}{E}$ (Electric Force)

$LaTeX: \vec{F}_e=q_0\vec{E}$ $\vec{F}_e=q_0\vec{E}$

Electric Fields

$LaTeX: E=k_e\displaystyle{\frac{|q|}{r^2}}$ $E=k_e\displaystyle{\frac{|q|}{r^2}}$ (Electric Field)

$LaTeX: E_z^p=\displaystyle{\frac{1}{2\pi \epsilon_0}\frac{p}{z^3}}$ $E_z^p=\displaystyle{\frac{1}{2\pi \epsilon_0}\frac{p}{z^3}}$ (Electric Field of a Dipole)

LaTeX: p=qd $p=qd$ (Electric Dipole Moment)

$LaTeX: E=\displaystyle{\frac{\sigma}{\epsilon _0}}$ $E=\displaystyle{\frac{\sigma}{\epsilon _0}}$ (Electric Field on Metal Surface)

$LaTeX: E=-\nabla V$ $E=-\nabla V$ (Electric Field from Potential)

$LaTeX: E=-\displaystyle{\frac{\mathrm{d}V(r)}{\mathrm{d}r}}$ $E=-\displaystyle{\frac{\mathrm{d}V(r)}{\mathrm{d}r}}$ (Electric Field from Potential)

Gauss' Law

$LaTeX: \Phi_E=\displaystyle{\frac{Q_\text{inside}}{\epsilon _0}}$ $\Phi_E=\displaystyle{\frac{Q_\text{inside}}{\epsilon _0}}$

$LaTeX: \Phi_E=\displaystyle{\oint \overset{\rightharpoonup}{E}\cdot \mathrm{d}\overset{\rightharpoonup}{A}}$ $\Phi_E=\displaystyle{\oint \overset{\rightharpoonup}{E}\cdot \mathrm{d}\overset{\rightharpoonup}{A}}$

$LaTeX: \Phi_E=\displaystyle{\oint \vec{E}\cdot \mathrm{d}\vec{A}}$ $\Phi_E=\displaystyle{\oint \vec{E}\cdot \mathrm{d}\vec{A}}$

$LaTeX: \Phi = EA\cos\theta$ $\Phi = EA\cos\theta$

Charge Densities

$LaTeX: \lambda=\displaystyle\frac{q}{L}$ $\lambda=\displaystyle\frac{q}{L}$ (Linear)

$LaTeX: \lambda=\displaystyle\frac{\mathrm{d}q}{\mathrm{d}x}$ $\lambda=\displaystyle\frac{\mathrm{d}q}{\mathrm{d}x}$ (Linear)

$LaTeX: \sigma=\displaystyle\frac{q}{A}$ $\sigma=\displaystyle\frac{q}{A}$ (Surface)

$LaTeX: \sigma=\displaystyle\frac{\mathrm{d}q}{\mathrm{d}A}$ $\sigma=\displaystyle\frac{\mathrm{d}q}{\mathrm{d}A}$ (Surface)

$LaTeX: \rho=\displaystyle\frac{q}{V}$ $\rho=\displaystyle\frac{q}{V}$ (Volume)

$LaTeX: \rho=\displaystyle\frac{\mathrm{d}q}{\mathrm{d}V}$ $\rho=\displaystyle\frac{\mathrm{d}q}{\mathrm{d}V}$ (Volume)

Electric Potential

$LaTeX: \Delta U=-qE_x\Delta x$ $\Delta U=-qE_x\Delta x$ (Potential Energy)

$LaTeX: \Delta U=q\Delta V$ $\Delta U=q\Delta V$ (Electric Potential)

$LaTeX: \Delta V=-E_x\Delta x$ $\Delta V=-E_x\Delta x$ (Electric Potential)

$LaTeX: V=k_e\displaystyle\frac{q}{r}$ $V=k_e\displaystyle\frac{q}{r}$ (Electric Potential of a Point Charge)

$LaTeX: V=\displaystyle\sum\limits_0^nk_e\frac{q_n}{r_n}$ $V=\displaystyle\sum\limits_0^nk_e\frac{q_n}{r_n}$ (Superposition Principle)

$LaTeX: V=k_e\displaystyle\frac{q}{R}$ $V=k_e\displaystyle\frac{q}{R}$ (Electric Potential of a Sphere)

$LaTeX: U=k_e\displaystyle\frac{q_1q_2}{r}$ $U=k_e\displaystyle\frac{q_1q_2}{r}$ (Potential Energy of Two Point Charges)

$LaTeX: \Delta V=\displaystyle\int\limits_i^f\overset{\rightharpoonup}{E}\cdot \mathrm{d}\overset{\rightharpoonup}{s}$ $\Delta V=\displaystyle\int\limits_i^f\overset{\rightharpoonup}{E}\cdot \mathrm{d}\overset{\rightharpoonup}{s}$ (Electric Potential)

$LaTeX: \Delta V=\displaystyle\int\limits_i^f\vec{E}\cdot \mathrm{d}\vec{s}$ $\Delta V=\displaystyle\int\limits_i^f\vec{E}\cdot \mathrm{d}\vec{s}$

Current

$LaTeX: I=\displaystyle\frac{\Delta Q}{\Delta t}$ $I=\displaystyle\frac{\Delta Q}{\Delta t}$ (Average Current)

LaTeX: I=nqv_dA $I=nqv_dA$ (Average Current)

$LaTeX: J=\displaystyle\frac{i}{A}$ $J=\displaystyle\frac{i}{A}$ (Current Density)

$LaTeX: \overset{\rightharpoonup}{J}=ne\overset{\rightharpoonup}{v_d}$ $\overset{\rightharpoonup}{J}=ne\overset{\rightharpoonup}{v_d}$ (Current Density)

$LaTeX: \Delta V=IR$ $\Delta V=IR$ (Ohm's Law)

$LaTeX: P=I\Delta V$ $P=I\Delta V$ (Power in Resistor)

LaTeX: P=I^2R $P=I^2R$ (Power in Resistor)

$LaTeX: \Delta V=\varepsilon - Ir$ $\Delta V=\varepsilon - Ir$ (Terminal Voltage)

Resistors

$LaTeX: R=\rho\displaystyle\frac{l}{A}$ $R=\rho\displaystyle\frac{l}{A}$ (Resistance)

$LaTeX: \rho = \rho_0[1+\alpha(T-T_0)]$ $\rho = \rho_0[1+\alpha(T-T_0)]$ (Resistivity)

$LaTeX: R =R_0[1+\alpha(T-T_0)]$ $R =R_0[1+\alpha(T-T_0)]$ (Resistance)

$LaTeX: R_S= \displaystyle \sum \limits_{i=1}^n R_i=R_1+R_2+R_3+\cdots+R_n$ $R_S= \displaystyle \sum \limits_{i=1}^n R_i=R_1+R_2+R_3+\cdots+R_n$ (Series)

$LaTeX: \displaystyle\frac{1}{R_P}=\sum \limits_{i=1}^n \frac{1}{R_i}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\cdots +\frac{1}{R_n}$ $\displaystyle\frac{1}{R_P}=\sum \limits_{i=1}^n \frac{1}{R_i}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\cdots +\frac{1}{R_n}$ (Parallel)

Capacitors

$LaTeX: Q=C\Delta V$ $Q=C\Delta V$ (Capacitance)

$LaTeX: C=\epsilon_0\displaystyle\frac{A}{d}$ $C=\epsilon_0\displaystyle\frac{A}{d}$ (Parallel Plate Capacitance)

$LaTeX: C=4\pi \kappa \epsilon_0R$ $C=4\pi \kappa \epsilon_0R$ (Capacitance of a Sphere)

$LaTeX: C_P=\sum \limits_{i=1}^n C_i=C_1+C_2+C_3+\cdots +C_n$ $C_P=\sum \limits_{i=1}^n C_i=C_1+C_2+C_3+\cdots +C_n$ (Parallel)

$LaTeX: \displaystyle\frac{1}{C_S}=\sum \limits_{i=1}^n\frac{1}{C_i}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\cdots +\frac{1}{C_n}$ $\displaystyle\frac{1}{C_S}=\sum \limits_{i=1}^n\frac{1}{C_i}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\cdots +\frac{1}{C_n}$ (Series)

$LaTeX: C=\kappa\epsilon_0\displaystyle\frac{A}{d}$ $C=\kappa\epsilon_0\displaystyle\frac{A}{d}$ (Dielectrics)

$LaTeX: \kappa=\displaystyle\frac{\epsilon}{\epsilon_0}$ $\kappa=\displaystyle\frac{\epsilon}{\epsilon_0}$ (Dielectrics)

$LaTeX: \text{Energy Stored}=\displaystyle\frac{1}{2}Q\Delta V$ $\text{Energy Stored}=\displaystyle\frac{1}{2}Q\Delta V$ (Energy in a Charged Capacitor)

$LaTeX: \text{Energy Stored}=\displaystyle\frac{1}{2}C(\Delta V)^2$ $\text{Energy Stored}=\displaystyle\frac{1}{2}C(\Delta V)^2$ (Energy in a Charged Capacitor)

$LaTeX: \text{Energy Stored}=\displaystyle\frac{Q^2}{2C}$ $\text{Energy Stored}=\displaystyle\frac{Q^2}{2C}$ (Energy in a Charged Capacitor)

$LaTeX: u=\displaystyle\frac{U}{V}$ $u=\displaystyle\frac{U}{V}$ (Electric Density)

$LaTeX: u=\displaystyle\frac{1}{2}\epsilon E^2$ $u=\displaystyle\frac{1}{2}\epsilon E^2$ (Electric Density)

RC Circuits

$LaTeX: \tau=RC$ $\tau=RC$ (RC Time Constant)

$LaTeX: q=Q\Big(1-e^{-t / \tau}\Big)$ $q=Q\Big(1-e^{-t / \tau}\Big)$ (Charging RC Circuit)

$LaTeX: q(t)=CV_T\Big(1-e^{-t / \tau}\Big)$ $q(t)=CV_T\Big(1-e^{-t / \tau}\Big)$ (Charging RC Circuit)

$LaTeX: I=\displaystyle\frac{V_T}{R}\Big(e^{-t / \tau}\Big)$ $I=\displaystyle\frac{V_T}{R}\Big(e^{-t / \tau}\Big)$ (Charging RC Circuit)

$LaTeX: q=Q\Big(e^{-t / \tau}\Big)$ $q=Q\Big(e^{-t / \tau}\Big)$ (Discharging RC Circuit)

$LaTeX: I=\displaystyle\frac{q}{RC}\Big(e^{-t / \tau}\Big)$ $I=\displaystyle\frac{q}{RC}\Big(e^{-t / \tau}\Big)$ (Discharging RC Circuit)

$LaTeX: I=I_\text{max}\Big(e^{-t / \tau}\Big)$ $I=I_\text{max}\Big(e^{-t / \tau}\Big)$ (Discharging RC Circuit)

Magnetism

$LaTeX: F_B=qvB\sin\theta$ $F_B=qvB\sin\theta$ (Magnetic Force)

$LaTeX: \overset{\rightharpoonup}{F}_B=q\overset{\rightharpoonup}{v}\times\overset{\rightharpoonup}{B}$ $\overset{\rightharpoonup}{F}_B=q\overset{\rightharpoonup}{v}\times\overset{\rightharpoonup}{B}$ (Magnetic Force)

$LaTeX: F_B=BIL\sin\theta$ $F_B=BIL\sin\theta$ (Current Carrying Wire)

$LaTeX: \overset{\rightharpoonup}{F}_B=I\overset{\rightharpoonup}{L}\times\overset{\rightharpoonup}{B}$ $\overset{\rightharpoonup}{F}_B=I\overset{\rightharpoonup}{L}\times\overset{\rightharpoonup}{B}$ (Current Carrying Wire)

$LaTeX: \tau=BIA\sin\theta$ $\tau=BIA\sin\theta$ (Torque on a Loop of Wire)

$LaTeX: r=\displaystyle\frac{mv}{qB}$ $r=\displaystyle\frac{mv}{qB}$ (Cyclotron Motion)

$LaTeX: \mathrm{d}\overset{\rightharpoonup}{B}=\displaystyle\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\overset{\rightharpoonup}{s}\times\overset{\rightharpoonup}{r}}{r^3}$ $\mathrm{d}\overset{\rightharpoonup}{B}=\displaystyle\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\overset{\rightharpoonup}{s}\times\overset{\rightharpoonup}{r}}{r^3}$ (Biot-Savart Law)

$LaTeX: B=\displaystyle\frac{\mu_0I}{2\pi r}$ $B=\displaystyle\frac{\mu_0I}{2\pi r}$ (Biot-Savart Law)

$LaTeX: \displaystyle\frac{F}{L}=\frac{\mu_0I_1I_2}{2\pi d}$ $\displaystyle\frac{F}{L}=\frac{\mu_0I_1I_2}{2\pi d}$ (Magnetic Force between Two Wires)

$LaTeX: B=N\displaystyle\frac{\mu_0I}{2R}$ $B=N\displaystyle\frac{\mu_0I}{2R}$ (Magnetic Field of a Coil)

$LaTeX: B=\mu_0nI$ $B=\mu_0nI$ (Magnetic Field of a Solenoid)

$LaTeX: n=\displaystyle\frac{N}{l}$ $n=\displaystyle\frac{N}{l}$ (Turns in a Solenoid)

$LaTeX: B=\displaystyle\frac{\mu_0IN}{2\pi r}$ $B=\displaystyle\frac{\mu_0IN}{2\pi r}$ (Magnetic Field of a Toroid)

$LaTeX: \displaystyle\oint\overset{\rightharpoonup}{B}\cdot \mathrm{d}\overset{\rightharpoonup}{s}=\mu_0I_\text{enc}$ $\displaystyle\oint\overset{\rightharpoonup}{B}\cdot \mathrm{d}\overset{\rightharpoonup}{s}=\mu_0I_\text{enc}$ (Ampere's Law)

Induced EMF & Inductance

$LaTeX: \Phi_B=BA\cos\theta$ $\Phi_B=BA\cos\theta$ (Magnetic Flux)

$LaTeX: \Phi_B=\displaystyle\iint\overset{\rightharpoonup}{B}\cdot \mathrm{d}\overset{\rightharpoonup}{A}$ $\Phi_B=\displaystyle\iint\overset{\rightharpoonup}{B}\cdot \mathrm{d}\overset{\rightharpoonup}{A}$ (Magnetic Flux)

$LaTeX: \varepsilon=-N\displaystyle\frac{\Delta \Phi_B}{\Delta t}$ $\varepsilon=-N\displaystyle\frac{\Delta \Phi_B}{\Delta t}$ (Faraday's Law of Induction)

$LaTeX: \varepsilon=-\displaystyle\frac{\mathrm{d}}{\mathrm{d}t}\Phi_B$ $\varepsilon=-\displaystyle\frac{\mathrm{d}}{\mathrm{d}t}\Phi_B$ (Faraday's Law of Induction)

$LaTeX: \varepsilon=-\displaystyle\frac{\mathrm{d}}{\mathrm{d}t}\iint\overset{\rightharpoonup}{B}\cdot \mathrm{d}\overset{\rightharpoonup}{A}$ $\varepsilon=-\displaystyle\frac{\mathrm{d}}{\mathrm{d}t}\iint\overset{\rightharpoonup}{B}\cdot \mathrm{d}\overset{\rightharpoonup}{A}$ (Faraday's Law of Induction)

$LaTeX: |\varepsilon|=Blv$ $|\varepsilon|=Blv$ (Motional EMF)

$LaTeX: \varepsilon=NAB\omega \sin \omega t$ $\varepsilon=NAB\omega \sin \omega t$ (Generators)

$LaTeX: \varepsilon=-L\displaystyle\frac{\mathrm{d}I}{\mathrm{d}t}$ $\varepsilon=-L\displaystyle\frac{\mathrm{d}I}{\mathrm{d}t}$ (Self-Induced EMF)

$LaTeX: \varepsilon=-L\displaystyle\frac{\Delta I}{\Delta t}$ $\varepsilon=-L\displaystyle\frac{\Delta I}{\Delta t}$ (Self-Induced EMF)

$LaTeX: L=\displaystyle\frac{N \Phi_B}{I}$ $L=\displaystyle\frac{N \Phi_B}{I}$ (Inductance of a Coil)

$LaTeX: L=\displaystyle\frac{\mu_0N^2 A}{l}$ $L=\displaystyle\frac{\mu_0N^2 A}{l}$ (Inductance of a Solenoid)

$LaTeX: U_L=\displaystyle\frac{1}{2}LI^2$ $U_L=\displaystyle\frac{1}{2}LI^2$ (Inductor Potential Energy)

AC Circuits

$LaTeX: V=V_0\sin\omega t$ $V=V_0\sin\omega t$ (Time-Dependent Voltage)

$LaTeX: I=I_0\sin\omega t$ $I=I_0\sin\omega t$ (Time-Dependent Current)

$LaTeX: \Delta V_\text{rms}=\displaystyle\frac{\Delta V_\text{max}}{\sqrt{2}}$ $\Delta V_\text{rms}=\displaystyle\frac{\Delta V_\text{max}}{\sqrt{2}}$ (RMS & Max Relationship - Voltage)

$LaTeX: \Delta I_\text{rms}=\displaystyle\frac{\Delta I_\text{max}}{\sqrt{2}}$ $\Delta I_\text{rms}=\displaystyle\frac{\Delta I_\text{max}}{\sqrt{2}}$ (RMS & Max Relationship - Current)

$LaTeX: \Delta V_\text{R,rms}=I_\text{rms}R$ $\Delta V_\text{R,rms}=I_\text{rms}R$ (Ohm's Law, RMS Version)

$LaTeX: X_C=\displaystyle\frac{1}{2\pi f C}$ $X_C=\displaystyle\frac{1}{2\pi f C}$ (Capacitive Reactance)

$LaTeX: \Delta V_\text{C,rms}=I_\text{rms}X_C$ $\Delta V_\text{C,rms}=I_\text{rms}X_C$ (RMS Voltage - Capacitor)

$LaTeX: X_L=2\pi f L$ $X_L=2\pi f L$ (Inductive Reactance)

$LaTeX: \Delta V_\text{L,rms}=I_\text{rms}X_L$ $\Delta V_\text{L,rms}=I_\text{rms}X_L$ (RMS Voltage - Inductor)

RLC Circuit

$LaTeX: V_{rms}^2 = V_R^2 + \left( V_L -V_C \right) ^2$ $V_{rms}^2 = V_R^2 + \left( V_L -V_C \right) ^2$ (RMS Voltage)

$LaTeX: Z = \sqrt{ R^2 + \left( X_L - X_C \right) ^2 }$ $Z = \sqrt{ R^2 + \left( X_L - X_C \right) ^2 }$ (Impedance)

$LaTeX: V_\text{rms} = I_\text{rms} Z$ $V_\text{rms} = I_\text{rms} Z$ (RMS Voltage/Current)

$LaTeX: V_\text{max} = I_\text{max} Z$ $V_\text{max} = I_\text{max} Z$ (Maximum Voltage/Current)

$LaTeX: \displaystyle tan \space \phi = { X_L - X_C \over R } = { V_L -V_C \over V_R }$ $\displaystyle tan \space \phi = { X_L - X_C \over R } = { V_L -V_C \over V_R }$ (Phase Angle)

$LaTeX: \bar{P} = I_{rms} V_{rms} \space cos \space \phi$ $\bar{P} = I_{rms} V_{rms} \space cos \space \phi$ (Average Power)

$LaTeX: f_0 = \displaystyle{ 1 \over 2 \pi \sqrt{ L C } }$ $f_0 = \displaystyle{ 1 \over 2 \pi \sqrt{ L C } }$ (Resonance Frequency)

Transformers

LaTeX: P_s = P_p $P_s = P_p$ (Power)

$LaTeX: \displaystyle V_s = { N_s \over N_p } V_p$ $\displaystyle V_s = { N_s \over N_p } V_p$ (Voltage Step-Up/Down)

$LaTeX: I_s = \displaystyle{ N_p \over N_s } I_p$ $I_s = \displaystyle{ N_p \over N_s } I_p$ (Current Step-Up/Down)

EM Waves

$LaTeX: c=\displaystyle{ E \over B }$ $c=\displaystyle{ E \over B }$ (Speed of Light)

$LaTeX: \displaystyle c = { 1 \over \sqrt{ \mu_o \epsilon_0 } }$ $\displaystyle c = { 1 \over \sqrt{ \mu_o \epsilon_0 } }$ (Speed of Light)

$LaTeX: \displaystyle I = { E_{max} B_{max} \over 2 \mu_0 }$ $\displaystyle I = { E_{max} B_{max} \over 2 \mu_0 }$ (Intensity)

$LaTeX: \displaystyle I = { E_{max}^2 \over 2 \mu_0 }$ $\displaystyle I = { E_{max}^2 \over 2 \mu_0 }$ (Intensity)

$LaTeX: \displaystyle I = { C \over 2 \mu_0 } B_{max}^2$ $\displaystyle I = { C \over 2 \mu_0 } B_{max}^2$ (Intensity)

$LaTeX: p = \displaystyle{ U \over c }$ $p = \displaystyle{ U \over c }$ (Momentum: Photon is Absorbed)

$LaTeX: p = \displaystyle{ 2 U \over c }$ $p = \displaystyle{ 2 U \over c }$ (Momentum: Photon is Reflected)

$LaTeX: p =\displaystyle { h \over \lambda }$ $p =\displaystyle { h \over \lambda }$ (Compton's Relation)

Energy

$LaTeX: \displaystyle E = h f = {h c \over \lambda }$ $\displaystyle E = h f = {h c \over \lambda }$ (Planck's Relation)

Optics

$LaTeX: c = \lambda f$ $c = \lambda f$ (Speed of Light)

$LaTeX: n =\displaystyle { c \over v }$ $n =\displaystyle { c \over v }$ (Index of Refraction)

$LaTeX: n =\displaystyle { \lambda_0 \over \lambda_n }$ $n =\displaystyle { \lambda_0 \over \lambda_n }$ (Index of Refraction)

$LaTeX: n_1 \space sin \space \theta_1 = n_2 \space sin \space \theta_2$ $n_1 \space sin \space \theta_1 = n_2 \space sin \space \theta_2$ (Snell's Law)

$LaTeX: \displaystyle sin \space \theta_c = { n_2 \over n_1 }$ $\displaystyle sin \space \theta_c = { n_2 \over n_1 }$ (Total Internal Reflection)

Mirrors & Lenses

$LaTeX: M =\displaystyle { h' \over h }$ $M =\displaystyle { h' \over h }$ (Convex Mirrors)

$LaTeX: M = - \displaystyle{ q \over p }$ $M = - \displaystyle{ q \over p }$ (Convex Mirrors)

$LaTeX: \displaystyle{ 1 \over p } + { 1 \over q } = { 1 \over f }$ $\displaystyle{ 1 \over p } + { 1 \over q } = { 1 \over f }$ (Convex Mirrors)

$LaTeX: \displaystyle{ n_1 \over p } + { n_2 \over q } = { n_2 - n_1 \over R }$ $\displaystyle{ n_1 \over p } + { n_2 \over q } = { n_2 - n_1 \over R }$ (Refraction Images)

$LaTeX: M = \displaystyle{ h' \over h }$ $M = \displaystyle{ h' \over h }$ (Refraction Images)

$LaTeX: M = - \displaystyle{ n_1 q \over n_2 p }$ $M = - \displaystyle{ n_1 q \over n_2 p }$ (Refraction Images)

$LaTeX: M =\displaystyle { h' \over h }$ $M =\displaystyle { h' \over h }$ (Thin Lenses)

$LaTeX: M = - \displaystyle{ q \over p }$ $M = - \displaystyle{ q \over p }$ (Thin Lenses)

$LaTeX: \displaystyle{ 1 \over p } + { 1 \over q } = { 1 \over f }$ $\displaystyle{ 1 \over p } + { 1 \over q } = { 1 \over f }$ (Thin Lenses)

Constants

$LaTeX: k_e=8.99\:\times\:10^9\:\displaystyle\frac{\text{N}\cdot \text{m}^2}{\text{C}^2}$ $k_e=8.99\:\times\:10^9\:\displaystyle\frac{\text{N}\cdot \text{m}^2}{\text{C}^2}$ (Coulomb's Constant)

$LaTeX: \epsilon_0=8.854\:\times\:10^{-12}\:\displaystyle\frac{\text{C}^2}{\text{N}\cdot\text{m}^2}$ $\epsilon_0=8.854\:\times\:10^{-12}\:\displaystyle\frac{\text{C}^2}{\text{N}\cdot\text{m}^2}$ (Permittivity of Free Space)

$LaTeX: q_e=-1.602\:\times\:10^{-19}\:\text{C}^2$ $q_e=-1.602\:\times\:10^{-19}\:\text{C}^2$ (Charge of Electron)

$LaTeX: q_p=1.602\:\times\:10^{-19}\:\text{C}^2$ $q_p=1.602\:\times\:10^{-19}\:\text{C}^2$ (Charge of Proton)

$LaTeX: m_e=9.109\:\times\:10^{-31}\:\text{kg}$ $m_e=9.109\:\times\:10^{-31}\:\text{kg}$ (Electron Mass)

$LaTeX: m_p=1.673\:\times\:10^{-27}\:\text{kg}$ $m_p=1.673\:\times\:10^{-27}\:\text{kg}$ (Proton Mass)

$LaTeX: \mu_0=4\pi\:\times\:10^{-7}\:\displaystyle\frac{\text{T}\cdot \text{m}}{\text{A}}$ $\mu_0=4\pi\:\times\:10^{-7}\:\displaystyle\frac{\text{T}\cdot \text{m}}{\text{A}}$ (Permeability of Free Space)

$LaTeX: h=6.626\:\times\:10^{-34}\:\text{J}\cdot \text{s}$ $h=6.626\:\times\:10^{-34}\:\text{J}\cdot \text{s}$ (Plank's Constant)

LaTeX: n=1.00 $n=1.00$ (Index of Refraction - Air)

LaTeX: n=1.333 $n=1.333$ (Index of Refraction - Water)

LaTeX: n=1.52 $n=1.52$ (Index of Refraction - Crown Glass)