Electric Forces

$LaTeX: F_e = k_e { \lvert q_1 \rvert \lvert q_2 \rvert \over r^2 }$ (Coulomb's Law)

$LaTeX: k_e = {1 \over 4 \pi \epsilon _0 }$ (Coulomb's Constant)

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

Electric Fields

$LaTeX: E = k_e { \lvert q \rvert \over r^2 }$ (Electric Field)

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

LaTeX: p = q d (Electric Field of a Dipole)

$LaTeX: E = { \sigma \over \epsilon_0 }$ (Electric Field on Metal Surface)

Gauss' Law

$LaTeX: \Phi_E = { Q_{inside} \over \epsilon_0 }$

$LaTeX: \Phi_E = E A \space cos \space \theta$

Charge Densities

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

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

$LaTeX: \rho = { p \over V }$ (Volume)

Electric Potential

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

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

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

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

$LaTeX: V = \displaystyle\sum\limits_{n=0}^N k_e { q_n \over r_n }$ (Superposition Principle)

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

$LaTeX: U = k_e { q_1 q_2 \over r }$ (Electric Potential of Two Point Charges)

Current

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

LaTeX: I = n q v_d A (Average Current)

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

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

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

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

LaTeX: P = I^2 R (Power Dissipation/Joule Heating)

$LaTeX: \Delta V = \epsilon - I r$ (Terminal Voltage)

Resistors

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

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

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

$LaTeX: R_s = \displaystyle \sum \limits_{i=1}^n R_i = R_1 + R_2 + R_3 + \dots + R_n$ (Resistors in Series)

$LaTeX: { 1 \over R_p } = \displaystyle \sum \limits_{i=1}^n { 1 \over R_i} = { 1 \over R_1} + { 1 \over R_2 } + { 1 \over R_3 } + \dots + { 1 \over R_n }$ (Resistors in Parallel)

Capacitors

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

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

$LaTeX: C = 4 \pi \kappa \epsilon_0 R$ (Capacitance of a Sphere)

$LaTeX: C_p = \displaystyle \sum \limits_{i=1}^n C_i = C_1 + C_2 + C_3 + \dots + C_n$ (Capacitors in Parallel)

$LaTeX: { 1 \over C_s } = \displaystyle \sum \limits_{i=1}^n { 1 \over C_i } = { 1\over C_1 } + { 1 \over C_2 } + { 1 \over C_3 } + \dots + { 1 \over C_n }$ (Capacitors in Series)

AC Circuits

$LaTeX: V = V_0 \space sin \space \omega t$

$LaTeX: I = I_0 \space sin \space \omega t$

$LaTeX: I_{rms} = { I_{max} \over \sqrt{2} }$

$LaTeX: V_{rms} = { V_{max} \over \sqrt{2} }$

$LaTeX: V_{rms} = I_{rms} R$

$LaTeX: X_C = { 1 \over 2 \pi f c }$

$LaTeX: V_{C,rms} = I_{rms} X_C$

$LaTeX: X_L = 2 \pi f L$

$LaTeX: V_{L,rms} = I_{rms} X_L$

RLC Circuit

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

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

$LaTeX: V_{rms} = I_{rms} Z$

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

$LaTeX: \bar{P} = I_{rms} V_{rms} \space cos \space \phi$

$LaTeX: f_0 = { 1 \over 2 \pi \sqrt{ L C } }$

Transformers

LaTeX: P_s = P_p (Power)

$LaTeX: \displaystyle V_s = { N_s \over N_p } V_p$ (Voltage step-up/down)

$LaTeX: I_s = { N_p \over N_s } I_p$ (Current step-up/down)

Electromagnetic Waves

Speed of Light

$LaTeX: c = \lambda f$

$LaTeX: { E \over B } = c$

$LaTeX: \displaystyle c = { 1 \over \sqrt{ \mu_o \epsilon_0 } }$

Intensity

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

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

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

Momentum

$LaTeX: p = { U \over c }$ (photon is absorbed)

$LaTeX: p = { 2 U \over c }$ (photon is reflected)

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

Energy

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

Optics

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

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

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

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

Mirrors and Lenses

Convex Mirrors

$LaTeX: M = { h' \over h }$

$LaTeX: M = - { q \over p }$

$LaTeX: { 1 \over p } + { 1 \over q } = { 1 \over f }$

Refraction Images

$LaTeX: { n_1 \over p } + { n_2 \over q } = { n_2 - n_1 \over R }$

$LaTeX: M = { h' \over h }$

$LaTeX: M = - { n_1 q \over n_2 p }$

Thin Lenses

$LaTeX: M = { h' \over h }$

$LaTeX: M = - { q \over p }$

$LaTeX: { 1 \over p } + { 1 \over q } = { 1 \over f }$