Science—Physics 2 Equations Trig Version

Electric Forces

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

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

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

 

Electric Fields

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

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

$p = q d$  (Electric Field of a Dipole)

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

 

Gauss' Law

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

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

 

Charge Densities

$\lambda = { q \over L }$  (Linear)

$\sigma = { q \over A }$  (Surface)

$\rho = { p \over V }$  (Volume)

 

Electric Potential

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

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

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

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

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

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

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

 

Current

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

$I = n q v_d A$  (Average Current)

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

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

$\Delta V = I R$  (Ohm's Law)

$P = I \Delta V$  (Power in Resistor)

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

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

 

Resistors

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

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

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

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

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

 

Capacitors

$Q = C \Delta V$ (Capacitance)

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

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

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

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

 

 

 

 

AC Circuits

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

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

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

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

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

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

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

$X_L = 2 \pi f L$

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

 

RLC Circuit

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

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

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

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

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

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

 

Transformers

$P_s = P_p$  (Power)

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

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

 

Electromagnetic Waves

Speed of Light

$c = \lambda f$

${ E \over B } = c$  

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

Intensity

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

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

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

Momentum

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

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

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

Energy

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

 

Optics

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

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

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

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

 

Mirrors and Lenses

Convex Mirrors

$M = { h' \over h }$

$M = - { q \over p }$

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

Refraction Images

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

$M = { h' \over h }$

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

Thin Lenses

$M = { h' \over h }$

$M = - { q \over p }$

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