$ \newcommand{\e}[1]{ \times 10^{#1}} $

constants

$m_e = 9.11\e{-31} kg = .511 \frac{Mev}{c^2} = 5.4858\e{-4} u$

$m_p = 1.673\e{-27} kg = 938 \frac{Mev}{c^2} = 1.007276 u$

$m_n = 1.675\e{-27} kg = 940 \frac{Mev}{c^2} = 1.008665 u$

$u = 1.6605\e{-27} kg = 931.5 \frac{Mev}{c^2}$

$e = 1.6012\e{-19} C$

$\mu_0 = 4\pi\e{-7}$

$k = 8.988\e9 \frac{Nm^2}{C^2}$

$\varepsilon_0 = 8.854\e{-12} \frac{F}{m}$

$c = 2.998\e8 \frac{m}{s}$

$h = 6.626\e{-34} Js = 4.136\e{-15} eVs$

$T = 1.6\e{-19}$

$E_1 = -13.6 eV$

$r_0 = 1.2\e{-15} m$

equations

$\varepsilon_0 = \frac1{4\pi k} = \frac1{\mu_0c^2}$

electric fields

$E = \frac{\sigma}{\varepsilon_0}$

$\Phi_E = \vec E \cdot \vec A = EA\cos \theta = \frac{q_A}{\varepsilon_0}$

$\vec F_E = \frac{kqQ}{r^2} = Q \vec E$

$W = \vec F \Delta x \cos \theta$

$\Delta U = -\Delta E_k = -W$

$\Delta V = \frac{\Delta U}{q_0} = -\vec E \Delta x$

$V = \frac{kQ}r$

capacitance

$V = Ed$

$Q = \sigma A$

$C = \frac{Q}V = kC_0$

$U = \frac{CV^2}2$

electric currents

$V = IR$

$P = IV$

$I = \frac{\Delta Q}{\Delta t}$

$I = v_DAnq$

$I_{rms} = \frac{I_0}{\sqrt2}$

$R = \frac{\rho \ell}A$

dc circuits

$\tau = RC$

$V_0 = \frac{Q_0}C$

$I_0 = \frac{V_0}R$

$Q_{max} = CV_B$

$\sum I_{in} = \sum I_{out}$

$\sum V_{loop} = 0$

series

$\sum Q = Q_1 = Q_2 = \cdots = Q_n$

$\frac1{\sum C} = \frac1{C_1} + \frac1{C_2} + \cdots + \frac1{C_n}$

$\sum U = \frac{Q_1^2}{2C_1} + \frac{Q_2^2}{2C_2} + \cdots + \frac{Q_n^2}{2C_n}$

$\sum R = R_1 + R_2 + \cdots + R_n$

parallel

$\sum V = V_1 = V_2 = \cdots + R_n$

$\sum C = C_1 + C_2 + \cdots + C_n$

$\sum U = \frac{Q_1}{2C_1} + \frac{Q_2}{2C_2} + \cdots + \frac{Q_n}{2C_n}$

$\frac1{\sum R} = \frac1{R_1} + \frac1{R_2} + \cdots + \frac1{R_n}$

rc circuits

$i = I_0 e^{\frac{-t}\tau}$

$V_R = I_0 R e^{\frac{-t}\tau}$

$U = \frac{q^2}{2C}$

$P = i^2 R$

charging

$q = Q_{max} \left(1 - e^{\frac{-t}\tau}\right)$

$V_C = V_B \left(1 - e^{\frac{-t}\tau}\right)$

discharging

$q = Q_{max} e^{\frac{-t}\tau}$

$V_C = V_B e^{\frac{-t}\tau}$

magnetism

$\vec F_B = q \vec v \cdot \vec B = qvB\sin\theta$

$F_B = \frac{mv^2}{R} = qvB$

$\frac{F_M}{\ell} = BI\sin\theta$

$B = \frac{\mu_0 I}{2 \pi r} = \frac{\mu_0 I N}{\ell}$

$\frac{F_{21}}{\Delta \ell} = \frac{\mu_0 I_1 I_2}{2 \pi d}$

electromagnetic induction

$\mathcal{E} = \left|\frac{\Delta \Phi_B}{\Delta t}\right| = -vBL = NBAq$

$I_{avg} = \frac{\left|\mathcal{E}\right|}R$

$\Delta \Phi_B = B \Delta A = \Delta B A$

$U = \frac{LI^2}2 = \frac{B^2V_{ol}}{2\mu_0}= \frac{B^2\pi r^2\ell}{2\mu_0}$

$\tau = \vec \mu \cdot \vec B$

$P = \vec F \cdot \vec v = \frac{\left(B \ell v\right)^2}R$

$\frac{N_P}{N_S} = \frac{V_P}{V_S} = \frac{I_S}{V_P}$

electromagnetic waves

$v = f\lambda$

$\vec{S} = \frac{EB}{2\mu_0} = \frac{P}A$

$E = \frac{I}{A\mathcal{E}_0} = cB$

$\sum U = U_E + U_B = \mathcal{E}_0E^2$

$U_E = \frac{\mathcal{E}_oE^2}2$

$U_B = \frac{B^2}{2\mu_0}$

$S = \frac{CB^2}{\mu_0} = \frac{\Delta U}{A\Delta t}$

optics

$\frac1{d_0} + \frac1{d_i} = \frac1{f} = \frac2{r}$

$\frac1{f} = (n-1)\left(\frac1{R_1}-\frac1{R_2}\right)$

$M = \frac{-d_i}{d_0} = \frac{h_i}{h_0}$

$n_1\sin\theta_1 = n_2\sin\theta_2$

$\lambda_m = \frac{\lambda_v}n$

special theory of relativity

$\Delta t = \gamma \Delta t_0$

$L = \frac{L_0}{\gamma}$

$\gamma = \frac1{\sqrt{1-\frac{v^2}{c^2}}}$

$v = c \sqrt{1-\frac1{\gamma^2}}$

quantum mechanics

$\hbar = \frac{h}{2\pi}$

$\Delta x \Delta p \gtrsim \hbar$

$\Delta E \Delta t \gtrsim \hbar$

$E_n = \frac{Z^2}{n^2}(-13.6eV)$

nuclear physics

$r = r_0 A^{1/3}$

$N = N_0e^{-\lambda t}$

$A = \lambda N$

info

prefixes

name prefix power
exa E $10^{18}$
peta P $10^{15}$
tera T $10^{12}$
giga G $10^9$
mega M $10^6$
kilo k $10^3$
hecto h $10^2$
deca da $10^1$
deci d $10^{-1}$
centi c $10^{-2}$
milli m $10^{-3}$
mirco μ $10^{-6}$
nano n $10^{-9}$
pico p $10^{-12}$
femto f $10^{-15}$
atto a $10^{-18}$

right hand rules

hand vector
fingers $\vec v$ or $I$
palm $\vec B$
thumb $\vec F$

quantum numbers

(n, ℓ, m, s)
n = 1, 2, 3 … ∞
ℓ = 0 … n-1
m = -ℓ … +ℓ
s = ±½