gen-phys-cs.md (4746B)
1 --- 2 title: "General Physics Cheatsheet" 3 date: 2017-06-02 4 tags: phys cheatsheet 5 categories: phys 6 math: true 7 --- 8 9 $ \newcommand{\e}[1]{ \times 10^{#1}} $ 10 11 ## constants 12 13 $m_e = 9.11\e{-31} kg = .511 \frac{MeV}{c^2} = 5.4858\e{-4} u$ 14 15 $m_p = 1.673\e{-27} kg = 938 \frac{MeV}{c^2} = 1.007276 u$ 16 17 $m_n = 1.675\e{-27} kg = 940 \frac{MeV}{c^2} = 1.008665 u$ 18 19 $u = 1.6605\e{-27} kg = 931.5 \frac{MeV}{c^2}$ 20 21 $e = 1.6012\e{-19} C$ 22 23 $\mu_0 = 4\pi\e{-7}$ 24 25 $k = 8.988\e9 \frac{Nm^2}{C^2}$ 26 27 $\varepsilon_0 = 8.854\e{-12} \frac{F}{m}$ 28 29 $c = 2.998\e8 \frac{m}{s}$ 30 31 $h = 6.626\e{-34} Js = 4.136\e{-15} eVs$ 32 33 $T = 1.6\e{-19}$ 34 35 $E_1 = -13.6 eV$ 36 37 $r_0 = 1.2\e{-15} m$ 38 39 ## equations 40 41 $\varepsilon_0 = \frac1{4\pi k} = \frac1{\mu_0c^2}$ 42 43 ### electric fields 44 45 $E = \frac{\sigma}{\varepsilon_0}$ 46 47 $\Phi_E = \vec E \cdot \vec A = EA\cos \theta = \frac{q_A}{\varepsilon_0}$ 48 49 $\vec F_E = \frac{kqQ}{r^2} = Q \vec E$ 50 51 $W = \vec F \Delta x \cos \theta$ 52 53 $\Delta U = -\Delta E_k = -W$ 54 55 $\Delta V = \frac{\Delta U}{q_0} = -\vec E \Delta x$ 56 57 $V = \frac{kQ}r$ 58 59 ### capacitance 60 61 $V = Ed$ 62 63 $Q = \sigma A$ 64 65 $C = \frac{Q}V = kC_0$ 66 67 $U = \frac{CV^2}2$ 68 69 ### electric currents 70 71 $V = IR$ 72 73 $P = IV$ 74 75 $I = \frac{\Delta Q}{\Delta t}$ 76 77 $I = v_DAnq$ 78 79 $I_{rms} = \frac{I_0}{\sqrt2}$ 80 81 $R = \frac{\rho \ell}A$ 82 83 ### dc circuits 84 85 $\tau = RC$ 86 87 $V_0 = \frac{Q_0}C$ 88 89 $I_0 = \frac{V_0}R$ 90 91 $Q_{max} = CV_B$ 92 93 $\sum I_{in} = \sum I_{out}$ 94 95 $\sum V_{loop} = 0$ 96 97 #### series 98 99 $\sum Q = Q_1 = Q_2 = \cdots = Q_n$ 100 101 $\frac1{\sum C} = \frac1{C_1} + \frac1{C_2} + \cdots + \frac1{C_n}$ 102 103 $\sum U = \frac{Q_1^2}{2C_1} + \frac{Q_2^2}{2C_2} + \cdots + \frac{Q_n^2}{2C_n}$ 104 105 $\sum R = R_1 + R_2 + \cdots + R_n$ 106 107 #### parallel 108 109 $\sum V = V_1 = V_2 = \cdots + R_n$ 110 111 $\sum C = C_1 + C_2 + \cdots + C_n$ 112 113 $\sum U = \frac{Q_1}{2C_1} + \frac{Q_2}{2C_2} + \cdots + \frac{Q_n}{2C_n}$ 114 115 $\frac1{\sum R} = \frac1{R_1} + \frac1{R_2} + \cdots + \frac1{R_n}$ 116 117 ### rc circuits 118 119 $i = I_0 e^{\frac{-t}\tau}$ 120 121 $V_R = I_0 R e^{\frac{-t}\tau}$ 122 123 $U = \frac{q^2}{2C}$ 124 125 $P = i^2 R$ 126 127 #### charging 128 129 $q = Q_{max} \left(1 - e^{\frac{-t}\tau}\right)$ 130 131 $V_C = V_B \left(1 - e^{\frac{-t}\tau}\right)$ 132 133 #### discharging 134 135 $q = Q_{max} e^{\frac{-t}\tau}$ 136 137 $V_C = V_B e^{\frac{-t}\tau}$ 138 139 ### magnetism 140 141 $\vec F_B = q \vec v \cdot \vec B = qvB\sin\theta$ 142 143 $F_B = \frac{mv^2}{R} = qvB$ 144 145 $\frac{F_M}{\ell} = BI\sin\theta$ 146 147 $B = \frac{\mu_0 I}{2 \pi r} = \frac{\mu_0 I N}{\ell}$ 148 149 $\frac{F_{21}}{\Delta \ell} = \frac{\mu_0 I_1 I_2}{2 \pi d}$ 150 151 ### electromagnetic induction 152 153 $\mathcal{E} = \left\|\frac{\Delta \Phi_B}{\Delta t}\right\| = -vBL = NBAq$ 154 155 $I_{avg} = \frac{\left\|\mathcal{E}\right\|}R$ 156 157 $\Delta \Phi_B = B \Delta A = \Delta B A$ 158 159 $U = \frac{LI^2}2 = \frac{B^2V_{ol}}{2\mu_0}= \frac{B^2\pi r^2\ell}{2\mu_0}$ 160 161 $\tau = \vec \mu \cdot \vec B$ 162 163 $P = \vec F \cdot \vec v = \frac{\left(B \ell v\right)^2}R$ 164 165 $\frac{N_P}{N_S} = \frac{V_P}{V_S} = \frac{I_S}{V_P}$ 166 167 ### electromagnetic waves 168 169 $v = f\lambda$ 170 171 $\vec{S} = \frac{EB}{2\mu_0} = \frac{P}A$ 172 173 $E = \frac{I}{A\mathcal{E}_0} = cB$ 174 175 $\sum U = U_E + U_B = \mathcal{E}_0E^2$ 176 177 $U_E = \frac{\mathcal{E}_oE^2}2$ 178 179 $U_B = \frac{B^2}{2\mu_0}$ 180 181 $S = \frac{CB^2}{\mu_0} = \frac{\Delta U}{A\Delta t}$ 182 183 ### optics 184 185 $\frac1{d_0} + \frac1{d_i} = \frac1{f} = \frac2{r}$ 186 187 $\frac1{f} = (n-1)\left(\frac1{R_1}-\frac1{R_2}\right)$ 188 189 $M = \frac{-d_i}{d_0} = \frac{h_i}{h_0}$ 190 191 $n_1\sin\theta_1 = n_2\sin\theta_2$ 192 193 $\lambda_m = \frac{\lambda_v}n$ 194 195 ### special theory of relativity 196 197 $\Delta t = \gamma \Delta t_0$ 198 199 $L = \frac{L_0}{\gamma}$ 200 201 $\gamma = \frac1{\sqrt{1-\frac{v^2}{c^2}}}$ 202 203 $v = c \sqrt{1-\frac1{\gamma^2}}$ 204 205 ### quantum mechanics 206 207 $\hbar = \frac{h}{2\pi}$ 208 209 $\Delta x \Delta p \gtrsim \hbar$ 210 211 $\Delta E \Delta t \gtrsim \hbar$ 212 213 $E_n = \frac{Z^2}{n^2}(-13.6eV)$ 214 215 ### nuclear physics 216 217 $r = r_0 A^{1/3}$ 218 219 $N = N_0e^{-\lambda t}$ 220 221 $A = \lambda N$ 222 223 ## info 224 225 ### prefixes 226 227 | name | prefix | power | 228 | ---- | ------ | ---------- | 229 | exa | E | $10^{18}$ | 230 | peta | P | $10^{15}$ | 231 | tera | T | $10^{12}$ | 232 | giga | G | $10^9$ | 233 | mega | M | $10^6$ | 234 | kilo | k | $10^3$ | 235 | hecto | h | $10^2$ | 236 | deca | da | $10^1$ | 237 | - | - | - | 238 | deci | d | $10^{-1}$ | 239 | centi | c | $10^{-2}$ | 240 | milli | m | $10^{-3}$ | 241 | mirco | μ | $10^{-6}$ | 242 | nano | n | $10^{-9}$ | 243 | pico | p | $10^{-12}$ | 244 | femto | f | $10^{-15}$ | 245 | atto | a | $10^{-18}$ | 246 247 ### right hand rules 248 249 | hand | vector | 250 | ------- | --------------- | 251 | fingers | $\vec v$ or $I$ | 252 | palm | $\vec B$ | 253 | thumb | $\vec F$ | 254 255 ### quantum numbers 256 257 | (n, ℓ, m, s) | 258 | --------------- | 259 | n = 1, 2, 3 … ∞ | 260 | ℓ = 0 … n-1 | 261 | m = -ℓ … +ℓ | 262 | s = ±½ |