Carnot Engine Efficiency: $\epsilon = 1 - T_C/T_H$

Coulomb's Law: $F = k \frac{|q_1 q_2|}{r^2}$, $k = 1/(4\pi\epsilon_0) = 8.99 \times 10^9 \text{ N m}^2/\text{C}^2$
Electric Field: $\vec{E} = \vec{F}/q_0 = k \frac{q}{r^2} \hat{r}$
Electric Flux: $\Phi_E = \oint \vec{E} \cdot d\vec{A}$
Gauss' Law: $\epsilon_0 \Phi_E = q_{enc}$
Electric Potential Energy: $U = qV$
Electric Potential: $V = k \frac{q}{r}$, $\vec{E} = -\nabla V$
Capacitance: $C = q/V$
Parallel Plate Capacitor: $C = \epsilon_0 A/d$
Energy Stored in Capacitor: $U = \frac{1}{2} CV^2 = \frac{1}{2} qV = \frac{q^2}{2C}$
Current: $I = dq/dt = n A v_d q$
Resistance: $R = \rho L/A$
Ohm's Law: $V = IR$
Power (Electric): $P = IV = I^2 R = V^2 / R$
Resistors: Series $R_{eq} = \sum R_i$, Parallel $1/R_{eq} = \sum 1/R_i$
Capacitors: Series $1/C_{eq} = \sum 1/C_i$, Parallel $C_{eq} = \sum C_i$
RC Circuits: Charging $q(t) = C\mathcal{E}(1 - e^{-t/RC})$, Discharging $q(t) = Q_0 e^{-t/RC}$

Magnetic Force on Charge: $\vec{F}_B = q \vec{v} \times \vec{B}$
Magnetic Force on Current: $\vec{F}_B = I \vec{L} \times \vec{B}$
Magnetic Field (Biot-Savart): $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{s} \times \hat{r}}{r^2}$
Magnetic Field (Long Straight Wire): $B = \frac{\mu_0 I}{2\pi r}$
Magnetic Field (Solenoid): $B = \mu_0 n I$
Ampere's Law: $\oint \vec{B} \cdot d\vec{s} = \mu_0 I_{enc}$
Magnetic Flux: $\Phi_B = \int \vec{B} \cdot d\vec{A}$
Faraday's Law of Induction: $\mathcal{E} = -N \frac{d\Phi_B}{dt}$
Motional EMF: $\mathcal{E} = BLv$
Inductance: $L = N \Phi_B / I$
Energy Stored in Inductor: $U = \frac{1}{2} L I^2$
RL Circuits: Current growth $I(t) = (\mathcal{E}/R)(1 - e^{-tL/R})$, Current decay $I(t) = (I_0) e^{-tL/R}$
LC Oscillations: $\omega = 1/\sqrt{LC}$
Transformers: $V_S/V_P = N_S/N_P = I_P/I_S$

Speed of Light in Vacuum: $c = 1/\sqrt{\mu_0 \epsilon_0} = 3 \times 10^8 \text{ m/s}$
Wave Speed: $c = \lambda f$
Energy Density: $u = u_E + u_B = \frac{1}{2}\epsilon_0 E^2 + \frac{1}{2\mu_0} B^2$
Poynting Vector: $\vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B})$. Magnitude $S = EB/\mu_0$
Intensity (Average Poynting Vector): $I = S_{avg} = \frac{1}{2\mu_0} E_{max} B_{max} = \frac{E_{max}^2}{2\mu_0 c}$
Radiation Pressure: $P_r = I/c$ (absorbed), $P_r = 2I/c$ (reflected)

Index of Refraction: $n = c/v$
Snell's Law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$
Critical Angle: $\sin \theta_c = n_2/n_1$ ($n_1 > n_2$)
Mirror/Lens Equation: $1/f = 1/p + 1/i$
Magnification: $m = -i/p$
Spherical Mirrors: $f = R/2$ (concave +f, convex -f)
Thin Lenses: $f$ (converging +f, diverging -f)
Young's Double Slit:
- Constructive: $d \sin \theta = m\lambda$ ($m=0, \pm 1, \pm 2, ...$)
- Destructive: $d \sin \theta = (m + 1/2)\lambda$ ($m=0, \pm 1, \pm 2, ...$)
Single Slit Diffraction:
- Minima: $a \sin \theta = m\lambda$ ($m=