Coefficient of Performance (Refrigerator): $K = \frac{|Q_L|}{|W|}$

Carnot Cycle (Ideal Engine/Refrigerator):

Coulomb's Law: $F = k \frac{|q_1q_2|}{r^2}$ ($k = \frac{1}{4\pi\epsilon_0} = 8.99 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2$)
Electric Field: $\vec{E} = \frac{\vec{F}}{q_0}$
Electric Field of Point Charge: $E = k \frac{|q|}{r^2}$
Electric Dipole Moment: $\vec{p} = q\vec{d}$
Torque on Dipole in E-field: $\vec{\tau} = \vec{p} \times \vec{E}$
Potential Energy of Dipole: $U = -\vec{p} \cdot \vec{E}$

Electric Flux: $\Phi_E = \int \vec{E} \cdot d\vec{A}$
Gauss' Law: $\epsilon_0 \Phi_E = q_{enc}$
Applications: Finding E-field for symmetric charge distributions (e.g., infinite line, plane, sphere)

Electric Potential Energy: $\Delta U = -W = - \int \vec{F} \cdot d\vec{s}$
Electric Potential: $V = \frac{U}{q_0}$
Potential Difference: $\Delta V = V_f - V_i = -\int_i^f \vec{E} \cdot d\vec{s}$
Relation between E and V: $\vec{E} = -\nabla V = -(\frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k})$
Potential due to Point Charge: $V = k \frac{q}{r}$
Potential due to Dipole: $V = k \frac{p \cos\theta}{r^2}$

Capacitance: $C = \frac{q}{V}$ (Unit: Farad, F)
Parallel Plate Capacitor: $C = \frac{\epsilon_0 A}{d}$
Capacitors in Parallel: $C_{eq} = \sum C_i$
Capacitors in Series: $\frac{1}{C_{eq}} = \sum \frac{1}{C_i}$
Energy Stored in Capacitor: $U = \frac{1}{2}CV^2 = \frac{q^2}{2C} = \frac{1}{2}qV$
Energy Density: $u = \frac{1}{2}\epsilon_0 E^2$
Capacitor with Dielectric: $C = \kappa C_{air}$, $E = E_{air}/\kappa$

Electric Current: $I = \frac{dq}{dt}$ (Unit: Ampere, A)
Current Density: $\vec{J} = n e \vec{v}_d$ ($n$ charge carriers, $e$ charge, $v_d$ drift speed)
Ohm's Law: $V = IR$
Resistance: $R = \rho \frac{L}{A}$ ($\rho$ resistivity)
Resistivity (Temperature Dependence): $\rho - \rho_0 = \rho_0 \alpha (T - T_0)$
Power in Electric Circuits: $P = IV = I^2R = \frac{V^2}{R}$

Resistors in Series: $R_{eq} = \sum R_i$
Resistors in Parallel: $\frac{1}{R_{eq}} = \sum \frac{1}{R_i}$
Kirchhoff's Laws:
- Junction Rule: $\sum I_{in} = \sum I_{out}$
- Loop Rule: $\sum \Delta V = 0$ around any closed loop
RC Circuits (Charging Capacitor): $q(t) = C\mathcal{E}(1 - e^{-t/RC})$, $I(t) = \frac{\mathcal{E}}{R}e^{-t/RC}$
RC Circuits (Discharging Capacitor): $q(t) = q_0 e^{-t/RC}$, $I(t) = -\frac{q_0}{RC}e^{-t/RC}$
Time Constant: $\tau = RC$

Magnetic Force on Charge: $\vec{F}_B = q\vec{v} \times \vec{B}$ (magnitude $F_B = |q|vB\sin\phi$)
Magnetic Force on Current: $\vec{F}_B = I\vec{L} \times \vec{B}$ (magnitude $F_B = ILB\sin\phi$)
Torque on Current Loop: $\vec{\tau} = \vec{\mu} \times