$q = ne, \quad e = 1.6\times10^{-19}\ \text{C}, \quad [q] = [AT]$

$F = \frac{kq_1q_2}{r^2}, \quad k = 9\times10^9\ \text{N m}^2\text{C}^{-2}, \quad \varepsilon_0 = 8.85\times10^{-12}\ \text{C}^2\text{N}^{-1}\text{m}^{-2}$

E = \frac{kQ}{r^2} = \frac{F}{q_0}, \quad [E] = [M$LT^{-3}A^{-1}$], \quad \text{unit: N/C}$$

$E_{\text{axial}} = \frac{2kp}{r^3}, \quad E_{\text{eq}} = \frac{kp}{r^3}, \quad p = q \cdot 2l, \quad [p] = [ATL]$

\Phi = \oint \vec{E}\cdot d\vec{A} = \frac{q_{\text{enc}}}{\varepsilon_0}, \quad [\Phi] = [ML^3$T^{-3}A^{-1}$], \quad \text{unit: V·m}$$

$E_{\text{wire}} = \frac{\lambda}{2\pi\varepsilon_0 r}, \quad E_{\text{plane}} = \frac{\sigma}{2\varepsilon_0}, \quad E_{\text{sphere, inside}} = \frac{kQr}{R^3}$

V = \frac{kQ}{r}, \quad E = -\frac{dV}{dr}, \quad [V] = [ML^2$T^{-3}A^{-1}$], \quad \text{unit: volt}$$

U = \frac{kq_1q_2}{r}, \quad [U] = [ML^2$T^{-2}$], \quad \text{unit: joule}

C = \frac{Q}{V} = \frac{\varepsilon_0 A}{d}, \quad [C] = [$M^{-1}L^{-2}$T^4A^2], \quad \text{unit: farad (F)}$$

U_{\text{cap}} = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{1}{2}QV, \quad [U] = [ML^2$T^{-2}$]

Key Numerical Values:

• k = $9 \times 10^{9}$ N $m^{2}$ $C^{-2}$
• ε_{0} = $8.85 \times 10^{-12}$ $C^{2}$ $N^{-1}$ $m^{-2}$
• e = $1.6 \times 10^{-1}$^{9} C
• 1 μF = 10^{-6} F; 1 pF = 10^{-12} F; 1 μC = 10^{-6} C