Electrostatics

(1) Coulomb’s inverse square law:

$$ F = {q_1 q_2}/{4π ε_0 ε_r r^2} $$

$ε_0 = 8.854 x 10^{-12} =$ F/m


${1}/{4π ε_0}$ = 9 x $10^9$

(2) Electric flux: ψ

Eletric flux density: $D = ψ/A$ C/$m^2$

Field intensity: F = E x Q

$ D = ε_0 ε_r E $

Relative Permitivity ($ε_r$):

Absolute permitivity, $ε = ε_r ε_0$ F/m

(3) Capacitance, C = Q/V
$ C = {ε_0 ε_r A}/{d} $ farad
d = distance between capacitor plates

(4) Capacitors in Series:
$$ 1/C_{eq} = 1/C_1 + 1/C_2 + … + 1/C_n $$

(5) Capacitors in parallel:

$$ C_{eq} = C_1 + C_2 + … + C_n $$

(6) Multiplate Capacitor:

$$ C = (n-1) {ε_0 ε_r A}/{d} $$

(7) Energy stored by a capacitor:

$$ E = 1/2 Q V $$
$$ E = 1/2 C V^2 $$

(8) Charging of capacitor:
Capacitor voltage: $ V_c = V(1-e^{{-t}/{τ}}) $

where, τ = Time constant = R x C

Capacitor current, $i = I_0 e^{{-t}/{τ}}$

(9) Discharging of capacitor:

$ V_c = Ve^{{-t}/{τ}} $
$i = -V/R e^{{-t}/{τ}}$