Electrostatics

(1) Gauss’s Theorem: TNEI = Σq

(2) No. of tubes of induction: ${q}/{kε_o}$

(3) NEI = ε E

TNEI over close surface = ∮εE ds cosθ

(4) Sphere: $E = {q}/{4πε} {1}/{r^2}$
Cylinder: $E = {q}/{4πε} {2}/{r}$

(5) Surface charge density, $σ = Q/A$

(6) $E_{outside}$ (any shape) = $σ/{kε_o}$

(7) E (plane sheet) = ${σ}/{2kε_o}$

(8) $f = F/{ds} \text" (Mechanical force) "$ = $1/2 {σ^2}/{kε_o} $ = $1/2 kε_o E^2$

(9) Energy density, $u = {dw}/{dv}$ = $1/2 kε_o E^2$ = ${dU}/{dv}$

(10) $C = Q/v$ or $Q = CV$

(11) parallel plate capacitor,
$C = {k A ε_o}/{d}$     d -> distance between parallel plates

(12) Energy stored,

$U = 1/2 C V^2$ = $1/2 Q^2/C$ = $1/2 QV$

(13) Series (capacitor): $1/C_s = 1/C_1 + 1/C_2 +…+ 1/C_n$

(14) $E = V/d$

(15) $dw = {ds cosθ}/{r^2}$

(16) $∫dw = 4π$