List of formulas related to Electrostatics
Coulomb's Law
q: size of charges(c), ε: relative permittivity (in vaccum ε=1), r: distance between the charges(m)
$$ F = F_{12}= F_{21} = k \frac{|q_1 q_2|}{er^2} $$ $$ k = 9 x 10^9(Nm^2/C^2) $$
Electric Fields
E: electric field strength (N/C)
$$ \vec{E} = \frac{\vec{F}}{q} => \vec{F} = q \vec{E} $$ $$ E = k \frac{|q|}{e.r^2} $$ $$ q > 0 => \vec{F} \uparrow \uparrow \vec{E}$$ $$ q < 0 => \vec{F} \uparrow \downarrow \vec{E}$$
The Principle Of Superposition For electric Fields
$$ \vec{E} = \vec{E_1} + \vec{E_2} + .... + \vec{E_n} $$ $$ \text{In case of 2 electric fields} $$ $$ \vec{E} = \vec{E_1} + \vec{E_2} $$ $$ \vec{E_1} \uparrow \uparrow \vec{E_2} => E = E_1 + E_2 $$ $$ \vec{E_1} \uparrow \downarrow \vec{E_2} => E = E_1 - E_2 $$ $$ \vec{E_1} \perp \vec{E_2} => {E} = \sqrt{E_1 ^2 + E_2 ^2} $$ $$ ( \vec{E_1} , \vec{E_2} ) = \alpha $$ $$ => E = \sqrt{E_1 ^2 + {E_2 ^2} + 2 E_1 E_{2} cos \alpha} $$ $$ W_{MN} = _qV_M - _qV_N $$Work Of Electric Force
$$ W_{MN} = q Ed _{MN} $$ $$ d_{MN} = M'N' $$
Electric Potential Difference
$$ W_{MN} = qV _{M} - qV _{N} $$ $$ = q(V_M - V_N) $$ $$ = qU_{MN} $$ $$ U_{MN} = V_M - V_N = \frac{W_{MN}}{q} = Ed_{MN}$$Relation Between E And U
$$ E = \frac{U _{MN}}{\overline{M'N'}} $$ $$ E = \frac{U}{d} $$Capacitance
C: capacitance (F), Q: total electric charge(c), U: electric potential (V)
$$ C = \frac{Q}{U}(F) $$Capacitor
A: are of each electrode plate (m2), d: distance between the electrodes (m), ε: relative permittivity (F/m)
$$ C = \frac{\epsilon A}{9.10^9 .4 \pi d}(F) $$Capacitances In Series
$$ Q = Q_1 = Q_2 = ...... = Q_n $$
$$ U_{AB} = U_1 + U_2 + ...... + U_n $$
$$ C = \frac{1}{C_1} + \frac{1}{C_2} + ...... + \frac{1}{C_n} $$
Capacitances In Parallel
$$ Q = Q_1 = Q_2 = ...... = Q_n $$
$$ U_{AB} = U_1 = U_2 = ...... = U_n $$
$$ C = {C_1} + {C_2} + ...... + {C_n} $$
Electric Field Energy
$$ W = \frac{1}{2}QU = \frac{1}{2}CU^2 = \frac{Q^2}{2C} $$Energy Of A Capacitor
V: A.d: volume between two electrode plates
$$ W = \frac{\epsilon E^2 V}{k8 \pi} $$