# 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

$$W = \frac{\epsilon E^2 V}{k8 \pi}$$