# Electrostatic

### Electric Potential and Potential Energy

##### 1. Electric Potential

Electric potential of a point r meter from a charge:

$$V = k \: \dfrac{Q}{r}$$

##### 2. Electric Potential Difference

Electric potential difference between 2 points:

$$\Delta V = V_2 - V_1$$

$$\Delta V = k \: \dfrac{Q}{r_2} - k \: \dfrac{Q}{r_2}$$

$$\Delta V = k \: Q \left(\dfrac{1}{r_2} - \dfrac{1}{r_1}\right)$$

If two points have different potential, higher potential symbolized with (+) and lower potential with (−).

Between two points which have different potential, electric field will produced.

$$\Delta V = E \:.\: d$$

##### 2. Electric Potential Energy

electric potential energy between two charges:

\begin{equation*} E_p = k \: \frac{q \: Q}{r} \\ Joule & = q \: V \end{equation*} A charge can move from one point to another which have different potentials. The work done by the charge is:

\begin{equation*} \begin{split} W & = \Delta E_p \\\\ W & = E_{p_2} - E_{p_1} \\\\ W & = q \: V_2 - q \: V_1 \\\\ W & = q (V_2 - V_1) \\\\ W & = q \:.\: \Delta V \end{split} \end{equation*}