# PHYS 172

Lecture 20a - Electric Potential

## Introduction

Electric potential is more commonly known as voltage. It is produced by all electric charges, but unlike electric field, electric potential is a scalar (as opposed to a vector). The symbol for electric potential is $V$, but confusingly we use the same symbol $V$ to represent the SI unit, volts. Voltage could be positive or negative, for example: $$\begin{eqnarray} V_1 &=& +5V\\ V_2 &=& -7V \end{eqnarray}$$

## Electric Potential from Point Charges

The electric potential at distance $r$ from a point charge $q$ is given by:

$$\begin{eqnarray} V &=&\frac{q}{4\pi \epsilon_0 r} \end{eqnarray}$$

Just like before, we often use $k = \frac{1}{4\pi \epsilon_0} \approx 8.99\times 10^9 N m^2 C^{-2}$ to write the above equation as: $$\begin{eqnarray} V &=&\frac{k q}{r} \end{eqnarray}$$

Electric Potential $V$ $V$ useful in computing energy
Work $W$ $J$ energy transfer
Kinetic energy $KE$ $J$ energy of motion
Power $P$ $W$ rate of energy transfer