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: $$ \begin{eqnarray} V &=&\frac{k q}{r} \end{eqnarray} $$

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Notations

Name Symbol Unit Meaning
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