Suppose there are many source charges $q_1\text{,}{q}_2\text{,}\dots$. The electric potential V at a point in space is the sum of the potentials due to each charge:

where $r_i$ is the distance from charge $q_i$ to the point in space where the potential is being calculated. In other words, the electric potential, like the electric field, obeys the principle of superposition.

As an example, the contour map and elevation graph in FIGURE 25.28 show that the potential of an electric dipole is the sum of the potentials of the positive and negative charges. Potentials such as these have many practical applications. For example, electrical activity within the body can be monitored by measuring equipotential lines on the skin. Figure 25.28c shows that the equipotentials near the heart are a slightly distorted but recognizable electric dipole. This is the potential measured by an electrocardiogram.

FIGURE 25.28 The electric potential of an electric dipole.

Full Alternative Text

EXAMPLE 25.9 The potential of two charges

What is the electric potential at the point indicated in FIGURE 25.29?

FIGURE 25.29 Finding the potential of two charges.

FIGURE 25.29 Full Alternative Text

MODEL The potential is the sum of the potentials due to each charge.

SOLVE The potential at the indicated point is

$$\begin{array}{lll}V\hfill & =\hfill & {\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{q_1}{r_1}}+{\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{q_2}{r_2}}\hfill \\ \hfill & =\hfill & \left(9.0\times {10}^9{\text{Nm}}^2{\text{/C}}^2\right)\left({\displaystyle \frac{2.0\times {10}^{-9}\text{\hspace{0.17em}C}}{0.050\text{m}}}+{\displaystyle \frac{-1.0\times {10}^{-9}\text{\hspace{0.17em}C}}{0.040\text{m}}}\right)\hfill \\ \hfill & =\hfill & 135\text{V}\hfill \end{array}$$

REVIEW The potential is a scalar, so we found the net potential by adding two numbers. We don’t need any angles or components to calculate the potential.