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# 7: Electric Potential

[ "article:topic-guide", "authorname:openstax", "electric potential", "license:ccby" ]

In this chapter, we examine the relationship between voltage and electrical energy, and begin to explore some of the many applications of electricity.

• 7.0: Prelude to Electric Potential
Two terms commonly used to describe electricity are its energy and voltage, which we show in this chapter is directly related to the potential energy in a system. We know, for example, that great amounts of electrical energy can be stored in batteries, are transmitted cross-country via currents through power lines, and may jump from clouds to explode the sap of trees. In a similar manner, at the molecular level, ions cross cell membranes and transfer information.
• 7.1: Electric Potential Energy
When a free positive charge q is accelerated by an electric field, it is given kinetic energy (Figure). The process is analogous to an object being accelerated by a gravitational field, as if the charge were going down an electrical hill where its electric potential energy is converted into kinetic energy, although of course the sources of the forces are very different.
• 7.2: Electric Potential and Potential Difference
Electric potential is potential energy per unit charge. The potential difference between points A and B, VB−VA, that is, the change in potential of a charge q moved from A to B, is equal to the change in potential energy divided by the charge. Potential difference is commonly called voltage, represented by the symbol ΔV.
• 7.3: Calculations of Electric Potential
Point charges, such as electrons, are among the fundamental building blocks of matter. Furthermore, spherical charge distributions (such as charge on a metal sphere) create external electric fields exactly like a point charge. The electric potential due to a point charge is, thus, a case we need to consider.
• 7.4: Determining Field from Potential
In certain systems, we can calculate the potential by integrating over the electric field. As you may already suspect, this means that we may calculate the electric field by taking derivatives of the potential, although going from a scalar to a vector quantity introduces some interesting wrinkles. We frequently need E to calculate the force in a system; since it is often simpler to calculate the potential directly, there are systems in which it is useful to calculate V and then derive E.
• 7.5: Equipotential Surfaces and Conductors
We can represent electric potentials pictorially, just as we drew pictures to illustrate electric fields. This is not surprising, since the two concepts are related. We use arrows to represent the magnitude and direction of the electric field, and we use green lines to represent places where the electric potential is constant. These are called equipotential surfaces in three dimensions, or equipotential lines in two dimensions.
• 7.6: Applications of Electrostatics
The study of electrostatics has proven useful in many areas. This module covers just a few of the many applications of electrostatics.