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848 Chapter 19 | Electric Potential and Electric Field
• 2.E.2.2 The student is able to predict the structure of isolines of electric potential by constructing them in a given electric field and make connections between these isolines and those found in a gravitational field. (S.P. 6.4, 7.2)
• 2.E.2.3 The student is able to qualitatively use the concept of isolines to construct isolines of electric potential in an electric field and determine the effect of that field on electrically charged objects. (S.P. 1.4)
We can represent electric potentials (voltages) pictorially, just as we drew pictures to illustrate electric fields. Of course, the two are related. Consider Figure 19.12, which shows an isolated positive point charge and its electric field lines. Electric field lines radiate out from a positive charge and terminate on negative charges. While we use blue arrows to represent the magnitude and direction of the electric field, we use green lines to represent places where the electric potential is constant. These are called equipotential lines in two dimensions, or equipotential surfaces in three dimensions. The term equipotential is also used as a noun, referring to an equipotential line or surface. The potential for a point charge is the same anywhere on an imaginary sphere of radius surrounding the charge. This is true since the potential for a point charge is given by and, thus, has the
same value at any point that is a given distance from the charge. An equipotential sphere is a circle in the two-dimensional view of Figure 19.12. Since the electric field lines point radially away from the charge, they are perpendicular to the equipotential
lines.
Figure 19.12 An isolated point charge with its electric field lines in blue and equipotential lines in green. The potential is the same along each equipotential line, meaning that no work is required to move a charge anywhere along one of those lines. Work is needed to move a charge from one
equipotential line to another. Equipotential lines are perpendicular to electric field lines in every case.
Applying the Science Practices: Electric Potential and Peaks
Starting with Figure 19.13 as a rough example, draw diagrams of isolines for both positive and negative isolated point charges. Be sure to take care with what happens to the spacing of the isolines as you get closer to the charge. Then copy both of these sets of lines, but relabel them as gravitational equipotential lines. Then try to draw the sort of hill or hole or other shape that would have equipotential lines of this form. Does this shape exist in nature?
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