Between the plates, the equipotentials are evenly spaced and parallel. One of the most important cases is that of the familiar parallel conducting plates shown in Figure 4. The electric field and equipotential lines between two metal plates. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the earth.įigure 4. One of the uses of this fact is that a conductor can be fixed at zero volts by connecting it to the earth with a good conductor-a process called grounding. There can be no voltage difference across the surface of a conductor, or charges will flow. This implies that a conductor is an equipotential surface in static situations. One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. In other words, motion along an equipotential is perpendicular to E. Neither q nor E nor d is zero, and so cos θ must be 0, meaning θ must be 90º. Note that in the above equation, E and F symbolize the magnitudes of the electric field strength and force, respectively. More precisely, work is related to the electric field by Force is in the same direction as E, so that motion along an equipotential must be perpendicular to E. Work is zero if force is perpendicular to motion. No work is required to move a charge along an equipotential, since Δ V = 0. It is important to note that equipotential lines are always perpendicular to electric field lines. Equipotential lines are perpendicular to electric field lines in every case. Work is needed to move a charge from one equipotential line to another. 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. An isolated point charge Q with its electric field lines in blue and equipotential lines in green. Since the electric field lines point radially away from the charge, they are perpendicular to the equipotential lines.įigure 1. An equipotential sphere is a circle in the two-dimensional view of Figure 1. This is true since the potential for a point charge is given by V=\frac\\ and, thus, has the same value at any point that is a given distance r from the charge. The potential for a point charge is the same anywhere on an imaginary sphere of radius r surrounding the charge. The term equipotential is also used as a noun, referring to an equipotential line or surface. These are called equipotential lines in two dimensions, or equipotential surfaces in three dimensions. 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. Electric field lines radiate out from a positive charge and terminate on negative charges. Consider Figure 1, which shows an isolated positive point charge and its electric field lines. We can represent electric potentials (voltages) pictorially, just as we drew pictures to illustrate electric fields. Compare electric field and equipotential lines.Describe the action of grounding an electrical appliance.Explain equipotential lines and equipotential surfaces.By the end of this section, you will be able to:
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