What Is An Equipotential Line

Learning Objectives

By the end of this section, you will exist able to:

Explain equipotential lines and equipotential surfaces.
Draw the action of grounding an electrical apparatus.
Compare electrical field and equipotential lines.

We tin can correspond electric potentials (voltages) pictorially, but every bit nosotros drew pictures to illustrate electric fields. Of course, the two are related. Consider Effigy 19.8, which shows an isolated positive point charge and its electric field lines. Electric field lines radiate out from a positive charge and cease on negative charges. While nosotros use blue arrows to represent the magnitude and direction of the electric field, nosotros employ green lines to represent places where the electric potential is abiding. These are chosen equipotential lines in ii dimensions, or equipotential surfaces in three dimensions. The term equipotential is also used every bit a noun, referring to an equipotential line or surface. The potential for a indicate charge is the same anywhere on an imaginary sphere of radius $r$ surrounding the accuse. This is true since the potential for a point charge is given by $V = kQ / r$ and, thus, has the same value at any point that is a given distance $r$ from the charge. An equipotential sphere is a circle in the ii-dimensional view of Figure 19.8. Since the electric field lines betoken radially abroad from the accuse, they are perpendicular to the equipotential lines.

The figure shows a positive charge Q at the center of four concentric circles of increasing radii. The electric potential is the same along each of the circles, called equipotential lines. Straight lines representing electric field lines are drawn from the positive charge to intersect the circles at various points. The equipotential lines are perpendicular to the electric field lines.

Effigy xix.eight An isolated point charge $Q$ with its electric field lines in blue and equipotential lines in light-green. The potential is the same along each equipotential line, pregnant 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 electrical field lines in every instance.

Information technology is important to annotation that equipotential lines are always perpendicular to electric field lines. No piece of work is required to move a charge along an equipotential, since $Δ Five = 0$ . Thus the work is

W = -Δ PE = - q Δ V = 0 .

nineteen.43

Work is zero if force is perpendicular to motion. Force is in the same direction as $E$ , so that motion forth an equipotential must be perpendicular to $Eastward$ . More precisely, work is related to the electrical field by

Westward = Fd cos θ = qEd cos θ = 0 .

19.44

Note that in the above equation, $E$ and $F$ symbolize the magnitudes of the electric field strength and strength, respectively. Neither $q$ nor $E$ nor $d$ is aught, and and then $cos θ$ must be 0, meaning $θ$ must be $90º$ . In other words, motion along an equipotential is perpendicular to $Due east$ .

Ane of the rules for static electrical fields and conductors is that the electrical field must be perpendicular to the surface of whatever usher. This implies that a conductor is an equipotential surface in static situations. There can exist no voltage difference beyond the surface of a conductor, or charges volition menstruation. One of the uses of this fact is that a conductor can be stock-still at zilch volts by connecting information technology to the globe with a good conductor—a process called grounding. Grounding can be a useful safety tool. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the globe.

Grounding

A conductor can be fixed at nada volts by connecting it to the earth with a good conductor—a process chosen grounding.

Because a conductor is an equipotential, it can replace any equipotential surface. For case, in Figure 19.8 a charged spherical conductor can replace the signal charge, and the electrical field and potential surfaces outside of it will exist unchanged, confirming the contention that a spherical charge distribution is equivalent to a bespeak charge at its center.

Figure xix.ix shows the electric field and equipotential lines for ii equal and opposite charges. Given the electric field lines, the equipotential lines tin be drawn merely past making them perpendicular to the electric field lines. Conversely, given the equipotential lines, every bit in Figure 19.x(a), the electrical field lines tin can be drawn by making them perpendicular to the equipotentials, as in Figure 19.x(b).

The figure shows two sets of concentric circles, called equipotential lines, drawn with positive and negative charges at their centers. Curved electric field lines emanate from the positive charge and curve to meet the negative charge. The lines form closed curves between the charges. The equipotential lines are always perpendicular to the field lines.

Figure 19.9 The electric field lines and equipotential lines for 2 equal just contrary charges. The equipotential lines tin be drawn past making them perpendicular to the electric field lines, if those are known. Note that the potential is greatest (most positive) about the positive accuse and to the lowest degree (most negative) near the negative charge.

Figure (a) shows two circles, called equipotential lines, along which the potential is negative ten volts. A dumbbell-shaped surface encloses the two circles and is labeled negative five volts. This surface is surrounded by another surface labeled negative two volts. Figure (b) shows the same equipotential lines, each set with a negative charge at its center. Blue electric field lines curve toward the negative charges from all directions.

Figure 19.x (a) These equipotential lines might be measured with a voltmeter in a laboratory experiment. (b) The corresponding electric field lines are found by cartoon them perpendicular to the equipotentials. Notation that these fields are consistent with two equal negative charges.

One of the most important cases is that of the familiar parallel conducting plates shown in Figure nineteen.xi. Betwixt the plates, the equipotentials are evenly spaced and parallel. The aforementioned field could be maintained by placing conducting plates at the equipotential lines at the potentials shown.

The figure shows two parallel plates A and B separated by a distance d. Plate A is positively charged, and B is negatively charged. Electric field lines are parallel to one another between the plates and curved near the ends of the plates. The voltages range from a hundred volts at Plate A to zero volts at plate B.

Effigy 19.11 The electric field and equipotential lines between 2 metal plates.

An important awarding of electric fields and equipotential lines involves the heart. The heart relies on electrical signals to maintain its rhythm. The movement of electric signals causes the chambers of the heart to contract and relax. When a person has a eye attack, the motion of these electrical signals may be disturbed. An artificial pacemaker and a defibrillator tin can be used to initiate the rhythm of electrical signals. The equipotential lines around the heart, the thoracic region, and the axis of the middle are useful ways of monitoring the construction and functions of the heart. An electrocardiogram (ECG) measures the pocket-size electric signals existence generated during the activity of the heart. More about the relationship between electric fields and the heart is discussed in Energy Stored in Capacitors.

PhET Explorations

Charges and Fields

Move point charges effectually on the playing field and then view the electric field, voltages, equipotential lines, and more. Information technology's colorful, it'due south dynamic, information technology'south free.