Explain equipotential lines and equipotential surfaces.Describe the action of ground connection an electric appliance.Compare electric field and equipotential lines.

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We can represent electric potentials (voltages) pictorially, simply as we drew pictures to illustrate electric fields. Of course, the two space related. Take into consideration Figure 1, which shows an isolated positive point charge and its electrical field lines. Electric field lines radiate out from a confident charge and also terminate on an adverse charges. When we usage blue arrows to stand for the magnitude and also direction the the electric field, us use environment-friendly lines come represent areas where the electric potential is constant. These are dubbed equipotential lines in 2 dimensions, or equipotential surfaces in 3 dimensions. The hatchet equipotential is additionally used together a noun, referring to one equipotential line or surface. The potential because that a suggest charge is the same all over on one imaginary round of radius r surrounding the charge. This is true because the potential because that a allude charge is provided by V=\frackQr\\ and, thus, has the very same value in ~ any allude that is a offered distance r from the charge. An equipotential round is a circle in the two-dimensional view of figure 1. Because the electric field lines allude radially far from the charge, they room perpendicular to the equipotential lines.

Figure 1. An isolated point charge Q with its electrical field currently in blue and also equipotential present in green. The potential is the exact same along every equipotential line, meaning that no work is forced to relocate a charge all over along among those lines. Work-related is needed to move a charge from one equipotential heat to another. Equipotential lines room perpendicular to electric field lines in every case.

It is necessary to note that equipotential lines are always perpendicular to electric field lines. No job-related is required to move a charge follow me an equipotential, because ΔV = 0. Thus the occupational is

W = −ΔPE = −qΔV = 0.

Work is zero if force is perpendicular to motion. Force is in the very same direction as E, therefore that activity along an equipotential should be perpendicular to E. Much more precisely, work-related is regarded the electrical field by

WFd cos θqEd cos θ = 0.

Note that in the above equation, E and F signify the magnitudes that the electric field strength and force, respectively. Neither q no one E nor d is zero, and also so cos θ must be 0, meaning θ need to be 90º. In other words, activity along an equipotential is perpendicular come E.

One the the rules because that static electric fields and conductors is the the electrical field have to be perpendicular come the surface of any conductor. This suggests that a conductor is one equipotential surface ar in static situations. There can be no voltage difference across the surface ar of a conductor, or charges will flow. Among the supplies of this fact is that a conductor have the right to be solved at zero volts by connecting it to the earth with a an excellent conductor—a procedure called grounding. Grounding can be a beneficial safety tool. For example, ground connection the metal instance of an electric appliance ensures the it is at zero volts relative to the earth.

### Grounding

A conductor can be resolved at zero volts by connecting it to the earth with a an excellent conductor—a procedure called grounding.

Because a conductor is one equipotential, it have the right to replace any kind of equipotential surface. Because that example, in figure 1 a fee spherical conductor deserve to replace the suggest charge, and also the electrical field and potential surfaces external of it will certainly be unchanged, confirming the contention the a spherical charge distribution is identical to a suggest charge at its center.

Figure 2 shows the electrical field and equipotential currently for two equal and also opposite charges. Offered the electric field lines, the equipotential lines have the right to be attracted simply by making them perpendicular come the electrical field lines. Conversely, provided the equipotential lines, together in number 3a, the electric field lines can be attracted by making castle perpendicular come the equipotentials, as in number 3b.

Figure 2. The electric field lines and equipotential present for two equal yet opposite charges. The equipotential lines deserve to be attracted by making castle perpendicular to the electric field lines, if those space known. Note that the potential is greatest (most positive) close to the positive charge and also least (most negative) near the an unfavorable charge.

Figure 3. (a) these equipotential lines can be measured through a voltmeter in a laboratory experiment. (b) The equivalent electric field lines are found by illustration them perpendicular come the equipotentials. Keep in mind that these fields are regular with 2 equal negative charges.

Figure 4. The electric field and also equipotential lines in between two metal plates.

One that the many important instances is the of the acquainted parallel conducting plates displayed in figure 4. Between the plates, the equipotentials room evenly spaced and parallel. The exact same field can be preserved by placing conducting plates at the equipotential lines in ~ the potentials shown.

An necessary application of electrical fields and also equipotential lines entails the heart. The heart relies on electrical signals to preserve its rhythm. The activity of electrical signals reasons the chambers the the heart to contract and also relax. When a person has a heart attack, the motion of these electric signals might be disturbed. An man-made pacemaker and also a defibrillator can be provided to start the rate of electric signals. The equipotential lines approximately the heart, the thoracic region, and also the axis the the heart are useful ways of security the structure and also functions of the heart. An electrocardiogram (ECG) procedures the tiny electric signals gift generated throughout the activity of the heart. An ext about the relationship between electric fields and also the love is questioned in energy Stored in Capacitors.

## PhET Explorations: Charges and Fields

Move allude charges approximately on the playing field and then see the electrical field, voltages, equipotential lines, and more. It’s colorful, it’s dynamic, it’s free.

Click to run the simulation.

## Section Summary

An equipotential line is a line follow me which the electric potential is constant.An equipotential surface ar is a three-dimensional variation of equipotential lines.Equipotential present are constantly perpendicular to electric field lines.The process by i beg your pardon a conductor have the right to be resolved at zero volts by connecting it come the planet with a great conductor is dubbed grounding.

### Conceptual Questions

What is an equipotential line? What is one equipotential surface?Explain in your very own words why equipotential lines and also surfaces must be perpendicular to electric field lines.Can various equipotential lines cross? Explain.

### Problems & Exercises

(a) map out the equipotential lines close to a allude charge +q. Suggest the direction of raising potential. (b) carry out the same for a suggest charge −3q.Sketch the equipotential lines because that the two equal confident charges presented in figure 5. Suggest the direction of increasing potential.

Figure 5. The electrical field near two equal hopeful charges is directed far from each of the charges.

Figure 6 reflects the electrical field lines near two charges q1 and q2, the very first having a magnitude four times that of the second. Sketch the equipotential lines because that these 2 charges, and indicate the direction of raising potential.Sketch the equipotential lines a lengthy distance indigenous the charges displayed in number 6. Indicate the direction of increasing potential.

Figure 6. The electric field near two charges.

Sketch the equipotential currently in the vicinity of two opposite charges, wherein the an unfavorable charge is three times as great in magnitude together the positive. See figure 6 for a similar situation. Show the direction of boosting potential.Sketch the equipotential lines in the vicinity that the negatively fee conductor in number 7. Exactly how will this equipotentials look at a long distance native the object?

Figure 7. A negatively fee conductor.

Sketch the equipotential lines neighboring the 2 conducting plates presented in number 8, provided the top plate is positive and the bottom plate has an same amount of negative charge. Be details to indicate the circulation of charge on the plates. Is the field strongest whereby the plates are closest? Why have to it be?

Figure 8.

(a) sketch the electrical field present in the vicinity the the charged insulator in number 9. Note its non-uniform fee distribution. (b) map out equipotential lines neighboring the insulator. Show the direction of enhancing potential.

Figure 9. A charged insulating rod together as might be supplied in a class demonstration.

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The naturally developing charge ~ above the soil on a well day out in the open country is –1.00 nC/m2. (a) What is the electrical field loved one to ground at a elevation of 3.00 m? (b) calculate the electric potential at this height. (c) Sketch electric field and equipotential lines for this scenario.The lesser electric ray (Narcine bancroftii) maintains an tremendous charge top top its head and also a charge equal in magnitude yet opposite in authorize on that is tail (Figure 10). (a) sketch the equipotential lines surrounding the ray. (b) map out the equipotentials as soon as the ray is close to a ship with a conducting surface. (c) How can this charge circulation be of usage to the ray?

Figure 10. Lesser electrical ray (Narcine bancroftii) (credit: national Oceanic and also Atmospheric Administration, NOAA’s Fisheries Collection).

## Glossary

equipotential line: a line along which the electrical potential is constant

grounding: fixing a conductor in ~ zero volts by connecting it to the planet or ground