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

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We have the right to represent electric potentials (voltages) pictorially, just as we attracted pictures to illustrate electric fields. Of course, the two space related. Think about Figure 1, which reflects an diverted positive point charge and also its electrical field lines. Electrical field lines radiate the end from a confident charge and also terminate on an adverse charges. When we use blue arrows to represent the magnitude and direction of the electrical field, us use green lines come represent areas where the electric potential is constant. This are called equipotential lines in two dimensions, or equipotential surfaces in three dimensions. The ax equipotential is also used as a noun, referring to an equipotential line or surface. The potential because that a allude charge is the same anywhere on an imaginary sphere of radius r bordering the charge. This is true because the potential for a suggest charge is provided by V=frackQr\ and, thus, has actually the same value in ~ any point that is a offered distance r indigenous the charge. An equipotential sphere is a one in the two-dimensional view of figure 1. Because the electrical field lines allude radially away from the charge, they room perpendicular to the equipotential lines.


Figure 1. One isolated allude charge Q with its electrical field lines in blue and also equipotential currently in green. The potential is the same along every equipotential line, meaning that no occupational is compelled to relocate a charge almost everywhere along one of those lines. Job-related is needed to relocate a charge from one equipotential heat to another. Equipotential lines space perpendicular to electric field present in every case.


It is crucial to note that equipotential lines are constantly perpendicular to electrical field lines. No work-related is forced to relocate a charge follow me an equipotential, due to the fact that ΔV = 0. Hence the work is

W = −ΔPE = −qΔV = 0.

Work is zero if pressure is perpendicular come motion. Pressure is in the very same direction as E, for this reason that movement along one equipotential must be perpendicular to E. Much more precisely, occupational is regarded the electrical field by

WFd cos θqEd cos θ = 0.

Note that in the above equation, E and F represent the magnitudes of the electrical field strength and force, respectively. No q nor E nor d is zero, and also so cos θ must be 0, definition θ need to be 90º. In other words, motion along an equipotential is perpendicular to E.

One of the rules for static electrical fields and conductors is the the electrical field must be perpendicular come the surface of any conductor. This means that a conductor is one equipotential surface ar in revolution situations. There have the right to be no voltage difference across the surface of a conductor, or charges will flow. Among the uses of this truth is that a conductor have the right to be fixed at zero volts through connecting it come the earth with a good conductor—a process called grounding. Grounding deserve to be a valuable safety tool. Because that example, grounding the metal situation of an electrical appliance ensures that it is at zero volts loved one to the earth.


Grounding

A conductor have the right to be solved at zero volts by connecting it come the earth with a good conductor—a procedure called grounding.


Because a conductor is one equipotential, it deserve to replace any equipotential surface. For example, in number 1 a fee spherical conductor can replace the suggest charge, and the electric field and potential surfaces exterior of it will be unchanged, confirming the contention the a spherical charge circulation is tantamount to a point charge at its center.

Figure 2 shows the electric field and equipotential lines for two equal and opposite charges. Provided the electric field lines, the equipotential lines have the right to be drawn simply by making castle perpendicular to the electric field lines. Conversely, provided the equipotential lines, as in figure 3a, the electric field lines can be drawn by making castle perpendicular come the equipotentials, together in figure 3b.


Figure 2. The electric field lines and also equipotential present for two equal yet opposite charges. The equipotential lines can be attracted by making castle perpendicular to the electrical field lines, if those room known. Keep in mind that the potential is best (most positive) close to the optimistic charge and also least (most negative) near the an unfavorable charge.


Figure 3. (a) these equipotential lines can be measured with a voltmeter in a activities experiment. (b) The matching electric field lines are found by drawing them perpendicular come the equipotentials. Keep in mind that these fields are consistent with 2 equal an adverse charges.


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


One that the many important instances is the of the acquainted parallel conducting plates presented in number 4. Between the plates, the equipotentials space evenly spaced and parallel. The exact same field can be kept by put conducting plates in ~ the equipotential lines in ~ the potentials shown.

An important application of electrical fields and also equipotential lines entails the heart. The heart relies on electrical signals to maintain its rhythm. The motion of electric signals reasons the chambers of the heart to contract and relax. When a person has actually a love attack, the movement of these electrical signals may be disturbed. An fabricated pacemaker and a defibrillator have the right to be used to begin the valuation of electric signals. The equipotential lines approximately the heart, the thoracic region, and the axis of the heart are useful ways of surveillance the structure and also functions of the heart. One electrocardiogram (ECG) procedures the little electric signals gift generated throughout the task of the heart. More about the relationship in between electric fields and also the love is debated in energy Stored in Capacitors.


PhET Explorations: Charges and Fields

Move point charges around on the playing field and then watch the electric field, voltages, equipotential lines, and more. It’s colorful, it’s dynamic, it’s free.


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Click to operation the simulation.


Section Summary

An equipotential line is a line along which the electrical potential is constant.An equipotential surface is a three-dimensional variation of equipotential lines.Equipotential currently are constantly perpendicular to electric field lines.The procedure by i m sorry a conductor have the right to be addressed at zero volts through connecting it to the planet with a good conductor is called grounding.

Conceptual Questions

What is one equipotential line? What is one equipotential surface?Explain in your own words why equipotential lines and also surfaces need to be perpendicular to electrical field lines.Can different equipotential present cross? Explain.

Problems & Exercises

(a) map out the equipotential lines close to a suggest charge +q. Suggest the direction of enhancing potential. (b) perform the same for a allude charge −3q.Sketch the equipotential lines because that the 2 equal hopeful charges shown in figure 5. Indicate the direction of boosting potential.

Figure 5. The electric field near two equal confident charges is directed far from every of the charges.


Figure 6 reflects the electrical field lines close to two charges q1 and also q2, the an initial having a magnitude four times the of the second. Map out the equipotential lines for these 2 charges, and indicate the direction of boosting potential.Sketch the equipotential currently a lengthy distance native the charges shown in figure 6. Suggest the direction of increasing potential.

Figure 6. The electrical field close to two charges.


Sketch the equipotential lines in the vicinity of 2 opposite charges, whereby the an unfavorable charge is three times as great in magnitude as the positive. See number 6 for a similar situation. Suggest the direction of boosting potential.Sketch the equipotential present in the vicinity of the negatively charged conductor in number 7. How will these equipotentials look a long distance from the object?

Figure 7. A negatively fee conductor.


Sketch the equipotential lines neighboring the 2 conducting plates presented in figure 8, provided the optimal plate is positive and the bottom plate has an equal amount of an adverse charge. Be particular to indicate the circulation of charge on the plates. Is the field strongest whereby the plates space closest? Why need to it be?

Figure 8.


(a) map out the electrical field present in the vicinity of the charged insulator in figure 9. Note its non-uniform fee distribution. (b) lay out equipotential lines neighboring the insulator. Indicate the direction of raising potential.

Figure 9. A fee insulating rod together as could be offered in a great demonstration.

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The naturally emerging charge ~ above the ground on a fine day the end in the open nation is –1.00 nC/m2. (a) What is the electrical field family member to ground in ~ a height of 3.00 m? (b) calculate the electrical potential at this height. (c) Sketch electric field and equipotential lines because that this scenario.The lesser electrical ray (Narcine bancroftii) maintains an tremendous charge on its head and also a fee equal in magnitude however opposite in authorize on that tail (Figure 10). (a) sketch the equipotential lines bordering the ray. (b) map out the equipotentials as soon as the ray is near a ship v a conducting surface. (c) How could this charge distribution be of use 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 follow me which the electrical potential is constant

grounding: fixing a conductor at zero volts through connecting it come the earth or ground