Summary

Exordinary equipotential lines and equipotential surfaces.Describe the activity of grounding an electrical appliance.Compare electrical area and equipotential lines.

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We deserve to recurrent electrical potentials (voltages) pictorially, simply as we attracted images to show electrical fields. Of course, the 2 are connected. Consider Figure 1, which mirrors an isolated positive suggest charge and also its electrical field lines. Electric area lines radiate out from a positive charge and terminate on negative charges. While we usage blue arrows to recurrent the magnitude and direction of the electric area, we usage green lines to recurrent areas wbelow the electric potential is continuous. These are called equipotential lines in 2 dimensions, or equipotential surfaces in three dimensions. The term equipotential is additionally offered as a noun, referring to an equipotential line or surconfront. The potential for a allude charge is the exact same anywhere on an imaginary spbelow of radius oldsymbolr neighboring the charge. This is true considering that the potential for a allude charge is provided by oldsymbolV = kQ/r and, for this reason, has actually the very same worth at any allude that is a provided distance oldsymbolr from the charge. An equipotential spbelow is a circle in the two-dimensional check out of Figure 1. Since the electric field lines point radially ameans from the charge, they are perpendicular to the equipotential lines.

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Figure 1. An isolated allude charge Q via its electric field lines in blue and also equipotential lines in green. The potential is the very same alengthy each equipotential line, interpretation that no job-related is compelled to move a charge everywhere alengthy one of those lines. Work is required to relocate a charge from one equipotential line to an additional. Equipotential lines are perpendicular to electric field lines in eincredibly case.

It is vital to note that equipotential lines are constantly perpendicular to electrical area lines. No occupational is compelled to move a charge alengthy an equipotential, since oldsymbolDelta V = 0. Thus the work is


oldsymbolW = - Delta ; extbfPE = -q Delta V = 0.

Work is zero if force is perpendicular to movement. Force is in the very same direction as oldsymbolE, so that movement alengthy an equipotential need to be perpendicular to oldsymbolE. More specifically, work-related is pertained to the electric field by


oldsymbolW = Fd ; extbfcos heta = qEd ; extbfcos heta = 0.

Keep in mind that in the over equation, oldsymbolE and oldsymbolF signify the magnitudes of the electric field strength and also force, respectively. Neither oldsymbolq nor extbfE nor oldsymbold is zero, and so oldsymbol extbfcos heta have to be 0, definition oldsymbol heta should be oldsymbol90 ^circ. In other words, movement along an equipotential is perpendicular to oldsymbolE.

One of the rules for static electrical areas and conductors is that the electrical field need to be perpendicular to the surconfront of any conductor. This suggests that a conductor is an equipotential surface in static situations. Tbelow have the right to be no voltage distinction throughout the surconfront of a conductor, or charges will flow. One of the supplies of this fact is that a conductor deserve to be resolved at zero volts by connecting it to the earth through a great conductor—a procedure dubbed grounding. Grounding have the right to be a helpful security tool. For instance, grounding the steel situation of an electric appliance ensures that it is at zero volts relative to the earth.


Grounding

A conductor deserve to be solved at zero volts by connecting it to the earth with a great conductor—a procedure called grounding.


Due to the fact that a conductor is an equipotential, it have the right to relocation any type of equipotential surconfront. For instance, in Figure 1 a charged spherical conductor deserve to relocation the allude charge, and also the electrical area and potential surencounters external of it will certainly be unreadjusted, confirming the contention that a spherical charge distribution is tantamount to a suggest charge at its facility.

Figure 2 reflects the electric area and equipotential lines for 2 equal and also oppowebsite charges. Given the electric field lines, the equipotential lines have the right to be drawn simply by making them perpendicular to the electric field lines. Conversely, offered the equipotential lines, as in Figure 3(a), the electric field lines have the right to be attracted by making them perpendicular to the equipotentials, as in Figure 3(b).

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Figure 2. The electrical field lines and also equipotential lines for two equal however oppowebsite charges. The equipotential lines can be drawn by making them perpendicular to the electric field lines, if those are well-known. Keep in mind that the potential is greatest (the majority of positive) near the positive charge and leastern (the majority of negative) close to the negative charge.
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Figure 3. (a) These equipotential lines could be measured via a voltmeter in a laboratory experiment. (b) The equivalent electrical area lines are uncovered by drawing them perpendicular to the equipotentials. Note that these fields are consistent with two equal negative charges

One of the a lot of important instances is that of the acquainted parallel conducting plates shown in Figure 4. Between the plates, the equipotentials are evenly spaced and parallel. The exact same area can be kept by placing conducting plates at the equipotential lines at the potentials displayed.

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Figure 4. The electrical area and also equipotential lines between 2 steel plates.

An important application of electric fields and also equipotential lines requires the heart. The heart counts on electric signals to keep its rhythm. The activity of electric signals causes the chambers of the heart to contract and relax. When a perboy has a heart strike, the motion of these electric signals may be disturbed. An fabricated pacemaker and also a defibrillator have the right to be offered to initiate the rhythm of electrical signals. The equipotential lines around the heart, the thoracic area, and the axis of the heart are beneficial ways of surveillance the framework and also functions of the heart. An electrocardiogram (ECG) actions the little electric signals being produced during the task of the heart. More about the relationship in between electrical fields and also the heart is disputed in Chapter 19.7 Energy Stored in Capacitors.


PhET Explorations: Charges and Fields

Move allude charges approximately on the playing area and then view the electric field, voltages, equipotential lines, and more. It’s vibrant, it’s dynamic, it’s complimentary.

 
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Figure 5. Charges and also Fields
Section SummaryAn equipotential line is a line along which the electrical potential is consistent.An equipotential surface is a three-dimensional version of equipotential lines.Equipotential lines are constantly perpendicular to electric field lines.The process whereby a conductor deserve to be solved at zero volts by connecting it to the earth through an excellent conductor is referred to as grounding.

Conceptual Questions

1: What is an equipotential line? What is an equipotential surface?

2: Exsimple in your own words why equipotential lines and surfaces need to be perpendicular to electric area lines.

3: Can various equipotential lines cross? Exsimple.


Problems & Exercises

1: (a) Lay out the equipotential lines close to a suggest charge + oldsymbolq. Indicate the direction of increasing potential. (b) Do the very same for a allude charge oldsymbol-3 ; q.

2: Sketch the equipotential lines for the two equal positive charges shown in Figure 6. Indicate the direction of increasing potential.

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Figure 6. The electrical field near 2 equal positive charges is directed ameans from each of the charges.

3: Figure 7 shows the electrical field lines near two charges oldsymbolq_1 and also oldsymbolq_2, the first having a magnitude four times that of the second. Sketch the equipotential lines for these 2 charges, and show the direction of increasing potential.

4: Lay out the equipotential lines a lengthy distance from the charges presented in Figure 7. Indicate the direction of enhancing potential.

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Figure 7. The electric field close to two charges.

5: Sketch the equipotential lines in the vicinity of two oppowebsite charges, wbelow the negative charge is three times as great in magnitude as the positive. See Figure 7 for a comparable situation. Indicate the direction of boosting potential.

6: Map out the equipotential lines in the vicinity of the negatively charged conductor in Figure 8. How will certainly these equipotentials look a lengthy distance from the object?

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Figure 8. A negatively charged conductor.

7: Lay out the equipotential lines surrounding the 2 conducting plates presented in Figure 9, given the peak plate is positive and also the bottom plate has an equal amount of negative charge. Be particular to indicate the distribution of charge on the plates. Is the field strongest where the plates are closest? Why must it be?

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Figure 9.

8: (a) Map out the electrical field lines in the vicinity of the charged insulator in Figure 10. Keep in mind its non-unidevelop charge distribution. (b) Lay out equipotential lines neighboring the insulator. Indicate the direction of raising potential.

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Figure 10. A charged insulating rod such as might be offered in a classroom demonstration.

9: The naturally arising charge on the ground on a fine day out in the open up country is oldsymbol-1.00 ; extbfnC / extbfm^2. (a) What is the electric field loved one to ground at a height of 3.00 m? (b) Calculate the electrical potential at this elevation. (c) Sketch electrical area and equipotential lines for this scenario.

10: The lesser electrical ray (Narcine bancroftii) maintains an remarkable charge on its head and also a charge equal in magnitude however oppowebsite in authorize on its tail (Figure 11). (a) Map out the equipotential lines bordering the ray. (b) Sketch the equipotentials once the ray is near a ship with a conducting surchallenge. (c) How could this charge distribution be of use to the ray?

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Figure 11.

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

Glossary

equipotential linea line along which the electrical potential is constantgroundingresolving a conductor at zero volts by connecting it to the earth or ground