How To Draw Equipotential Lines Groundwater Map

Learning Objectives

By the end of this department, yous will exist able to:

Explain equipotential lines and equipotential surfaces.
Describe the activity of grounding an electrical appliance.
Compare electrical field and equipotential lines.

Nosotros can represent electrical potentials (voltages) pictorially, just as we drew pictures to illustrate electric fields. Of course, the two are related. Consider Figure i, which shows an isolated positive point charge and its electrical field lines. Electric field lines radiate out from a positive accuse and terminate on negative charges. While we use blueish arrows to represent the magnitude and direction of the electric field, nosotros use green lines to represent places where the electrical potential is constant. These are chosen equipotential lines in two dimensions, or equipotential surfaces in three dimensions. The term equipotential is also used as a noun, referring to an equipotential line or surface. The potential for a betoken charge is the same anywhere on an imaginary sphere of radius r surrounding the charge. This is true since the potential for a point charge is given by [latex]V=\frac{kQ}{r}\\[/latex] and, thus, has the same value at whatever point that is a given distance r from the charge. An equipotential sphere is a circle in the two-dimensional view of Figure i. Since the electrical field lines point radially away from the charge, 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.

Figure 1. An isolated indicate charge Q with its electrical 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 accuse anywhere along one of those lines. Work is needed to move a accuse from one equipotential line to another. Equipotential lines are perpendicular to electric field lines in every case.

It is important to note that equipotential lines are always perpendicular to electric field lines . No work is required to move a accuse along an equipotential, since ΔV = 0. Thus the piece of work is

West = −ΔPE = −qΔFive = 0.

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

Westward =Fd cosθ =qEd cosθ = 0.

Note that in the to a higher place equation, East and F symbolize the magnitudes of the electrical field strength and force, respectively. Neither q nor E nor d is zip, and so cosθ must be 0, meaning θ must exist 90º. In other words, motility along an equipotential is perpendicular to E.

Ane of the rules for static electrical fields and conductors is that the electrical field must be perpendicular to the surface of whatever conductor. This implies that a usher is an equipotential surface in static situations. In that location can exist no voltage difference across the surface of a usher, or charges will menstruation. 1 of the uses of this fact is that a conductor can be fixed at zero volts by connecting information technology to the earth with a skilful conductor—a process called grounding. Grounding can be a useful prophylactic tool. For example, grounding the metal case of an electric appliance ensures that it is at zero volts relative to the world.

Grounding

A usher can be stock-still at zero volts by connecting information technology to the world with a good conductor—a process called grounding.

Because a conductor is an equipotential, it can replace whatsoever equipotential surface. For instance, in Figure ane a charged spherical usher tin can replace the betoken charge, and the electric field and potential surfaces exterior of information technology will be unchanged, confirming the contention that a spherical charge distribution is equivalent to a point charge at its eye.

Figure two shows the electric field and equipotential lines for two equal and reverse charges. Given the electric field lines, the equipotential lines can be drawn just by making them perpendicular to the electric field lines. Conversely, given the equipotential lines, every bit in Figure 3a, the electric field lines can be drawn by making them perpendicular to the equipotentials, equally in Effigy 3b.

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 ii. The electric field lines and equipotential lines for two equal but opposite charges. The equipotential lines can be drawn by making them perpendicular to the electric field lines, if those are known. Notation that the potential is greatest (most positive) near the positive charge and least (nigh negative) virtually the negative charge.

Effigy iii. (a) These equipotential lines might be measured with a voltmeter in a laboratory experiment. (b) The corresponding electric field lines are plant past cartoon them perpendicular to the equipotentials. Note that these fields are consistent with two equal negative charges.

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.

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

1 of the most important cases is that of the familiar parallel conducting plates shown in Figure four. Between the plates, the equipotentials are evenly spaced and parallel. The same field could be maintained by placing conducting plates at the equipotential lines at the potentials shown.

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

PhET Explorations: Charges and Fields

Movement point charges effectually on the playing field and then view the electrical field, voltages, equipotential lines, and more than. Information technology'south colorful, information technology'south dynamic, information technology's costless.

Charges and Fields screenshot.

Click to run the simulation.

Section Summary

An equipotential line is a line along which the electrical potential is constant.
An equipotential surface is a three-dimensional version of equipotential lines.
Equipotential lines are always perpendicular to electric field lines.
The process by which a conductor can be stock-still at aught volts by connecting it to the earth with a good conductor is chosen grounding.

Conceptual Questions

What is an equipotential line? What is an equipotential surface?
Explain in your ain words why equipotential lines and surfaces must be perpendicular to electric field lines.
Can different equipotential lines cross? Explain.

Issues & Exercises

(a) Sketch the equipotential lines near a point charge +q. Indicate the management of increasing potential. (b) Do the aforementioned for a indicate charge −3q.
Sketch the equipotential lines for the two equal positive charges shown in Figure 5. Indicate the direction of increasing potential.

Figure five. The electrical field near two equal positive charges is directed away from each of the charges.
Figure half dozen shows the electrical field lines near ii charges q ₁ and q _ii, the starting time having a magnitude four times that of the second. Sketch the equipotential lines for these two charges, and indicate the direction of increasing potential.
Sketch the equipotential lines a long distance from the charges shown in Effigy 6. Betoken the direction of increasing potential.

Figure 6. The electric field near two charges.
Sketch the equipotential lines in the vicinity of two contrary charges, where the negative charge is three times as nifty in magnitude as the positive. See Figure 6 for a similar situation. Indicate the direction of increasing potential.
Sketch the equipotential lines in the vicinity of the negatively charged conductor in Figure 7. How will these equipotentials expect a long distance from the object?

Figure 7. A negatively charged usher.
Sketch the equipotential lines surrounding the two conducting plates shown in Figure 8, given the acme plate is positive and the lesser plate has an equal amount of negative accuse. Be certain to indicate the distribution of charge on the plates. Is the field strongest where the plates are closest? Why should it exist?

Figure 8.
(a) Sketch the electric field lines in the vicinity of the charged insulator in Effigy 9. Note its not-uniform charge distribution. (b) Sketch equipotential lines surrounding the insulator. Betoken the management of increasing potential.

Effigy 9. A charged insulating rod such equally might exist used in a classroom demonstration.
The naturally occurring charge on the ground on a fine day out in the open country is –i.00 nC/m². (a) What is the electric field relative to basis at a elevation of 3.00 g? (b) Calculate the electrical potential at this height. (c) Sketch electric field and equipotential lines for this scenario.
The lesser electric ray (Narcine bancroftii) maintains an incredible charge on its head and a accuse equal in magnitude but reverse in sign on its tail (Figure 10). (a) Sketch the equipotential lines surrounding the ray. (b) Sketch the equipotentials when the ray is well-nigh a ship with a conducting surface. (c) How could this charge distribution exist of use to the ray?

Figure 10. Bottom electric ray (Narcine bancroftii) (credit: National Oceanic and Atmospheric Assistants, NOAA'south Fisheries Collection).