You are watching: Why are equipotential lines perpendicular to field lines
We deserve to recurrent electric potentials (voltages) pictorially, just as we drew pictures to show electric areas. Of course, the two are connected. Consider Figure 1, which shows an isolated positive suggest charge and its electrical area lines. Electric field lines radiate out from a positive charge and terminate on negative charges. While we usage blue arrows to represent the magnitude and direction of the electrical area, we use green lines to reexisting places where the electrical potential is consistent. These are dubbed equipotential lines in 2 dimensions, or equipotential surfaces in 3 dimensions. The term equipotential is also supplied as a noun, referring to an equipotential line or surconfront. The potential for a allude charge is the exact same all over on an imaginary sphere of radius r neighboring the charge. This is true since the potential for a allude charge is given by
Figure 1. An isolated point charge Q via its electrical field lines in blue and equipotential lines in green. The potential is the very same alengthy each equipotential line, meaning that no occupational is forced to move a charge everywhere along one of those lines. Work is essential to move a charge from one equipotential line to an additional. Equipotential lines are perpendicular to electrical field lines in every situation.
It is vital to note that equipotential lines are constantly perpendicular to electrical field lines. No job-related is required to relocate a charge along an equipotential, considering that ΔV = 0. Thus the job-related is
W = −ΔPE = −qΔV = 0.
Work is zero if force is perpendicular to motion. Force is in the exact same direction as E, so that motion along an equipotential should be perpendicular to E. More exactly, work-related is pertained to the electrical area by
W = Fd cos θ = qEd cos θ = 0.
Note that in the over equation, E and also F symbolize the magnitudes of the electrical field stamina and also force, respectively. Neither q nor E nor d is zero, and also so cos θ must be 0, interpretation θ must be 90º. In various other words, motion alengthy an equipotential is perpendicular to E.
One of the rules for static electrical areas and also conductors is that the electrical field need to be perpendicular to the surchallenge of any type of conductor. This implies that a conductor is an equipotential surconfront in static situations. Tbelow have the right to be no voltage distinction across the surconfront of a conductor, or charges will certainly flow. One of the provides of this truth is that a conductor can be addressed at zero volts by connecting it to the earth through a good conductor—a procedure dubbed grounding. Grounding have the right to be a useful security tool. For instance, grounding the steel instance of an electric appliance ensures that it is at zero volts loved one to the earth.
A conductor can be fixed at zero volts by connecting it to the earth with a great conductor—a procedure referred to as grounding.
Because a conductor is an equipotential, it can relocation any equipotential surface. For example, in Figure 1 a charged spherical conductor can rearea the point charge, and also the electrical field and potential surdeals with external of it will certainly be unreadjusted, confirming the contention that a spherical charge circulation is indistinguishable to a point charge at its facility.
Figure 2 shows the electrical field and also equipotential lines for 2 equal and also oppowebsite charges. Given the electric area lines, the equipotential lines can be drawn sindicate by making them perpendicular to the electric area lines. Conversely, given the equipotential lines, as in Figure 3a, the electrical field lines deserve to be attracted by making them perpendicular to the equipotentials, as in Figure 3b.
Figure 2. The electrical field lines and also equipotential lines for two equal yet opposite charges. The equipotential lines have the right to be drawn by making them perpendicular to the electric field lines, if those are known. Note that the potential is best (many positive) near the positive charge and also least (a lot of negative) near the negative charge.
Figure 3. (a) These equipotential lines might be measured with a voltmeter in a laboratory experiment. (b) The equivalent electrical area lines are discovered by drawing them perpendicular to the equipotentials. Keep in mind that these areas are consistent through two equal negative charges.
Figure 4. The electric area and equipotential lines between two metal plates.
One of the many vital instances is that of the familiar parallel conducting plates displayed in Figure 4. Between the plates, the equipotentials are evenly spaced and parallel. The very same field might be maintained by placing conducting plates at the equipotential lines at the potentials shown.
An essential application of electrical areas and also equipotential lines entails the heart. The heart relies on electric signals to maintain its rhythm. The motion of electrical signals reasons the chambers of the heart to contract and also relax. When a person has a heart attack, the motion of these electrical signals might be disturbed. An artificial pacemaker and also a defibrillator can be supplied to initiate the rhythm of electric signals. The equipotential lines around the heart, the thoracic area, and also the axis of the heart are useful ways of surveillance the framework and features of the heart. An electrocardiogram (ECG) actions the small electric signals being generated in the time of the task of the heart. More about the connection between electrical areas and the heart is disputed in Energy Stored in Capacitors.
PhET Explorations: Charges and Fields
Move suggest charges around on the playing field and then check out the electrical field, volteras, equipotential lines, and also more. It’s colorful, it’s dynamic, it’s complimentary.
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Section SummaryAn equipotential line is a line along which the electrical potential is constant.An equipotential surconfront is a three-dimensional version of equipotential lines.Equipotential lines are always perpendicular to electrical field lines.The process whereby a conductor have the right to be solved at zero volts by connecting it to the earth with an excellent conductor is dubbed grounding.
Conceptual QuestionsWhat is an equipotential line? What is an equipotential surface?Explain in your very own words why equipotential lines and surencounters have to be perpendicular to electrical field lines.Can various equipotential lines cross? Exsimple.
Problems & Exercises(a) Lay out the equipotential lines close to a allude charge +q. Indicate the direction of raising potential. (b) Do the exact same for a allude charge −3q.Sketch the equipotential lines for the 2 equal positive charges presented in Figure 5. Indicate the direction of boosting potential.
Figure 5. The electrical field near two equal positive charges is directed ameans from each of the charges.
Figure 6 reflects the electric field lines close to 2 charges q1 and q2, the initially having actually a magnitude four times that of the second. Lay out the equipotential lines for these 2 charges, and also suggest the direction of boosting potential.Sketch the equipotential lines a lengthy distance from the charges shown in Figure 6. Indicate the direction of increasing potential.
Figure 6. The electrical field near 2 charges.
Map out the equipotential lines in the vicinity of 2 oppowebsite charges, wright here the negative charge is 3 times as good in magnitude as the positive. See Figure 6 for a similar case. Indicate the direction of boosting potential.Lay out the equipotential lines in the vicinity of the negatively charged conductor in Figure 7. How will certainly these equipotentials look a long distance from the object?
Figure 7. A negatively charged conductor.
Sketch the equipotential lines bordering the two conducting plates shown in Figure 8, given the height plate is positive and the bottom plate has actually an equal amount of negative charge. Be specific to show the circulation of charge on the plates. Is the area strongest wbelow the plates are closest? Why must it be?
(a) Sketch the electric area lines in the vicinity of the charged insulator in Figure 9. Note its non-unicreate charge distribution. (b) Sketch equipotential lines neighboring the insulator. Indicate the direction of raising potential.
Figure 9. A charged insulating rod such as could be offered in a classroom demonstration.
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The normally arising charge on the ground on a fine day out in the open up country is –1.00 nC/m2. (a) What is the electric field loved one to ground at a elevation of 3.00 m? (b) Calculate the electrical potential at this elevation. (c) Sketch electric area and equipotential lines for this scenario.The lesser electric ray (Narcine bancroftii) maintains an tremendous charge on its head and a charge equal in magnitude but oppowebsite in authorize on its tail (Figure 10). (a) Lay out the equipotential lines surrounding the ray. (b) Lay out the equipotentials once the ray is near a ship through a conducting surface. (c) How might this charge circulation be of use to the ray?
Figure 10. Lesser electric ray (Narcine bancroftii) (credit: National Oceanic and Atmospheric Administration, NOAA’s Fisheries Collection).
equipotential line: a line along which the electrical potential is constant
grounding: fixing a conductor at zero volts by connecting it to the earth or ground