You are watching: Why must electric field lines be perpendicular
We deserve to reexisting electric potentials (voltages) pictorially, just as we attracted images to show electrical areas. Of course, the 2 are connected. Consider Figure 1, which mirrors an isolated positive allude charge and its electrical area lines. Electric area lines radiate out from a positive charge and also terminate on negative charges. While we use blue arrows to reexisting the magnitude and direction of the electrical field, we usage green lines to represent places where the electrical potential is constant. 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 surface. The potential for a allude charge is the same almost everywhere on an imaginary sphere of radius r neighboring the charge. This is true given that the potential for a suggest charge is offered by
Figure 1. An isolated allude charge Q via its electric area lines in blue and also equipotential lines in green. The potential is the very same along each equipotential line, interpretation that no work-related is required to relocate a charge almost everywhere along one of those lines. Work is essential to move a charge from one equipotential line to one more. Equipotential lines are perpendicular to electric field lines in eextremely case.
It is crucial to note that equipotential lines are constantly perpendicular to electric field lines. No work-related is required to move a charge along an equipotential, given that ΔV = 0. Therefore the occupational is
W = −ΔPE = −qΔV = 0.
Work is zero if pressure is perpendicular to movement. Force is in the very same direction as E, so that movement along an equipotential have to be perpendicular to E. More specifically, occupational is related to the electrical field by
W = Fd cos θ = qEd cos θ = 0.
Keep in mind that in the above equation, E and also F signify the magnitudes of the electrical area toughness and force, respectively. Neither q nor E nor d is zero, and so cos θ have to be 0, interpretation θ should be 90º. In various other words, motion along an equipotential is perpendicular to E.
One of the rules for static electric areas and conductors is that the electric area must be perpendicular to the surchallenge of any type of conductor. This indicates that a conductor is an equipotential surconfront in static situations. Tright here have the right to be no voltage distinction across the surchallenge of a conductor, or charges will circulation. One of the uses of this reality is that a conductor can be resolved at zero volts by connecting it to the earth with a good conductor—a procedure called grounding. Grounding can be a useful safety and security tool. For instance, grounding the metal situation 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 dubbed grounding.
Since a conductor is an equipotential, it deserve to replace any kind of equipotential surconfront. For instance, in Figure 1 a charged spherical conductor can replace the allude charge, and also the electric field and potential surfaces exterior of it will certainly be unadjusted, confirming the contention that a spherical charge distribution is identical to a point charge at its facility.
Figure 2 shows the electric area and also equipotential lines for 2 equal and opposite charges. Given the electrical area lines, the equipotential lines deserve to be attracted simply by making them perpendicular to the electrical field lines. Conversely, offered the equipotential lines, as in Figure 3a, the electric field lines deserve to be drawn by making them perpendicular to the equipotentials, as in Figure 3b.
Figure 2. The electrical area lines and equipotential lines for two equal however opposite charges. The equipotential lines deserve to be attracted by making them perpendicular to the electrical area lines, if those are known. Note that the potential is best (most positive) close to the positive charge and leastern (the majority of negative) near the negative charge.
Figure 3. (a) These equipotential lines could be measured via a voltmeter in a laboratory experiment. (b) The corresponding electric field lines are uncovered by illustration them perpendicular to the equipotentials. Keep in mind that these fields are continuous with two equal negative charges.
Figure 4. The electrical field and also equipotential lines between two steel plates.
One of the a lot of vital cases 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 could be maintained by placing conducting plates at the equipotential lines at the potentials presented.
An vital application of electric areas and equipotential lines entails the heart. The heart relies on electrical signals to maintain its rhythm. The activity of electric signals reasons the chambers of the heart to contract and also relax. When a perkid has a heart strike, the activity of these electric signals might be disturbed. An synthetic pacemaker and also a defibrillator have the right to be offered to initiate the rhythm of electric signals. The equipotential lines approximately the heart, the thoracic area, and the axis of the heart are valuable means of monitoring the structure and also attributes of the heart. An electrocardiogram (ECG) steps the small electrical signals being created during the task of the heart. More around the connection in between electric fields and the heart is questioned in Energy Stored in Capacitors.
PhET Explorations: Charges and Fields
Move allude charges roughly on the playing area and also then watch the electrical field, voltperiods, equipotential lines, and more. It’s colorful, it’s dynamic, it’s free.
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Section SummaryAn equipotential line is a line alengthy which the electric potential is constant.An equipotential surconfront is a three-dimensional variation of equipotential lines.Equipotential lines are constantly perpendicular to electric field lines.The process whereby a conductor deserve to be fixed at zero volts by connecting it to the earth through an excellent conductor is called grounding.
Conceptual QuestionsWhat is an equipotential line? What is an equipotential surface?Explain in your own words why equipotential lines and also surfaces should be perpendicular to electrical area lines.Can different equipotential lines cross? Explain.
Problems & Exercises(a) Sketch the equipotential lines close to a suggest charge +q. Indicate the direction of enhancing potential. (b) Do the same for a point charge −3q.Map out the equipotential lines for the two equal positive charges shown in Figure 5. Indicate the direction of raising potential.
Figure 5. The electrical area near 2 equal positive charges is directed ameans from each of the charges.
Figure 6 mirrors the electrical field lines close to two charges q1 and also q2, the first having actually a magnitude 4 times that of the second. Sketch the equipotential lines for these 2 charges, and also indicate the direction of raising potential.Lay out the equipotential lines a lengthy distance from the charges shown in Figure 6. Indicate the direction of raising potential.
Figure 6. The electric field close to 2 charges.
Map out the equipotential lines in the vicinity of two oppowebsite charges, where the negative charge is 3 times as great in magnitude as the positive. See Figure 6 for a similar situation. Indicate the direction of increasing potential.Lay out the equipotential lines in the vicinity of the negatively charged conductor in Figure 7. How will certainly these equipotentials look a lengthy distance from the object?
Figure 7. A negatively charged conductor.
Map out the equipotential lines surrounding the two conducting plates displayed in Figure 8, provided the optimal plate is positive and also the bottom plate has an equal amount of negative charge. Be particular to suggest the distribution of charge on the plates. Is the field strongest wright here the plates are closest? Why should it be?
(a) Sketch the electric area lines in the vicinity of the charged insulator in Figure 9. Keep in mind its non-unidevelop charge distribution. (b) Lay out equipotential lines surrounding the insulator. Indicate the direction of enhancing potential.
Figure 9. A charged insulating rod such as could be supplied in a classroom demonstration.
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The naturally occurring 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 family member to ground at a height of 3.00 m? (b) Calculate the electric potential at this height. (c) Map out electric area and also equipotential lines for this scenario.The lesser electrical ray (Narcine bancroftii) maintains an incredible charge on its head and also a charge equal in magnitude however oppowebsite in sign on its tail (Figure 10). (a) Sketch the equipotential lines bordering the ray. (b) Lay out the equipotentials when the ray is near a ship via 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).
equipotential line: a line alengthy which the electric potential is constant
grounding: fixing a conductor at zero volts by connecting it to the earth or ground