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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.
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. Note that the potential is greatest (most positive) near the positive charge and least (most negative) near the negative charge.
Figure (a) shows two circles, called equipotential lines, along which the potential is negative ten volts. A dumbbell-shaped surface encloses the two circles and is labeled negative five volts. This surface is surrounded by another surface labeled negative two volts. Figure (b) shows the same equipotential lines, each set with a negative charge at its center. Blue electric field lines curve toward the negative charges from all directions.
(a) These equipotential lines might be measured with a voltmeter in a laboratory experiment. (b) The corresponding electric field lines are found by drawing them perpendicular to the equipotentials. Note that these fields are consistent with two equal negative charges.

One of the most important cases is that of the familiar parallel conducting plates shown in [link] . 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.

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

An important application of electric 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 heart to contract and relax. When a person has a heart attack, the movement of these electrical 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 being generated during the activity of the heart.

Section summary

  • An equipotential line is a line along which the electric 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 fixed at zero volts by connecting it to the earth with a good conductor is called grounding.

Conceptual questions

What is an equipotential line? What is an equipotential surface?

Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.

Can different equipotential lines cross? Explain.

Problems&Exercises

(a) Sketch the equipotential lines near a point charge + q size 12{q} {} . Indicate the direction of increasing potential. (b) Do the same for a point charge 3 q size 12{ - 3 "." "00"q} {} .

Sketch the equipotential lines for the two equal positive charges shown in [link] . Indicate the direction of increasing potential.

The figure shows two positive charges with electric field lines curving away from each of the charges.
The electric field near two equal positive charges is directed away from each of the charges.

[link] shows the electric field lines near two charges q 1 size 12{q rSub { size 8{1} } } {} and q 2 size 12{q rSub { size 8{2} } } {} , the first 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 [link] . Indicate the direction of increasing potential.

The figure shows two nearby charges, q one and q two. Electric field lines move away from q two and toward q one.
The electric field near two charges.

Sketch the equipotential lines in the vicinity of two opposite charges, where the negative charge is three times as great in magnitude as the positive. See [link] for a similar situation. Indicate the direction of increasing potential.

Sketch the equipotential lines in the vicinity of the negatively charged conductor in [link] . How will these equipotentials look a long distance from the object?

The figure shows a negatively charged conductor that is shaped like an oblong.
A negatively charged conductor.

Sketch the equipotential lines surrounding the two conducting plates shown in [link] , given the top plate is positive and the bottom plate has an equal amount of negative charge. Be certain to indicate the distribution of charge on the plates. Is the field strongest where the plates are closest? Why should it be?

Two conducting plates with the top one positively charged and the bottom one with an equal amount of negative charge.

(a) Sketch the electric field lines in the vicinity of the charged insulator in [link] . Note its non-uniform charge distribution. (b) Sketch equipotential lines surrounding the insulator. Indicate the direction of increasing potential.

A rod marked with many plus symbols to indicate electric charge. Most of the pluses are concentrated near one end of the rod. A few are in the middle and one is at the other end.
A charged insulating rod such as might be used in a classroom demonstration.

The naturally occurring charge on the ground on a fine day out in the open country is –1 . 00 nC/m 2 size 12{"Š1" "." "00" "nC/m" rSup { size 8{2} } } {} . (a) What is the electric field relative to ground at a height of 3.00 m? (b) Calculate the electric 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 charge equal in magnitude but opposite in sign on its tail ( [link] ). (a) Sketch the equipotential lines surrounding the ray. (b) Sketch the equipotentials when the ray is near a ship with a conducting surface. (c) How could this charge distribution be of use to the ray?

The figure shows a photo of a Narcine bancroftii, an electric ray that maintains a strong charge on its head and a charge equal in magnitude but opposite in sign on its tail.
Lesser electric ray ( Narcine bancroftii ) (credit: National Oceanic and Atmospheric Administration, NOAA's Fisheries Collection).

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
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salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
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Abhi
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ninjadapaul
20/(×-6^2)
Salomon
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I got X =-6
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ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
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ninjadapaul
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Commplementary angles
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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