Text bookPhysics; John D. Cutnell and Kenneth

W. Johnson; 7th edition; Wiley; 2007.

Electric Potential Energy and the Electric Potential Energy and the Electric PotentialElectric Potential

The upper surface of this car is covered by solar cells. Sunlight penetrates the cells and provides the energy that separates positive and negative charges in the materials from which the cells are made. Thus, each cell develops positive and negative terminals, much like the terminals of a battery and, in effect, converts solar energy into the electric energy that powers the car. Electric potential energy and the related concept of electric potential are the subjects of this chapter. (© AP/Wide World Photos)

The work WAB done by the gravitational force when the ball falls from a height hA to a height hB is:WAB = mghA – mghB =

GPEA - GPEB

The work WAB done by the electric force equals the difference between the electric potential EPE at A and that at B:WAB = EPEA - EPEB

Definition of Electric Potential V:The electric potential V at a given point is the

electric potential energy EPE of a small test charge q0 situated at that point divided by the charge itself:

V = EPE/q0

SI Unit of Electric Potential: joule/coulomb = volt (V)

The potential difference between two points A and B is given by:

Where WAB is the work done by the electric force when a charge q0 moves from A to B.

OR

000 qW

qEPE

qEPEVV ABAB

AB

00 q

WqEPEV AB

If the work done by the electric force as the test charge (q0 = +2.0 x 10-6 C) moves from A to B is WAB = + 5.0 x 10-5 J. (a) Find the value of the difference, (EPE) = EPEB - EPEA, in the electric potential energies of the charge between these points. (b) Determine the potential difference, V = VB - VA, between the points.

Answer:Answer:a)a) (EPE) = EPEB – EPEA= -WAB = - 5.0 x 10-5 Jb)b) V = VB – VA = - 5.0 x 10-5 J/ +2.0 x 10-6 C = -25 V

A particle has a mass of 1.8 x 10-5 kg and a charge of +3.0 x 10-5 C. It is released from rest at point A and accelerates until it reaches point B, as in figure (a). The particle moves on a horizontal straight line and does not rotate. The only forces acting on the particle are the gravitational force and an electrostatic force. The electric potential at A is 25 V greater than that at B; in other words, VA – VB = 25V. What is the translational speed of the particle at point B?

energypotentialElectric

energypotentialElastic

energypotential

nalGravitatio

energykinetic

Rotational

energykinetic

nalTranslatio

EPExkhgmIvmE

222

21

21

21

021

21 22 xkI

BBBAAA EPEhgmvmEPEhgmvm 22

21

21

BBAA EPEvmEPEvm 22

21

21

Since EPEA – EPEB = q0 (VA – VB)

m

EPEEPEvv BAAB

22

m

VVqvv BAAB

02 2

smkg

VCvB /1.9108.1

25100.320 5

52

CapacitorCapacitor consists of two conductors of any shape placed near one another without touching

DielectricDielectric is the electrically insulated material filled in the region between the conductors or plates.

The magnitude q of the charge on each plate of a capacitor is directly proportional to the magnitude V of the potential difference between the plates:

q = C V

where C is the capacitance.

SI Unit of Capacitance: coulomb/volt = farad coulomb/volt = farad (F)(F)

The ability of a capacitor to store charge lies at the heart of the random-access memory (RAM) chips used in computers, where information is stored in the form of the “ones” and “zeros” that comprise binary numbers. A single RAM chip often contains millions of such transistor–capacitor units.

A charged capacitor means that a “one” has been stored, whereas an uncharged capacitor means that a “zero” has been stored.

During a heart attack, the heart produces a rapid, unregulated pattern of beats, a condition known as cardiac fibrillation. Cardiac fibrillation can often be stopped by sending a very fast discharge of electrical energy through the heart. Emergency medical personnel use defibrillators. A paddle is connected to each plate of a large capacitor, and the paddles are placed on the chest near the heart. The capacitor is charged to a potentialdifference of about a thousand volts. The capacitor is then discharged in a few thousandths of a second; the discharge currentpasses through a paddle, the heart, and theother paddle. Within a few seconds, the heartoften returns to its normal beating pattern.

Figure (a) The electric field lines inside an empty capacitor. (b) The electric field produced by the charges on the plates aligns the molecular dipoles within the dielectric end to end. (c) The surface charges on the dielectric reduce the electric field inside the dielectric. The space between the dielectric and the plates is added for clarity. In reality, the dielectric fills the region between the plates.

EE0

The field E0 without the dielectric is greater than the field E inside the dielectric.

Substance Dielectric Constant, κ

Vacuum 1Air 1.000 54

Teflon 2.1Benzene 2.28

Paper (royal gray)

3.3

Ruby mica 5.4Neoprene rubber 6.7Methyl alcohol 33.6

Water 80.4

Where:C is the capacitance. is the dielectric constant. o is the permittivity of free space.A is the area of the plate.d is the distance between the plates.

dAC o

Each key is mounted on one end of a plunger, the other end being attached to a movable metal plate. The movable plate is separated from a fixed plate, the two plates forming a capacitor. When the key is pressed, the movable plate is pushed closer to the fixed plate, and the capacitance increases. Electronic circuitry enables the computer to detect the change in capacitance, thereby recognizing which key has been pressed. The separation of the plates is normally 5.00 x 10-3 m but decreases to 0.150 x 10-3 m when a key is pressed. The plate area is 9.50 x 10-5 m2,and the capacitor is filled with a material whose dielectric constant is 3.50. Determine the change in capacitance that is detected by the computer. Answer:Answer:

pFFC

mmmNC

dAC

6.19106.19

10150.01050.91085.850.3

12

3

2522120

When a capacitor stores charge, it also When a capacitor stores charge, it also stores energy. stores energy.

CqEnergy

VCEnergy

VqEnergy

2

2121

2

2

Conduction of Electrical Signals in Neurons The human nervous system is remarkable for its ability to transmit information in the form of electrical signals. These signals are carried by the nerves, and the concept of concept of electric potential electric potential difference difference plays an important role in the process.

Several important medical diagnostic techniques depend on the fact that the surface of the human body is not an equi-potential surface. Between various points on the body there are small potential differences (approximately 30 – 500 μV), which provide the basis for electrocardiography, electroencephalography, and electroretinography. The potential differences can be traced to the electrical characteristics of muscle cells and nerve cells. In carrying out their biological functions, these cells utilize positively charged sodium and potassium ions and negatively charged chlorine ions that exist within the cells and in the extracellular fluid. As a result of such charged particles, electric fields are generated that extend to the surface of the body and lead to small potential differences.

The figure shows some locations on the body where electrodes are placed to measure potential differences in electrocardiography. The potential difference between two locations changes as the heart beats and forms a repetitive pattern. The recorded pattern of potential difference versus time is called an electrocardiogram, and its shape depends on which pair of points in the picture is used to locate the electrodes. The distinct differences between the healthy(normal) and damaged (abnormal) hearts provide physicians with a valuable diagnostic tool.

In electroencephalography the electrodes are placed at specific locations on the head, and they record the potential differences that characterize brain behavior. The graph of potential difference versus time is known as an electroencephalogram (EEG). The various parts of the patterns in an EEG are often referred to as “waves” or “rhythms.” The drawing shows an example of the main resting rhythm of the brain, the so-called alpha rhythm, and also illustrates the distinct differences that are found between the EEGs generated by healthy (normal) and diseased (abnormal) tissue.

The electrical characteristics of the retina of the eye lead to the potential differences measured in electroretinography. The figure shows a typical electrode placement used to record the pattern of potential difference versus time that occurs when the eye is stimulated by a flash of light. One electrode is mounted on a contact lens, while the other is often placed on the forehead. The recorded pattern is called an electroretinogram (ERG), parts of the pattern being referred to as the “A wave” and the “B wave.” As the graphs show, the ERGs of normal and diseased (abnormal) eyes can differ markedly.

1/2156) Suppose that the electric potential outside a living cell is higher than that inside the cell by 0.070 V. How much work is done by the electric force when a sodium ion (charge = +e) moves from the outside to the inside?

1.1 x 10-20 J

3/2156) Point A is at a potential of +250 V, and point B is at a potential of −150 V. An α-particle is a helium nucleus that contains two protons and two neutrons; the neutrons are electrically neutral. An α-particle starts from rest at A and accelerates toward B. When the α-particle arrives at B, what kinetic energy (in electron volts) does it have?

8.0 x 102 eV

36/2162) An axon is the relatively long tail-like part of a neuron, or nerve cell. The outer surface of the axon membrane (dielectric constant = 5, thickness = 1 x 10-8 m) is charged positively, and the inner portion is charged negatively. Thus, the membrane is a kind of capacitor. Assuming that an axon can be treated like a parallel plate capacitor with a plate area of 5 x 10-6 m2, what is its capacitance?

37/2162) The membrane that surrounds a certain type of living cell has a surface area of 5.0 x 10-9 m2 and a thickness of 1.0 x 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.0. (a) The potential on the outer surface of the membrane is +60.0 mV greater than that on the inside surface. How much charge resides on the outer surface? (b) If the charge in part (a) is due to K+ ions (charge +e), how many such ions are present on the outer surface?

1.3 x 10-12 C, 8.3 x 106

38/2162) What voltage is required to store 7.2 x 10-5 C of charge on the plates of a 6.0 μF capacitor?