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Chapter 1 Review

Key Terms

charging by induction
process by which an electrically charged object brought near a neutral object creates a charge separation in that object

conduction electron
electron that is free to move away from its atomic orbit

material that allows electrons to move separately from their atomic orbits; object with properties that allow charges to move about freely within it

continuous charge distribution
total source charge composed of so large a number of elementary charges that it must be treated as continuous, rather than discrete

SI unit of electric charge

Coulomb force
another term for the electrostatic force

Coulomb’s law
mathematical equation calculating the electrostatic force vector between two charged particles

two equal and opposite charges that are fixed close to each other

dipole moment
property of a dipole; it characterizes the combination of distance between the opposite charges, and the magnitude of the charges

electric charge
physical property of an object that causes it to be attracted toward or repelled from another charged object; each charged object generates and is influenced by a force called an electric force

electric field
physical phenomenon created by a charge; it “transmits” a force between a two charges

electric force
noncontact force observed between electrically charged objects

particle surrounding the nucleus of an atom and carrying the smallest unit of negative charge

electrostatic attraction
phenomenon of two objects with opposite charges attracting each other

electrostatic force
amount and direction of attraction or repulsion between two charged bodies; the assumption is that the source charges remain motionless

electrostatic repulsion
phenomenon of two objects with like charges repelling each other

study of charged objects which are not in motion

field line
smooth, usually curved line that indicates the direction of the electric field

field line density
number of field lines per square meter passing through an imaginary area; its purpose is to indicate the field strength at different points in space

induced dipole
typically an atom, or a spherically symmetric molecule; a dipole created due to opposite forces displacing the positive and negative charges

infinite plane
flat sheet in which the dimensions making up the area are much, much greater than its thickness, and also much, much greater than the distance at which the field is to be calculated; its field is constant

infinite straight wire
straight wire whose length is much, much greater than either of its other dimensions, and also much, much greater than the distance at which the field is to be calculated

material that holds electrons securely within their atomic orbits

atom or molecule with more or fewer electrons than protons

law of conservation of charge
net electric charge of a closed system is constant

linear charge density
amount of charge in an element of a charge distribution that is essentially one-dimensional (the width and height are much, much smaller than its length); its units are

neutral particle in the nucleus of an atom, with (nearly) the same mass as a proton

permanent dipole
typically a molecule; a dipole created by the arrangement of the charged particles from which the dipole is created

permittivity of vacuum
also called the permittivity of free space, and constant describing the strength of the electric force in a vacuum

slight shifting of positive and negative charges to opposite sides of an object

principle of superposition
useful fact that we can simply add up all of the forces due to charges acting on an object

particle in the nucleus of an atom and carrying a positive charge equal in magnitude to the amount of negative charge carried by an electron

static electricity
buildup of electric charge on the surface of an object; the arrangement of the charge remains constant (“static”)

concept that states that the net electric field of multiple source charges is the vector sum of the field of each source charge calculated individually

surface charge density
amount of charge in an element of a two-dimensional charge distribution (the thickness is small); its units are

volume charge density
amount of charge in an element of a three-dimensional charge distribution; its units are

Key Equations

Coulomb’s law
Superposition of electric forces
Electric force due to an electric field
Electric field at point
Field of an infinite wire
Field of an infinite plane
Dipole moment
Torque on dipole in external


Electric Charge

  • There are only two types of charge, which we call positive and negative. Like charges repel, unlike charges attract, and the force between charges decreases with the square of the distance.
  • The vast majority of positive charge in nature is carried by protons, whereas the vast majority of negative charge is carried by electrons. The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton.
  • An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons.
  • The SI unit for charge is the coulomb (), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of this basic charge is
  • Both positive and negative charges exist in neutral objects and can be separated by bringing the two objects into physical contact; rubbing the objects together can remove electrons from the bonds in one object and place them on the other object, increasing the charge separation.
  • For macroscopic objects, negatively charged means an excess of electrons and positively charged means a depletion of electrons.
  • The law of conservation of charge states that the net charge of a closed system is constant.

Conductors, Insulators, and Charging by Induction

  • A conductor is a substance that allows charge to flow freely through its atomic structure.
  • An insulator holds charge fixed in place.
  • Polarization is the separation of positive and negative charges in a neutral object. Polarized objects have their positive and negative charges concentrated in different areas, giving them a charge distribution.

Coulomb’s Law

  • Coulomb’s law gives the magnitude of the force between point charges. It is where and are two point charges separated by a distance . This Coulomb force is extremely basic, since most charges are due to point-like particles. It is responsible for all electrostatic effects and underlies most macroscopic forces.

Electric Field

  • The electric field is an alteration of space caused by the presence of an electric charge. The electric field mediates the electric force between a source charge and a test charge.
  • The electric field, like the electric force, obeys the superposition principle
  • The field is a vector; by definition, it points away from positive charges and toward negative charges.

Calculating Electric Fields of Charge Distributions

  • A very large number of charges can be treated as a continuous charge distribution, where the calculation of the field requires integration. Common cases are:
    • one-dimensional (like a wire); uses a line charge density
    • two-dimensional (metal plate); uses surface charge density
    • three-dimensional (metal sphere); uses volume charge density
  • The “source charge” is a differential amount of charge . Calculating

Electric Field Lines

  • Electric field diagrams assist in visualizing the field of a source charge.
  • The magnitude of the field is proportional to the field line density.
  • Field vectors are everywhere tangent to field lines.

Electric Dipoles

  • If a permanent dipole is placed in an external electric field, it results in a torque that aligns it with the external field.
  • If a nonpolar atom (or molecule) is placed in an external field, it gains an induced dipole that is aligned with the external field.
  • The net field is the vector sum of the external field plus the field of the dipole (physical or induced).
  • The strength of the polarization is described by the dipole moment of the dipole, .

Answers to Check Your Understanding

1.1 The force would point outward.

1.2 The net force would point

below the



1.4 We will no longer be able to take advantage of symmetry. Instead, we will need to calculate each of the two components of the electric field with their own integral.

1.5 The point charge would be



are the sides of the rectangle but otherwise identical.

1.6 The electric field would be zero in between, and have magnitude

everywhere else.

Conceptual Questions

Electric Charge

1. There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?

2. Why do most objects tend to contain nearly equal numbers of positive and negative charges?

3. A positively charged rod attracts a small piece of cork. (a) Can we conclude that the cork is negatively charged? (b) The rod repels another small piece of cork. Can we conclude that this piece is positively charged?

4. Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.

5. How would you determine whether the charge on a particular rod is positive or negative?

Conductors, Insulators, and Charging by Induction

6. An eccentric inventor attempts to levitate a cork ball by wrapping it with foil and placing a large negative charge on the ball and then putting a large positive charge on the ceiling of his workshop. Instead, while attempting to place a large negative charge on the ball, the foil flies off. Explain.

7. When a glass rod is rubbed with silk, it becomes positive and the silk becomes negative—yet both attract dust. Does the dust have a third type of charge that is attracted to both positive and negative? Explain.

8. Why does a car always attract dust right after it is polished? (Note that car wax and car tires are insulators.)

9. Does the uncharged conductor shown below experience a net electric force?

10. While walking on a rug, a person frequently becomes charged because of the rubbing between his shoes and the rug. This charge then causes a spark and a slight shock when the person gets close to a metal object. Why are these shocks so much more common on a dry day?

11. Compare charging by conduction to charging by induction.

12. Small pieces of tissue are attracted to a charged comb. Soon after sticking to the comb, the pieces of tissue are repelled from it. Explain.

13. Trucks that carry gasoline often have chains dangling from their undercarriages and brushing the ground. Why?

14. Why do electrostatic experiments work so poorly in humid weather?

15. Why do some clothes cling together after being removed from the clothes dryer? Does this happen if they’re still damp?

16. Can induction be used to produce charge on an insulator?

17. Suppose someone tells you that rubbing quartz with cotton cloth produces a third kind of charge on the quartz. Describe what you might do to test this claim.

18. A handheld copper rod does not acquire a charge when you rub it with a cloth. Explain why.

19. Suppose you place a charge

near a large metal plate. (a) If

is attracted to the plate, is the plate necessarily charged? (b) If

is repelled by the plate, is the plate necessarily charged?

Coulomb’s Law

20. Would defining the charge on an electron to be positive have any effect on Coulomb’s law?

21. An atomic nucleus contains positively charged protons and uncharged neutrons. Since nuclei do stay together, what must we conclude about the forces between these nuclear particles?

22. Is the force between two fixed charges influenced by the presence of other charges?

Electric Field

23. When measuring an electric field, could we use a negative rather than a positive test charge?

24. During fair weather, the electric field due to the net charge on Earth points downward. Is Earth charged positively or negatively?

25. If the electric field at a point on the line between two charges is zero, what do you know about the charges?

26. Two charges lie along the

-axis. Is it true that the net electric field always vanishes at some point (other than infinity) along the


Calculating Electric Fields of Charge Distributions

27. Give a plausible argument as to why the electric field outside an infinite charged sheet is constant.

28. Compare the electric fields of an infinite sheet of charge, an infinite, charged conducting plate, and infinite, oppositely charged parallel plates.

29. Describe the electric fields of an infinite charged plate and of two infinite, charged parallel plates in terms of the electric field of an infinite sheet of charge.

30. A negative charge is placed at the center of a ring of uniform positive charge. What is the motion (if any) of the charge? What if the charge were placed at a point on the axis of the ring other than the center?

Electric Field Lines

31. If a point charge is released from rest in a uniform electric field, will it follow a field line? Will it do so if the electric field is not uniform?

32. Under what conditions, if any, will the trajectory of a charged particle not follow a field line?

33. How would you experimentally distinguish an electric field from a gravitational field?

34. A representation of an electric field shows 10 field lines perpendicular to a square plate. How many field lines should pass perpendicularly through the plate to depict a field with twice the magnitude?

35. What is the ratio of the number of electric field lines leaving a charge 10

and a charge


Electric Dipoles

36. What are the stable orientation(s) for a dipole in an external electric field? What happens if the dipole is slightly perturbed from these orientations?


Electric Charge

37. Common static electricity involves charges ranging from nanocoulombs to microcoulombs. (a) How many electrons are needed to form a charge of

? (b) How many electrons must be removed from a neutral object to leave a net charge of


38. If

electrons move through a pocket calculator during a full day’s operation, how many coulombs of charge moved through it?

39. To start a car engine, the car battery moves

electrons through the starter motor. How many coulombs of charge were moved?

40. A certain lightning bolt moves

of charge. How many fundamental units of charge is this?

41. A

copper penny is given a charge of

. (a) How many excess electrons are on the penny? (b) By what percent do the excess electrons change the mass of the penny?

42. A

copper penny is given a charge of

. (a) How many electrons are removed from the penny? (b) If no more than one electron is removed from an atom, what percent of the atoms are ionized by this charging process?

Conductors, Insulators, and Charging by Induction

43. Suppose a speck of dust in an electrostatic precipitator has

protons in it and has a net charge of

(a very large charge for a small speck). How many electrons does it have?

44. An amoeba has

protons and a net charge of

. (a) How many fewer electrons are there than protons? (b) If you paired them up, what fraction of the protons would have no electrons?

45. A

ball of copper has a net charge of

. What fraction of the copper’s electrons has been removed? (Each copper atom has

protons, and copper has an atomic mass of


46. What net charge would you place on a

piece of sulfur if you put an extra electron on


of its atoms? (Sulfur has an atomic mass of


47. How many coulombs of positive charge are there in

of plutonium, given its atomic mass is

and that each plutonium atom has


Coulomb’s Law

48. Two point particles with charges


are held in place by

forces on each charge in appropriate directions. (a) Draw a free-body diagram for each particle. (b) Find the distance between the charges.

49. Two charges


are fixed

apart, with the second one to the right. Find the magnitude and direction of the net force on a

charge when placed at the following locations: (a) halfway between the two (b) half a meter to the left of the

charge (c) half a meter above the

charge in a direction perpendicular to the line joining the two fixed charges.

50. In a salt crystal, the distance between adjacent sodium and chloride ions is

. What is the force of attraction between the two singly charged ions?

51. Protons in an atomic nucleus are typically

apart. What is the electric force of repulsion between nuclear protons?

52. Suppose Earth and the Moon each carried a net negative charge

. Approximate both bodies as point masses and point charges. (a) What value of

is required to balance the gravitational attraction between Earth and the Moon? (b) Does the distance between Earth and the Moon affect your answer? Explain. (c) How many electrons would be needed to produce this charge?

53. Point charges


are placed

apart. What is the force on a third charge

placed midway between



54. Where must

of the preceding problem be placed so that the net force on it is zero?

55. Two small balls, each of mass

, are attached to silk threads

long, which are in turn tied to the same point on the ceiling, as shown below. When the balls are given the same charge

, the threads hang at

to the vertical, as shown below. What is the magnitude of

? What are the signs of the two charges?

56. Point charges


are located at


. What is the force of



57. The net excess charge on two small spheres (small enough to be treated as point charges) is

. Show that the force of repulsion between the spheres is greatest when each sphere has an excess charge

. Assume that the distance between the spheres is so large compared with their radii that the spheres can be treated as point charges.

58. Two small, identical conducting spheres repel each other with a force of