cleansing of the drum for the next copy.
Laser Printers
Laser printers use the xerographic process to make high-quality images on paper, employing a laser to produce an image on the photoconducting
drum as shown in Figure 18.40. In its most common application, the laser printer receives output from a computer, and it can achieve high-quality
output because of the precision with which laser light can be controlled. Many laser printers do significant information processing, such as making
sophisticated letters or fonts, and may contain a computer more powerful than the one giving them the raw data to be printed.
Figure 18.40 In a laser printer, a laser beam is scanned across a photoconducting drum, leaving a positive charge image. The other steps for charging the drum and
transferring the image to paper are the same as in xerography. Laser light can be very precisely controlled, enabling laser printers to produce high-quality images.
Ink Jet Printers and Electrostatic Painting
The ink jet printer, commonly used to print computer-generated text and graphics, also employs electrostatics. A nozzle makes a fine spray of tiny
ink droplets, which are then given an electrostatic charge. (See Figure 18.41.)
Once charged, the droplets can be directed, using pairs of charged plates, with great precision to form letters and images on paper. Ink jet printers
can produce color images by using a black jet and three other jets with primary colors, usually cyan, magenta, and yellow, much as a color television
produces color. (This is more difficult with xerography, requiring multiple drums and toners.)
650 CHAPTER 18 | ELECTRIC CHARGE AND ELECTRIC FIELD
Figure 18.41 The nozzle of an ink-jet printer produces small ink droplets, which are sprayed with electrostatic charge. Various computer-driven devices are then used to direct
the droplets to the correct positions on a page.
Electrostatic painting employs electrostatic charge to spray paint onto odd-shaped surfaces. Mutual repulsion of like charges causes the paint to fly
away from its source. Surface tension forms drops, which are then attracted by unlike charges to the surface to be painted. Electrostatic painting can
reach those hard-to-get at places, applying an even coat in a controlled manner. If the object is a conductor, the electric field is perpendicular to the
surface, tending to bring the drops in perpendicularly. Corners and points on conductors will receive extra paint. Felt can similarly be applied.
Smoke Precipitators and Electrostatic Air Cleaning
Another important application of electrostatics is found in air cleaners, both large and small. The electrostatic part of the process places excess
(usually positive) charge on smoke, dust, pollen, and other particles in the air and then passes the air through an oppositely charged grid that attracts
and retains the charged particles. (See Figure 18.42.)
Large electrostatic precipitators are used industrially to remove over 99% of the particles from stack gas emissions associated with the burning of
coal and oil. Home precipitators, often in conjunction with the home heating and air conditioning system, are very effective in removing polluting
particles, irritants, and allergens.
Figure 18.42 (a) Schematic of an electrostatic precipitator. Air is passed through grids of opposite charge. The first grid charges airborne particles, while the second attracts and collects them. (b) The dramatic effect of electrostatic precipitators is seen by the absence of smoke from this power plant. (credit: Cmdalgleish, Wikimedia Commons)
Problem-Solving Strategies for Electrostatics
1. Examine the situation to determine if static electricity is involved. This may concern separated stationary charges, the forces among them,
and the electric fields they create.
2. Identify the system of interest. This includes noting the number, locations, and types of charges involved.
3. Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is useful. Determine whether the
Coulomb force is to be considered directly—if so, it may be useful to draw a free-body diagram, using electric field lines.
4. Make a list of what is given or can be inferred from the problem as stated (identify the knowns). It is important to distinguish the Coulomb
force F from the electric field E , for example.
5. Solve the appropriate equation for the quantity to be determined (the unknown) or draw the field lines as requested.
6. Examine the answer to see if it is reasonable: Does it make sense? Are units correct and the numbers involved reasonable?
Integrated Concepts
The Integrated Concepts exercises for this module involve concepts such as electric charges, electric fields, and several other topics. Physics is most
interesting when applied to general situations involving more than a narrow set of physical principles. The electric field exerts force on charges, for
example, and hence the relevance of Dynamics: Force and Newton’s Laws of Motion. The following topics are involved in some or all of the
problems labeled “Integrated Concepts”:
• Dynamics: Force and Newton’s Laws of Motion
CHAPTER 18 | ELECTRIC CHARGE AND ELECTRIC FIELD 651
• Uniform Circular Motion and Gravitation
The following worked example illustrates how this strategy is applied to an Integrated Concept problem:
Example 18.5 Acceleration of a Charged Drop of Gasoline
If steps are not taken to ground a gasoline pump, static electricity can be placed on gasoline when filling your car’s tank. Suppose a tiny drop of
gasoline has a mass of 4.00×10–15 kg and is given a positive charge of 3.20×10–19 C . (a) Find the weight of the drop. (b) Calculate the
electric force on the drop if there is an upward electric field of strength 3.00×105 N/C due to other static electricity in the vicinity. (c) Calculate
the drop’s acceleration.
Strategy
To solve an integrated concept problem, we must first identify the physical principles involved and identify the chapters in which they are found.
Part (a) of this example asks for weight. This is a topic of dynamics and is defined in Dynamics: Force and Newton’s Laws of Motion. Part (b)
deals with electric force on a charge, a topic of Electric Charge and Electric Field. Part (c) asks for acceleration, knowing forces and mass.
These are part of Newton’s laws, also found in Dynamics: Force and Newton’s Laws of Motion.
The following solutions to each part of the example illustrate how the specific problem-solving strategies are applied. These involve identifying
knowns and unknowns, checking to see if the answer is reasonable, and so on.
Solution for (a)
Weight is mass times the acceleration due to gravity, as first expressed in
w = mg.
(18.20)
Entering the given mass and the average acceleration due to gravity yields
(18.21)
w = (4.00×10−15 kg)(9.80 m/s2 ) = 3.92×10−14 N.
Discussion for (a)
This is a small weight, consistent with the small mass of the drop.
Solution for (b)
The force an electric field exerts on a charge is given by rearranging the following equation:
F
(18.22)
= qE.
Here we are given the charge ( 3.20×10–19 C is twice the fundamental unit of charge) and the electric field strength, and so the electric force
is found to be
(18.23)
F = (3.20×10−19 C)(3.00×105 N/C) = 9.60×10−14 N.
Discussion for (b)
While this is a small force, it is greater than the weight of the drop.
Solution for (c)
The acceleration can be found using Newton’s second law, provided we can identify all of the external forces acting on the drop. We assume
only the drop’s weight and the electric force are significant. Since the drop has a positive charge and the electric field is given to be upward, the
electric force is upward. We thus have a one-dimensional (vertical direction) problem, and we can state Newton’s second law as
(18.24)
a = F net
m .
where F net = F − w . Entering this and the known values into the expression for Newton’s second law yields
(18.25)
a = F − w
m
= 9.60×10−14 N − 3.92×10−14 N
4.00×10−15 kg
= 14.2 m/s2.
Discussion for (c)
This is an upward acceleration great enough to carry the drop to places where you might not wish to have gasoline.
This worked example illustrates how to apply problem-solving strategies to situations that include topics in different chapters. The first step is to
identify the physical principles involved in the problem. The second step is to solve for the unknown using familiar problem-solving strategies.
These are found throughout the text, and many worked examples show how to use them for single topics. In this integrated concepts example,
you can see how to apply them across several topics. You will find these techniques useful in applications of physics outside a physics course,
such as in your profession, in other science disciplines, and in everyday life. The following problems will build your skills in the broad application
of physical principles.
652 CHAPTER 18 | ELECTRIC CHARGE AND ELECTRIC FIELD
Unreasonable Results
The Unreasonable Results exercises for this module have results that are unreasonable because some premise is unreasonable or because
certain of the premises are inconsistent with one another. Physical principles applied correctly then produce unreasonable results. The purpose
of these problems is to give practice in assessing whether nature is being accurately described, and if it is not to trace the source of difficulty.
Problem-Solving Strategy
To determine if an answer is reasonable, and to determine the cause if it is not, do the following.
1. Solve the problem using strategies as outlined above. Use the format followed in the worked examples in the text to solve the problem
as usual.
2. Check to see if the answer is reasonable. Is it too large or too small, or does it have the wrong sign, improper units, and so on?
3. If the answer is unreasonable, look for what specifically could cause the identified difficulty. Usually, the manner in which the answer is
unreasonable is an indication of the difficulty. For example, an extremely large Coulomb force could be due to the assumption of an
excessively large separated charge.
Glossary
Coulomb force: another term for the electrostatic force
Coulomb interaction: the interaction between two charged particles generated by the Coulomb forces they exert on one another
Coulomb’s law: the mathematical equation calculating the electrostatic force vector between two charged particles
conductor: a material that allows electrons to move separately from their atomic orbits
conductor: an object with properties that allow charges to move about freely within it
dipole: a molecule’s lack of symmetrical charge distribution, causing one side to be more positive and another to be more negative
electric charge: a 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 electromagnetic force
electric field lines: a series of lines drawn from a point charge representing the magnitude and direction of force exerted by that charge
electric field: a three-dimensional map of the electric force extended out into space from a point charge
electromagnetic force: one of the four fundamental forces of nature; the electromagnetic force consists of static electricity, moving electricity and
magnetism
electron: a particle orbiting the nucleus of an atom and carrying the smallest unit of negative charge
electrostatic equilibrium: an electrostatically balanced state in which all free electrical charges have stopped moving about
electrostatic force: the amount and direction of attraction or repulsion between two charged bodies
electrostatic precipitators: filters that apply charges to particles in the air, then attract those charges to a filter, removing them from the airstream
electrostatic repulsion: the phenomenon of two objects with like charges repelling each other
electrostatics: the study of electric forces that are static or slow-moving
Faraday cage: a metal shield which prevents electric charge from penetrating its surface
field: a map of the amount and direction of a force acting on other objects, extending out into space
free charge: an electrical charge (either positive or negative) which can move about separately from its base molecule
free electron: an electron that is free to move away from its atomic orbit
grounded: when a conductor is connected to the Earth, allowing charge to freely flow to and from Earth’s unlimited reservoir
grounded: connected to the ground with a conductor, so that charge flows freely to and from the Earth to the grounded object
induction: the process by which an electrically charged object brought near a neutral object creates a charge in that object
ink-jet printer: small ink droplets sprayed with an electric charge are controlled by electrostatic plates to create images on paper
insulator: a material that holds electrons securely within their atomic orbits
ionosphere: a layer of charged particles located around 100 km above the surface of Earth, which is responsible for a range of phenomena
including the electric field surrounding Earth
laser printer: uses a laser to create a photoconductive image on a drum, which attracts dry ink particles that are then rolled onto a sheet of paper
to print a high-quality copy of the image
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law of conservation of charge: states that whenever a charge is created, an equal amount of charge with the opposite sign is created
simultaneously
photoconductor: a substance that is an insulator until it is exposed to light, when it becomes a conductor
point charge: A charged particle, designated Q , generating an electric field
polar molecule: a molecule with an asymmetrical distribution of positive and negative charge
polarization: slight shifting of positive and negative charges to opposite sides of an atom or molecule
polarized: a state in which the positive and negative charges within an object have collected in separate locations
proton: a particle in the nucleus of an atom and carrying a positive charge equal in magnitude and opposite in sign to the amount of negative
charge carried by an electron
screening: the dilution or blocking of an electrostatic force on a charged object by the presence of other charges nearby
static electricity: a buildup of electric charge on the surface of an object
test charge: A particle (designated q ) with either a positive or negative charge set down within an electric field generated by a point charge
Van de Graaff generator: a machine that produces a large amount of excess charge, used for experiments with high voltage
vector addition: mathematical combination of two or more vectors, including their magnitudes, directions, and positions
vector: a quantity with both magnitude and direction
xerography: a dry copying process based on electrostatics
Section Summary
18.1 Static Electricity and Charge: Conservation of 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, while 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 (C), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of
this basic charge ∣ qe ∣ is
∣ qe ∣ = 1.60×10−19 C.
• Whenever charge is created or destroyed, equal amounts of positive and negative are involved.
• Most often, existing charges are separated from neutral objects to obtain some net charge.
• Both positive and negative charges exist in neutral objects and can be separated by rubbing one object with another. For macroscopic objects,
negatively charged means an excess of electrons and positively charged means a depletion of electrons.
• The law of conservation of charge ensures that whenever a charge is created, an equal charge of the opposite sign is created at the same time.
18.2 Conductors and Insulators
• Polarization is the separation of positive and negative charges in a neutral object.
• A conductor is a substance that allows charge to flow freely through its atomic structure.
• An insulator holds charge within its atomic structure.
• Objects with like charges repel each other, while those with unlike charges attract each other.
• A conducting object is said to be grounded if it is connected to the Earth through a conductor. Grounding allows transfer of charge to and from
the earth’s large reservoir.
• Objects can be charged by contact with another charged object and obtain the same sign charge.
• If an object is temporarily grounded, it can be charged by induction, and obtains the opposite sign charge.
• Polarized objects have their positive and negative charges concentrated in different areas, giving them a non-symmetrical charge.
• Polar molecules have an inherent separation of charge.
• Frenchman Charles Coulomb was the first to publish the mathematical equation that describes the electrostatic force between two objects.
• Coulomb’s law gives the magnitude of the force between point charges. It is
F = k| q 1 q 2|
r 2 ,
where q 1 and q 2 are two point charges separated by a distance r , and k ≈ 9.00×109 N · m2 / C2
• 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.
• The Coulomb force is extraordinarily strong compared with the gravitational force, another basic force—but unlike gravitational force it can
cancel, since it can be either attractive or repulsive.
• The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles.
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18.4 Electric Field: Concept of a Field Revisited
• The electrostatic force field surrounding a charged object extends out into space in all directions.
• The electrostatic force exerted by a point charge on a test charge at a distance r depends on the charge of both charges, as well as the
distance between the two.
• The electric field E is defined to be
E = F q,
where F is the Coulomb or electrostatic force exerted on a small positive test charge q . E has units of N/C.
• The magnitude of the electric field E created by a point charge Q is
E = k| Q|
r 2 .
where r is the distance from Q . The electric field E is a vector and fields due to multiple charges add like vectors.
18.5 Electric Field Lines: Multiple Charges
• Drawings of electric field lines are useful visual tools. The properties of electric field lines for any charge distribution are that:
• Field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges.
• The number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.
• The strength of the field is proportional to the closeness of the field lines—more precisely, it is proportional to the number of lines per unit area
perpendicular to the lines.
• The direction of the electric field is tangent to the field line at any point in space.
• Field lines can never cross.
18.6 Electric Forces in Biology
• Many molecules in living organisms, such as DNA, carry a charge.
• An uneven distribution of the positive and negative charges within a polar molecule produces a dipole.
• The effect of a Coulomb field generated by a charged object may be reduced or blocked by other nearby charged objects.
• Biological systems contain water, and because water molecules are polar, they have a strong effect on other molecules in living systems.
18.7 Conductors and Electric Fields in Static Equilibrium
• A conductor allows free charges to move about within it.
• The electrical forces around a conductor will cause free charges to move around inside the conductor until static equilibrium is reached.
• Any excess charge will collect along the surface of a conductor.
• Conductors with sharp corners or points will collect more charge at those points.
• A lightning rod is a conductor with sharply pointed ends that collect excess charge on the building caused by an electrical storm and allow it to
dissipate back into the air.
• Electrical storms result when the electrical field of Earth’s surface in certain locations becomes more strongly charged, due to changes in the
insulating effect of the air.
• A Faraday cage acts like a shield around an object, preventing electric charge from penetrating inside.
18.8 Applications of Electrostatics
• Electrostatics is the study of electric fields in static equilibrium.
• In addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including
photocopiers, laser printers, ink-jet printers and electrostatic air filters.
Conceptual Questions
18.1 Static Electricity and Charge: Conservation of 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?
18.2 Conductors and Insulators
3. An eccentric inventor attempts to levitate by first placing a large negative charge on himself and then putting a large positive charge on the ceiling
of his workshop. Instead, while attempting to place a large negative charge on himself, his clothes fly off. Explain.
4. If you have charged an electroscope by contact with a positively charged obje