Download Electric Charge

Chapter 17
Electric Forces
and Fields
Section 17-1: Electric Charge
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There are two kinds of electric charge.
Like charges repel.
Opposite or unlike charges attract.
Ben Franklin named the two different kinds
of charge positive and negative.
• Positive and negative charges are said to
be opposite because an object with an
equal amount of positive and negative
charge has no net charge.
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All matter is made up of atoms.
Every atom contains even smaller particles.
Protons are positive and found in the nucleus.
Neutrons are neutral and found in the nucleus.
Electrons are negative and move around in the
electron cloud surrounding the nucleus.
• Protons and neutrons are relatively fixed in the
nucleus of the atom, but electrons are easily
transferred from one atom to another.
• An atom has a net charge of zero when the
number of protons equals the number of
electrons.
• As atoms gain or lose electrons they
become negatively or positively charged
atoms called ions.
• Both a balloon and your hair contain a very
large number of neutral atoms.
• Charge has a natural tendency to be
transferred between unlike materials.
• Rubbing the two materials together serves
to increase the area of contact and enhance
the charge transfer process.
• When a balloon is rubbed against your hair,
some of your hair’s electrons are transferred
to the balloon.
• The balloon gains a certain amount of
negative charge while your hair loses an
equal amount of negative charge and is left
with a positive charge.
• Only a small portion of the total available
charge is transferred from one object to
another.
• The positive charge on your hair is equal in
magnitude to the negative charge on the
balloon.
• Electric charge is conserved in this process;
no charge is created or destroyed.
• This principle of conservation of charge is
one of the fundamental laws of nature.
• In 1909, Robert Millikan (1886-1953)
performed an experiment at the University of
Chicago in which he observed the motion of
tiny oil droplets between two parallel metal
plates.
• The oil droplets were charged by friction in an
atomizer and allowed to pass through a hole in the
top plate.
• Initially the droplets fell due to their weight.
• The top plate was given a positive charge as the
droplets fell, and the droplets with a negative
charge were attracted back upward toward the
positively charged plate.
• By turning the charge on this plate on and off,
Millikan was able to watch a single oil droplet
for many hours as it alternately rose and fell.
• After repeating this process for thousands of
drops, Millikan found than when an object is
charged, its charge is always a multiple of a
fundamental unit of charge, symbolized by
the letter e.
• Charge is said to be quantized meaning that
the charge occurs as discrete amounts in
nature.
• An object may have a charge of ±e, or ±2e, or
±3e, and so on.
• Other experiments in Millikan’s time
demonstrated that the electron has a charge of
–e and the proton has an equal and opposite
charge of +e.
• The value of e has since been determined to
be 1.60219 x 10-19 C, where the coulomb (C) is
the SI unit of electric charge.
• For calculations, this book will use the
approximate value of ±1.60 x 10-19.
• 1.0 C is a substantial amount of charge.
• When an object is charged by rubbing, a net
charge on the order of 1μC.
Transfer of Electric Charge
• It is convenient to classify substances in
terms of their ability to transfer electric
charge.
• Materials in which electric charges move
freely, such as copper and aluminum, are
called conductors.
• Most metals are conductors.
• Materials in which electric charges do
not move freely, such as glass, rubber,
silk, and plastic, are called insulators.
• Semiconductors are a third class of materials
characterized by electrical properties that
are somewhere between those of insulators
and conductors.
• In their pure state, semiconductors are
insulators.
• The carefully controlled addition of specific
atoms as impurities can dramatically
increase a semiconductor’s ability to conduct
electric charge.
• Silicon and germanium are two well-known
semiconductors that are used in a variety of
electronic devices.
• Certain metals belong to a fourth class of
materials, called superconductors.
• Superconductors become perfect
conductors when they are at or below a
certain temperature called the critical
temperature.
• Insulators and conductors can both
become charged by contact.
• When a conductor is connected to Earth
by means of a conducting wire or copper
pipe, the conductor is said to be
grounded.
• The earth can be considered an infinite
reservoir for electrons because it can accept
or supply an unlimited number of electrons.
• This is the key to understanding another
method of charging a conductor.
• Consider a negatively charged rubber rod
brought near a neutral (uncharged) conducting
sphere that is insulated so that there is no
conducting path to ground.
• The repulsive force between the electrons in the
rod and those in the sphere causes a
redistribution of negative charge on the sphere.
• As a result, the region of the sphere nearest the
negatively charged rod has an excess of positive
charge.
• If a grounded conducting wire is then connected
to the sphere, some of the electrons leave the
sphere and travel to earth.
• If the wire to the ground is then removed while
the negatively charged rod is held in place, the
conducting sphere is left with an excess of
induced positive charge.
• Finally, when the rubber rod is removed from
the vicinity of the sphere, the induced positive
charge remains on the ungrounded sphere.
• The positive charge then becomes uniformly
distributed over the outside surface of the
ungrounded sphere.
• This process is known as induction, and the
charge is said to be induced on the sphere.
• Induction– the process of charging a
conductor by bringing it near another
charged object and grounding the
conductor.
• Charging an object by induction requires
no contact with the object inducing the
charge but does require contact with a
third object, which serves as either a
source or a sink of electrons.
• A process very similar to charging by
induction in conductors takes place in
insulators.
• In most neutral atoms or molecules, the
center of positive charge coincides with the
center of negative charge.
• In the presence of a charged object, these
centers may shift slightly, resulting in more
positive charge on one side of a molecule
than on the other.
• Polarization– when charges on an atom
or molecule shift making one side more
positive and the other side more negative.
• This realignment of charge within
individual molecules produces an induced
charge on the surface of the insulator.
• When an object becomes polarized, it has
no net charge but is still able to attract or
repel objects due to this realignment of
charge.
• This is why a plastic comb can attract small
pieces of paper that have no net charge.
• Like induction, polarization does not
require physical contact.
Section 17-2: Electric Force
• We recall that forces cause a change in
motion.
• We have electric force.
• Electric force is attractive between
opposite charges and repulsive between
like charges.
• What determines how small or large the
electric force will be?
• The distance between two object affects the
magnitude of the electric force between
them.
• Further, it seems reasonable that the amount
of charge on the objects will also affect the
magnitude of the electric force.
• In the 1780’s, Charles Coulomb conducted a
variety of experiments in an attempt to
determine the magnitude of the electric
force between two charged objects.
• Coulomb found that the electric force
between two charges is proportional to the
product of the two charges.
• So, if one charge is doubled, the electric force
likewise doubles, and if both charges are
doubled, the electric force increases by a factor
of four.
• Coulomb also found that the electric force is
inversely proportional to the square of the
distance between the charges.
• When the distance between two charges is
halved, the force between them increases by a
factor of four.
• The following equation, known as
Coulomb’s law, expresses these conclusions
mathematically for two charges separated
by a distance, r.
• Felectric = kC(q1q2/r2)
• The symbol kC, called the Coulomb
constant, has SI units of N·m2/C2 because
this give N as the unit of electric force.
• This book will use the approximate value
of 8.99 x 109 N·m2/C2 for kC.
• When dealing with Coulomb’s law,
remember that force is a vector quantity and
must be treated accordingly.
• The electric force between two objects
always acts along the line between the
objects.
• Also note that Coulomb’s law applies
exactly only to point charges or particles
and to spherical distributions of charge.
• When applying Coulomb’s law to spherical
distributions of charge, use the distance
between the centers of the spheres as r.
• Electric force is a field force.
• Gravitational force is another type of field force.
• The mathematical form of the Coulomb force is very
similar to that of the gravitational force.
• That is, both forces are inversely proportional to the
square of the distance of separation.
• There are some important differences between
electric and gravitational forces.
• Electric forces can be either attractive or repulsive.
• Gravitational forces are always attractive.
• Electric force is significantly stronger than the
gravitational force.
• Frequently, more than two charges are
present, and it is necessary to find the net
electric force on one of them.
• Coulomb’s law applies even when more
than two charges are present.
• The resultant force on any single charge
equals the vector sum of the individual
forces exerted on that charge by all of the
other individual charges present.
Equilibrium
• Objects that are at rest or moving with a
constant velocity are said to be in
equilibrium.
• According to Newton’s 1st Law, the net
external force acting on a body in
equilibrium must equal zero.
• In electrostatic situations, the
equilibrium position of a charge is the
location at which the net electric force on
the charge is zero.
• To find this location, you must find the
position at which the electric force from one
charge is equal and opposite the electric
force from another charge.
• This can be done by setting the forces
(found by Coulomb’s law) equal and then
solving for the distance between either
charge and the equilibrium position.
Section 17-3: The Electric Field
• A charged object sets up an electric field in
the space around it.
• When a second charged object enters this
field, forces of an electrical nature arise.
• In other words, the second object interacts with
the field of the first particle.
• To define an electric field more precisely,
consider figure 17-10(a), which shows an object
with a small positive charge qo, placed near a
second object with a larger positive charge, Q.
• The strength of the electric field, E, at the
location of qo is defined as the magnitude of
the electric force acting on q0 divided by the
charge of q0:
• E = Felectric/qo
• Note that this is the electric field at the
location of q0 produced by the charge Q,
and not the field produced by q0.
• Because electric field strength is a ratio of
force to charge, the SI units of E are
newtons per coulomb (N/C).
• The electric field is a vector quantity.
• By convention, the direction of E at a
point is defined as the direction of the
electric force that would be exerted on a
small positive charge (called a test
charge) placed at that point.
• In other words, the direction of E depends
on the sign of the charge producing the
field.
• Consider the positively charged conducting
sphere in figure 17-11 (a).
• The field in the region surrounding the
sphere could be explored by placing a
positive test charge, q0, in a variety of
places near the sphere.
• To find electric field at each point, you
would first find the electric force on this
charge then divide this force by the
magnitude of the test charge.
• However, when the magnitude of the test
charge is great enough to influence the
charge on the conducting sphere, a difficulty
with our definition arises.
• According to Coulomb’s law, a strong test
charge will cause a rearrangement of the
charges on the sphere as shown in figure 1711 (b).
• As a result, the force exerted on the test
charge is different from what the force
would be if the movement of charge on the
sphere had not taken place.
• Furthermore, the strength of the measured
electric field is different from what it would
be in the absence of the test charge.
• To eliminate this problem, we assume that
the test charge is small enough to have
negligible effect on the location of the
charges on the sphere.
• To reformulate our equation for electric
field strength from a point charge, consider
a charge, q, located a distance, r, from a
small test charge, q0.
• According to Coulomb’s law, the magnitude of
the force on the test charge is given by the
following equation:
• Felectric = kcqq0/r2
• We can substitute this value into our previous
equation for electric field strength.
• E = Felectric/q0 = kcqq0/r2q0
• Notice that the q0 cancels, and we have a new
equation for electric field strength from a point
charge.
• E = kcq/r2 where q is the charge producing
the field.
• As stated earlier, electric field, E, is a
vector.
• If q is positive, the field due to this charge
is directed outward radially from q.
• If q is negative, the field is directed
toward q.
• As with electric force, the electric field due
to more than one charge is calculated by
applying the principle of superposition.
• Our new equation for electric field strength
points out an important property of electric
fields.
• As the equation indicates, an electric field at
a given point depends only on the charge, q,
of the object setting up the field and on the
distance, r, from that object to a specific
point in space.
• As a result, we can say that an electric
field exists at any point near a charged
body even when there is no test charge at
that point.
Electric Field Lines
• Electric field lines– lines that represent both
the magnitude and the direction of the
electric field.
• This is a convenient aid for visualizing electric
field patterns.
• Although the electric field lines do not really
exist, they offer a useful means of analyzing
fields by representing both the strength and
direction of the field at different points in space.
• With electric field lines, the number of lines per
unit area through a surface perpendicular to the
lines is proportional to the strength of the
electric field in a given region.
• E is stronger where the field lines are close
together and weaker when they are far apart.
• Figure 17-15 (a) on page 648 shows some
representative electric field lines for a positive
point charge.
• Note that this two-dimensional drawing contains
only the field lines that lie in the plane
containing the point charge.
• The lines are actually directed outward radially
from the charge in all directions.
• Because a positive test charge placed in this field
would be repelled by the positive charge q, the
lines are directed away from the positive charge,
extending to infinity.
• Similarly, the electric field lines for a single
negative point charge, which begin at infinity,
are directed inward toward the charge, as shown
in figure 17-15 (b).
• Note that the lines are closer together as they
get near the charge, indicating that the
strength of the field is increasing.
• This is consistent with our equation for
electric field strength, which is inversely
proportional to the distance squared.
Rules for Drawing Electric Field
Lines
• 1. The lines must begin on positive charges or
at infinity for negative charges, and they must
terminate on negative charges or at infinity.
• 2. The number of lines drawn leaving a
positive charge or approaching a negative
charge is proportional to the magnitude of the
charge.
• 3. No two field lines from the same field can
cross each other.
• Figure 17-16 on page 649 shows the electric field
lines for two point charges of equal magnitudes
but opposite signs.
• This configuration is called an electric dipole.
• Electric dipole– charge configuration for two
point charges of equal magnitudes but
opposite signs.
• In this case, the number of lines that begin at
the positive charge must equal the number of
lines that terminate on the negative charge.
• At points very near the charges, the lines are
nearly radial.
• The high density of lines between the charges
indicates a strong electric field in this region.
• Figure 17-17 shows the electric field lines in the
vicinity of two equal positive point charges.
• Again, close to either charge, the lines are nearly
radial.
• The same number of lines emerges from each
charge because the charges are equal in
magnitude.
• At great distances from the charges, the field
approximately equals that of a single point
charge of magnitude 2q.
• Figure 17-18 is a sketch of the electric field
lines associated with a positive charge +2q and
a negative charge –q.
• In this case, the number of lines leaving the
charge +2q is twice the number terminating on
the charge –q.
• Only half the lines that leave the positive charge
end at the negative charge.
• The remaining half terminate at infinity.
• At distances that are great compared with the
separation between the charges, the pattern of
electric field lines is equivalent to that of a
single charge, +q.
Conductors in Electrostatic
Equilibrium
• A good electric conductor, such as copper,
contains charges (electrons) that are not bound
to any atoms and are free to move about within
the material.
• When no net motion of charge is occurring
within a conductor, the conductor is said to
be in electrostatic equilibrium.
• Conductors in electrostatic equilibrium will
have the following four properties.
Characteristics
• 1. The electric field is zero everywhere inside the
conductor.
• 2. Any excess charge on an isolated conductor
resides entirely on the conductor’s outer surface.
• 3. The electric field just outside a charged
conductor is perpendicular to the conductor’s
surface.
• 4. On an irregularly shaped conductor, charge
tends to accumulate where the radius of
curvature of the surface is smallest, that is, at
sharp points.
• The first property, which states that the
electric field is zero inside a conductor in
electrostatic equilibrium, can be understood
by examining what would happen if this
were not true.
• If there were an electric field inside a
conductor, the free charges would move
and a flow of charge, or current, would
be created.
• If there were a net movement of charge,
the conductor would no longer be in
electrostatic equilibrium.
• The fact that any excess charge resides on
the outer surface of the conductor is a direct
result of the repulsion between like charges
described by Coulomb’s law.
• If an excess of charge is placed inside a
conductor, the repulsive forces arising
between the charges force them as far
apart as possible, causing them to quickly
migrate to the surface.
• If the electric field were not
perpendicular to the surface, the electric
field would have a component along the
surface.
• This would cause the free negative
charges within the conductor to move.
• If the charges moved, a current would be
created and there would no longer be
electrostatic equilibrium.
• E must be perpendicular to the surface.
• To understand why charge tends to accumulate at
sharp points, consider a conductor that is fairly flat
at one end and relatively pointed at the other.
• Any excess charge placed on the object moves to
its surface.
• Figure 17-20 on page 651 shows the forces
between two charges at each end of such an object.
• When one end of a conductor is sharper than
the other, excess charge tends to accumulate at
the sharper end, resulting in a larger charge
per unit area and a larger repulsive electric
force between charges at this end.
• At the sharp end, a larger electric field is
directed away from the surface.
• When the field becomes great enough, the
gases of the air around the sharp end of
the conductor become ionized and a
bluish glow called a corona is seen.
• A glow discharge known as St. Elmo’s
fire can sometimes be observed at night
at the tips of ship masts and at the
trailing edges of wing and tail surface of
aircraft.
• In nuclear physics research, a Van de Graaff
generator is often used to generate electric
charge.
• Some generators are designed to accumulate
positive charge.
• If protons are introduced into a tube attached to
the dome of a Van de Graaff generator, the large
electric field of the dome exerts a repulsive
force on the protons, causing them to accelerate
to energies high enough to initiate nuclear
reactions between the protons and various target
nuclei.
• The Van de Graaff generator is designed
to avoid ionizing the air, which would
allow charge to “leak off” into the
atmosphere.
• Figure 17-22 on page 652 shows the basic
construction of a Van de Graaff generator.
• A motor driven pulley moves a nonconducting belt around a loop.
• The pulley and belt are made of different
materials, and the friction of the pulley
driving the belt causes a separation of
charges.
• A strong positive charge builds up on the
pulley, while the belt becomes negatively
charged.
• The negative charge spreads over the length
of the belt.
• Because the positive charge is concentrated
on the comparatively small pulley while the
corresponding negative charge is spread
over the much larger belt, there is a net
positive charge in the area around the lower
pulley.
• A comb of conducting needles is located near
where the belt passes over the pulley with its
needles very close to, but not touching, the
moving belt.
• The comb is connected by a wire to ground.
• The net positive charge in the area around the
pulley attracts negative charge from ground onto
the needles of the comb.
• The electrostatic attraction of the positive charge
is great enough to cause the negative charges to
leap off toward the pulley.
• The negative charges hit the belt, and the
moving belt carries them up.
• The negative charges are drawn off the belt
by another comb of needles at the top.
• These charges distribute themselves over
the outer surface of the dome.
• A large amount of negative charge can be
accumulated on the dome in this manner.
• Because the electric field is greatest at
sharp points, a sphere is the most
effective shape for building up large
amounts of charge without producing a
corona.