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Fields and Forces
Chapter 14
Static Electricity
Section 14.1
• Electrostatics – the study of electrical charges
that can be collected and held in one place.
• Current electricity – the study of electricity
produced by batteries and generators;
movement of electrons (e-) or protons (p+).
• After being rubbed by another body, every object
obtains the ability to attract small bits of matter.
• Example – rubbing a comb against wool gives
the comb a negative charge and it can attract
small bits of paper.
• These bodies are said to be electrically
charged or electrified.
• Because the electric charges are usually
stationary, they are called static electrical
charges.
• Streams of moving electrons are called electric
currents. Ex. Wiring in houses.
• We will look at currents in a later chapter.
Structure of the Atom
• An atom consists of a massive, positively
charged nucleus which contains protons and
neutrons.
• The nucleus is surrounded by the negatively
charged electrons which balance the positively
charged nucleus.
• Therefore the atom is neutral.
• When energy is added to an atom, electrons can
be added on or leave the atom, leaving an ion.
• Cation –a positively charged ion. It has lost
electrons. (Metals)
• Anion – a negatively charged ion. It has gained
electrons. (Nonmetals)
Ways to Charge an Object
1. Friction
2. Charging by Conduction
3. Charging by Induction
Friction
• When 2 objects are rubbed together, each can
become charged. This occurs because they
either give up or receive electrons from the other
atom.
• Example –When a neutral rubber rod is rubbed
by fur, it gains electrons from the fur and
becomes negatively charged.
• Example – When a neutral glass rod is rubbed
with silk, it becomes positively charged because
it loses its electrons to the silk.
• Note – The total charge of the 2 objects remains
the same.
• Individual charges are never created or
destroyed.
• The positive and negative charges are said to be
separated because electrons are transferred.
• An electrically charged body attracts all neutral
objects.
• An electrically charged body attracts oppositely
charged objects.
•
• An electrically charged body repels objects of the
same charge.
• Like charges repel and unlike charges
attract each other.
• Conductors – materials that allow electrical
charges or heat to move about easily.
• Example – metals are good conductors because
at least 1 electron on each atom can be removed
easily. These electrons can then move freely
throughout the metal carrying their negative
charge.
• Other conductors include copper, aluminum,
graphite, and tap water.
• Insulators – materials through which electrical
charges do not move easily. Electrons are held
tightly by the nucleus so they cannot move freely
from one place to another.
• Insulators can gain or lose electrons when
touching other bodies but only at points of
contact.
• Charges removed from one area of an insulator
are not replaced by charges from another area.
• Common insulators include glass, dry air, cloth,
dry wood, and deionized water.
• To detect and identify small electric charges we
use an electroscope.
• An electroscope is a sensitive instrument that
consists of a metal knob connected by a metal
stem to 2 thin, lightweight pieces of metal foil
called leaves.
Charging by Conduction
• This is charging a neutral body by touching it with
a charged body.
• The neutral will have the same charge on it as the
charging body.
• Because the knob, rod, and leaves of an electroscope
are conductors, the charge put on the knob will
spread to the leaves.
• Both leaves acquire the same charge, so they repel
each other.
• The greater the charge on the leaves, the more they
spread apart.
• Diagrams
• To determine whether an electroscope is
positively or negatively charged, you only need
to observe what happens to the leaves of the
electroscope if a rod of known charge comes
close to the knob.
• If the leaves spread apart, the electroscope has
the same charge as the object, because like
charges repel.
• If the leaves come together, the electroscope has
the opposite charge of the object because unlike
charges attract.
• A negatively charged object will repel
electrons from the knob of a negatively
charged electroscope into the leaves leaving
them more negatively charged and they spread
further apart.
• A positively charged object will attract
electrons from the leaves of a negatively
charged electroscope leaving the leaves with
less negative charge and they come together.
Charging by Induction
• Charging an object without contact/touching
between them.
• Charging an object by induction gives it an equal
but opposite charge as the inducing body. See
Figure 20-8
Steps to Charging an Electroscope
Positively by Induction
• Bring a negatively charged object (rubber rod)
close to electroscope. The leaves will spread
apart.
• While the negatively charged object is close to
electroscope, touch electroscope with a finger to
create a ground, and the leaves come together.
• Remove the ground, then remove the rod. The
leaves are spread apart and stay apart because
they are both positively charged.
• Diagrams
• When the negative rod is close to the knob, free
electrons are repelled from the knob and go to
the leaves.
• The loss of electrons leaves the knob temporarily
positively charged and the leaves gain electrons
are temporarily negatively charged.
• When the knob is grounded, some of the
remaining electrons on the knob, are repelled to
the ground by the negative rod.
• The leaves lose some of the negative charge and
come together because electrons move up to the
knob replacing the electrons lost to the ground.
• When the ground connection is removed before
the charged body, the electroscope is left with a
net positive charge as it lost some electrons that
were not replaced.
• For a positively charged body and a negatively
charged electroscope, electrons move from the
ground into the electroscope, leaving the
electroscope with a negative charge.
Charge Separation or Charge Polarization
• The separation of charges within a neutral object
due to the presence of a nearby charged object.
• Example – a charged balloon sticks to a wall
- a charged comb picks up paper
• Charge polarization causes the attractive force
between a neutral insulator and charged object.
• When a charged object is brought near the
insulator, since there are no free electrons
moving in the insulator, the charges rearrange
positions in the atom.
• This causes one side to be slightly more positive
and the opposite side to be slightly more
negative.
• If the charged object is negative then the positive
side of the atom ends up toward it and the
negative side moves away from it.
Coulomb’s Law
• The forces that electrical charges exert on each
other influence the structure and properties of
matter (cohesion, adhesion, and friction).
• These electrical charges are the forces that bind
electrons and protons together in different kinds
of atoms and that bind atoms together to form
molecules.
• Charles Coulomb (1736-1806) found that the
strength of an attractive or repulsive force
between charged bodies is determined by:
▫ The size of the charges
▫ The distance between the charged bodies
• Coulomb said the strength of the force varies
directly with the product of the charges (q1 and
q2) and it varies inversely with the square of the
distance between the 2 charged bodies.
• Coulomb’s Law expresses the size and
direction of the force that a small sphere with
charge q1 exerts on a second sphere with charge
q2 and separated by a distance, d, as:
where k is the constant used to convert units of
charge (Coulomb) and distance (meter) into
units of force (N)
• Gravity is the attractive force between any 2
objects (-9.81 m/s2).
• Electrical forces must be strong because they can
produce acceleration larger than the acceleration
due to gravity.
• While gravity is only an attractive force,
electrical forces may be either attractive or
repulsive.
• Similar to gravity, the strength of the electrical
forces between objects varies with the distance
between them.
• If the objects are closer together, the force is
stronger.
• According to Newton’s Third Law (Law of
Action-Reaction) each charged object exerts an
equal but opposite force on the other charged
object.
▫ A repulsive force between charges has a positive
sign … like charges.
▫ An attractive force between charges has a negative
sign … unlike charges.
• Coulomb (C) – the SI unit of charge which is
determined by the force it produces. It has a
total charge of 6.25 × 1018 electrons (e-).
▫ 1 C = 6.25 × 1018 e-
• Elementary charge (q) – the size and
direction of the charge of one electron. It is
equal to -1.602 × 10-19 C (therefore the charge
on a proton is +1.602 × 10-19 C).
• See Model Problem on Page 637
• Do Practice Problems on Page 638 #s 1-5
• See Model Problem on Page 639
• Do Practice Problems on Page 640-641 #s 6-10
• Red Book Example Page 419
• Red Book Practice Problems Page 423 #s 15-19
Describing Fields
• Some forces act only when objects are in contact
(you push on door and door pushes on you;
Newton’s 3rd Law), other forces do not need
contact to act...action at a distance forces
(jump into the air and Earth’s gravity pulls you
back even without contact between the objects).
• Field: a property of space; a region in space
where one object can exert a force on another
object without touching it (proposed by Faraday)
3 Main Types of Fields
• Gravitational field - space around matter
where it is attracted to other matter
• Magnetic field - space around magnetized
materials where they can attract or repel,
depending on what is placed in the field
• Electric field - a region in space around a
charged object where a force is exerted on a
small positive test charge (qt).
▫ The object that produces field is called source of
field.
Electric Fields
• An electric charge creates a field around it in all
directions. If a second charge is placed at some
point in this field, the second charge is said to
interact (is repelled/attracted) with the field at
that point.
• There are 2 methods of illustrating the electric
field around a point charge:
Vector Method
• Use vector arrows to represent the size and
direction of the field at various locations.
• The length of arrow shows the strength of the
field at that location while the direction of arrow
shows the direction of the field.
• The direction of an electric field (E) at any
point is the direction in which the field
pushes a (+) test charge placed at that
point. (Fig14.6 Page 644 & 14.7 Page 645).
• A test charge (usually positive) is a point
charge with a magnitude so much smaller than
the source charge that any field generated by it is
negligible in relation to the field generated by
the source charge.
Electric Field Lines
• The electric lines of force represent the direction
that a positive test charge would move in an
electric field.
• These lines of force radiate outward from a (+)
charged object but inward toward a (-) charged
object.
• When two or more charges are in the field, the
field lines will become curved so as to always
leave (begin) at a (+) charge and enter (stop) at a
(-) charge.
• See Figures 14.9 & 14.10 on Page 659
• The existence of a force in electric fields can be
detected and the strength of the force can be
measured for any point in the field.
• This is done by placing a small (+) test charge at
some location in the field and observing it being
repelled or attracted by the field charge.
• The strength of an electric field at some point is
a measure of how great a force will be exerted on
a test charge by the field charge at that point.
• If a test charge “qt” experiences a force “ ” at
some point in the field, the strength of the
electric field ( ) at that point is given by the
equation:
• where “ ” is force expressed in Newtons (N)
and “q” is charge expressed in coulombs (C).
• Units of electric field intensity ( )are N/C.
• Consequently, any charge placed in an electric
field experiences a force on it as given by the
equation:
• Direction of is always the direction a
positive charge would move if placed in
field at that point!
• Model Problem on pages 645-646.
• Do Practice Problems on Pages 646 – 647 #s 1114
Gravitational Field Intensity
• A mass (i.e. Earth) can exert a gravitational force
on a test mass that is in its vicinity.
• The intensity of the gravitational field depends
upon the source and location of gravitational
field.
• Gravitational fields can also be illustrated using
field vector arrows. See Figure 14.8 on Page 649
• To find gravitational field intensity, use this
formula:
• units are N/kg
• is gravitational field intensity @ Earth’s
surface (same equation used to find weight of
object).
• See Model Problem on page 648
• Do Practice Problems on Page 649 #s 15 - 17
Magnetic Field Intensity
• Described differently than electric and
gravitational fields.
Fields Near Point Sources
• By substituting Coulomb’s Law into the equation
for electric field strength, we come up with an
equation to find the electric field intensity a
distance away from a point charge.
• This equation only applies for the field
surrounding an isolated point charge.
• Direction is radially out from positive point
charge .
• Direction is radially in toward negative point
charge.
• See Model Problems on pages 652-655.
• Do Practice Problems on Page 655 #s 20 - 30
Gravitational Field Intensity
• Likewise, the same substitution can be done with
the Universal Law of Gravitation equation into
the equation for the gravitational field intensity
equation to yield:
• Direction is inward toward center of object
creating field.
• See Model Problem on page 657.
• Do Practice Problems on Page 658 #s 31-37
• Chapter 14 Review Page 683-685
Chapter 15
Energy and Electrical Potential
• Since an electric field exerts a force on any
charged particle placed in it, there is energy
associated with the position of the particle in the
field.
• When a small (+) test charge is brought near a
(+) field charge, these like charges will repel and
an outside force is required to push them closer
together.
• A force applied over some distance on the test
charge represents work (W = F x d) done on the
test charge. Since work is needed to move the
small charged test particle against the electric
field of another charged body, this work
represents an increase in the electric potential
energy (Ep) of the test particle.
• If the force pushing the like charges together is
released, the small charged particle will fly away
and its electric Ep is changed into kinetic energy
(Ek).
• Since unlike charges attract, work is required to
pull them away from each other. The work done
in pulling apart two unlike charges increases the
Ep of the smaller particle.
• Electric Potential Energy – Ep- of a charge
due to its location in an electric field.
• Two similar charges moved to the same location
against an electric field require twice the work as
one.
• These two charges placed at the same location in
the field will have twice the electric Ep as one
charge at that location.
• Similarly, a group of 10 charges at a location will
have 10 times that Ep as 1 charge at the same
location.
• For convenience, electrical potential energy per
charge is considered.
• The electrical potential energy per charge is the
total electric potential at a location divided by
the amount of charge at the same location, so
that at any location, the potential energy per
charge - whatever the amount of charge - will be
the same.
• Example- At a particular location an object with
10 units of charge has 10 times as much energy
as an object with 1 unit of charge. (10 units of
Ep/10 units of charge = 1 unit of Ep/1 unit of
charge).
• Electrical Potential - the electrical potential
energy per charge at a location in an electric
field or the amount of energy contained in an
electric field.
• Energy can be transferred to a test charge by an
electric field if the electric force acting on the
charge causes it to move from one point to
another.
• These two points are said to differ in their
electric potential.
• The amount of the change in energy of the
charge by the electric field is a measure of the
difference in electrical potential between the two
points.
• Electrical Potential Difference - change in
energy per unit of charge as the charge is
moved between two points in an electric field.
(Expressed in Volts)
• The difference of potential between two points
also describes the work required to move a unit
of (+) charge from a point of lower potential to
one of higher potential.
• Volt (V) - the unit of electric potential
difference where one Newton of force is used to
move one Coulomb (C) of charge through a
distance of one meter.
or
• 1 Volt = 1 Newton-meter/Coulomb
• Also:
• 1 Volt = 1 joule/Coulomb
• Note: A 6 volt battery is capable of giving 6
joules of energy to every coulomb of charge
moved from one location to another.
• The potential difference between two points is
measured with a voltmeter and is sometimes
called the voltage between the points. The
electric potential at any point considered to be
the reference (starting point) is defined as 0. No
matter what reference point is used, the value of
the potential difference between the two points
is always the same.
• Electric potential energy is smaller when two
unlike charges are closer together and will
increase when they are separated.
• Electrical potential energy is larger when two
like charges are closer together and decreases as
the two like charges are moved further apart.
▫ In both cases work is needed to move the charges
against the field.
Electric Potential in a Uniform Field
• The strength of the electric field around two or
more charged particles is usually not constant.
• It changes from point to point, becoming less as
the (+) test charge is moved further away from a
charged body.
• An electric field in which the electric field
strength is constant at all points in the field is
made by placing two large, flat, conducting
plates parallel to each other and charging one
plate +, the other plate -.
• The direction of such a field is from the + plate
to the - plate.
• A small + test charge placed anywhere between
the plates will be repelled by + charged plate and
attracted to the - charged plate.
• If allowed to move, this + test charge A follows a
path perpendicular to both plates and toward
the (-) charged plate.
• The potential difference or change in Ep per unit
of charge (voltage) between two points in a
uniform field is the work required to move a +
test charge the distance (d) between the two
points against the electric field :
• That is
• Recall the 3 formulas for potential difference
(Voltage)
Sharing of Charge
• All systems, mechanical and electrical, come to
equilibrium when the energy of the system is at a
minimum. (Ball rolls to bottom of hill where it
has least PE).
• Similarly, when an insulated, - charged metal
sphere touches a neutral metal sphere (0 PE),
the - charges will repel each other and flow from
the charged sphere to the neutral one.
• Each - charge lost by the - charged sphere
reduces its PE and raises the PE of the neutral
sphere as work is needed to overcome the
repulsive force between increasing numbers of
like - charges as each move onto the neutral
sphere.
• This transfer of charges continues until the PE of
each sphere is the same (Fig 21-9).
• If the sharing of charge occurs between a large
and a small sphere that have the same kind and
amount of charge, the charges will move from
the one with more potential (smaller sphere) to
the one with less potential (larger sphere).
• The large sphere has less potential than the
small one because the charges on it can spread
further apart over its larger surface area than is
possible with the small sphere.
• This transfer of charges continues until both
spheres are at the same potential. This results in
the two spheres having the same potential but
the larger one will have greater charge (Fig 2110). Because the Earth is a huge sphere it has an
unlimited amount of potential and if grounded
with another charged body it will accept (give
up) charges until the body becomes neutral.
Electric Fields Near Conductors
• The charges on a conductor are spread (repel) as
far apart as possible to reduce its energy to a
minimum.
• If the conductor is a solid then excess charges
moves to the outer surface.
• If this conductor is a closed metal container
there will be no charges on its inside surface (no
electric field) as all are repelled to the outside.
(Inside of a car gives protection against the
electric fields when it is lightning.)
• The electric field around the outside a conductor
depends on the shape of the body as well as its
potential.
• The charges are closer together at sharp points
of the conductor resulting in the field also being
stronger at these same points (Fig 21-12).
• This stronger field around any points on an
object will attract other charges and allow for
discharge to the ground via a conductor.
• (Pointed lightning rod grounded to Earth, Fig
21-13)
Capacitors
• Capacitor - an electric device used to store or
hold an electric charge.
• A capacitor consists of two conductors separated
by an insulator (i.e. two metal plates separated
by a layer of air).
• The charge of a capacitor is used to control the
supply of electricity within an electric circuit.
• The capacitor is included in a circuit to release
its charge when needed.
• A capacitor is charged by removing some charge
from one plate and placing it on the other.
• This can be done by connecting the plates of the
capacitor briefly to a battery.
• When the circuit switch is closed the battery
pumps charge onto the capacitor charging one
plate + leaving the other with an equal - charge.
• The charges of the capacitor plates then become
supplies of electricity, like the oppositely
charged terminals of a battery.
• When the capacitor is charged, it is disconnected
from the battery.
• When the plates of the capacitor are connected
by another switch, the capacitor is discharged
almost instantaneously. (Flash camera)
• Capacitance (C) - the ability of a capacitor to
store a charge.
• Capacitance is increased by making the plates of
the capacitor larger and moving them closer
together.
• Capacitance is also influenced by the insulating
material that separates its plates.
• Farad (F) - the unit of measurement for the
capacitance of a capacitor.
• The farad is determined by dividing the charge
in coulombs of the capacitor by the electrical
force (Volts), applied to its plates
• that is 1 Farad = 1 coulomb / Volt
or
1F = 1C/V