Download Lecture Chapter 15

Chapter 14 Lecture
Electric Charge,
Force, and Energy
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What's new in this chapter
• What is the interaction responsible for holding the
particles together is the same interaction that
makes the toner stick to a copier drum and a
balloon stick to your hair, as well as many other
phenomena that we observe in our everyday world.
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What is Electrostatics?
Electrostatics is the study of the interactions
between
stationary
electrically
charged
particles.
Electrostatic laws deal with the attractive and
repelling forces that exist between positive
and negative electric charges.
A Quick Chemistry Review
History of the Atom
A Little More Review
Particle
Location
Charge
Mass
Proton
Electron
Neutron
Nucleus
Energy
Levels
Nucleus
+1.6 x 10-19 C -1.6 x 10-19 C
No Charge
1.67 x 10-27kg 9.11 x 10-31kg 1.68 x 10-27kg
What’s the Origin of the Word “Electricity”?
William Gilbert, a 17th century physician and
scientist coined the term from the Greek root
“elektron” meaning amber.
Amber was the
material that ancient Greek philosophers had
noticed would mysteriously attract small
particles after it had been rubbed with fur.
A Brief History…
We needed
bigger shocks…
Since electricity from frictional
sources was usually weak,
electricians of the eighteenth
century searched for ways to
increase
charge
and
to
accumulate as much of it as
possible on a substance. If
charge could be accumulated the
electricians could then broaden
their research with the mystical
phenomenon.
Stephen Gray (1666-1736)
This British chemist, is credited with discovering that
electricity can flow (1729), and was the first to
identify the properties of conductors and insulators.
He also transmitted electricity over a wire, which
eventually led to the development of the telegraph.
The figure shows that
the electric force of a
rubbed glass could be
sent, through a wire, to
the body of a person.
E.G. von Kleist (1700-1748) and
Pieter van Musschenbroek (1692-1761)
This German administrator and cleric, and
the Dutch physicist separately and
independently discovered the Leyden jar, a
fundamental electric circuit element for
storing electric charge, now referred to as a
capacitor. Musschenbroek nearly killed his
friend discharging the capacitor.
Jean-Antoine Nollet (1700-1770)
This French clergyman decided to test his theory that
electricity traveled far and fast. He did the natural
thing on a fine spring day in 1746, sending 200 of his
monks out in a line 1 mile long.
Once aligned, Nollet hooked up a Leyden jar to the
end of the line and all the monks started swearing,
contorting, or otherwise reacting simultaneously to
the electric shock. A successful experiment: an
electrical signal can travel a mile and it does so
quickly.
Charles-François de Cisternay Du Fay
(1698-1739)
Du Fay discovered two types of electric
charge and was the first to suggest that
electricity consisted of two fluids:
"vitreous" (from the Latin for "glass"), or
positive, electricity; and "resinous," or
negative, electricity, and recognized that
similar fluids repel, and dissimilar
attract.
Benjamin Franklin (1706-1790)
Benjamin Franklin invents the theory of
one-fluid electricity in which one of
Nollet's fluids exists and the other is just
the absence of the first. He proposes the
principle of conservation of charge and
calls the fluid that exists and flows
``positive''.
This
educated
guess
ensures that undergraduates will always
be confused about the direction of
current flow. He also discovers that
electricity can act at a distance in
situations where fluid flow makes no
sense.
Negative,Positive,
What’s the Difference???
The two ‘opposite’ charges may as well have
been called the ying and the yang. All that is
important to know is that they are different
beasts, and that opposites attract, and likes
repel…
Charles Augustin de Coulomb
(1736-1806)
Coulomb developed a theory
of attraction and repulsion
between bodies of the same
and opposite electrical charge.
He demonstrated an inverse
square law for such forces
and went on to examine
perfect
conductors
and
dielectrics. He also is credited
with creating the torsion
balance.
14.1 Electrostatic Interactions
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Electrostatic interactions
• If you rub two balloons
the same way with a wool
cloth, they will attract the
wool but repel each
other.
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Observational experiment
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Observational experiment
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Observational experiment
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Observational experiment
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Observational experiment
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More History
• Over time the new property acquired by the
materials caused by rubbing came to be known
as electric charge
• Objects that interact with each other because
they are charged are said to exert electrical
force on each other
• When the objects are at rest, the force is called
ELECTROSTATIC FORCE
• Static is because the objects are not moving
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Electrostatic interactions
1. Materials rubbed against each other acquire
electric charge.
2. Two objects with the same type of charge repel
each other.
3. Two objects with opposite types of charge
attract each other.
4. Two objects made of different materials rubbed
against each other acquire opposite charges.
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Electrostatic interactions
6. Sometimes more vigorous rubbing leads to a
greater force exerted by the rubbed objects on
each other.
7. The magnitude of the force that the charged
objects exert on each other increases when the
distance between the objects decreases.
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Conceptual Exercise 14.1
• Take two 9-inch-long pieces of transparent tape and
place them sticky side down on a plastic, glass, or
wooden tabletop. Now pull on one end of each tape to
remove them from the table. Bring the pieces of tape
near each other. They repel each other, as shown in the
figure. Can we explain the repulsion of the tapes as an
electric interaction?
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Charged objects attract uncharged objects
• Everyday observations show that uncharged lightweight
objects, such as small bits of paper that have not been
rubbed against anything, are attracted to charged objects.
• WHY?????
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Observational experiment
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Observational experiment
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Observational experiment
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Observational experiment
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Charged objects attract uncharged objects
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14.2 Explanation for
Electrostatic Interactions
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Historical models for electric charge
• Fluid models of electric charge (B. Franklin)
– Too much electric fluid in an object makes it
positively charged and too little makes it
negatively charged.
• Particle model of electric charge (JJ Thompson)
– Electric charge is carried by microscopic
particles. Removing or adding these particles
to an object changes the charge of the object.
• How could we test these models?
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The Millikan Oil Drop Experiment
Proved Particle Model of Electric Charge
1.Air was ionized with x-rays (ionized
given lots of electrons)
2. Oil drop picked up electrons from the
air as they moved.
3. Adjusted charge on the plates to
counter act drag, mg and Electrical
Force.
4. Adjusted electric charge on plates to
keep the drop velocity of the oil droplets
constant. If oil droplet charge changed
adjusted the plate charge to maintain
constant velocity.
4. Measurements showed that the electrical charge of each oil droplet changed
by multiples of some discrete unit of electrical charge.
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Contemporary model for electric charge
• Two objects start as neutral—the
total electric charge of each is zero.
• During rubbing, one object gains
electrons and becomes negatively
charged.
• The other object loses an equal
number of electrons and with this
deficiency of electrons becomes
positively charged.
• Sometimes you rub nothing
happens. e- in both materials are
bound equally strong and therefore
no e- occurs.
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Electric Charge
Opposite charges attract and like charges repel. As a result
negatively charged electrons are attracted to the positive
nucleus.
Despite the great mass difference, the charge on an electron is
exactly equal in magnitude to the charge on a proton, and its
magnitude is denoted by "e."
Electric charge
• Milliken’s experiment showed us charge is a discrete
number.
• +1 charge (e+) added to -1 (e-) charge we get no charge.
• Example:
1 e+ + 1 e+ =2e+
• Milliken determined the charge of 1e- = -1.6 X 10-16C
• Example: 2e+ can be converted to coulombs by
•
−19 𝐶
+ 1.6 𝑋 10
2𝑒
𝑒+
= 3.2 𝑋 10−19 𝐶
• q is the abbreviation used for charge
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Electric charge (1 More Time)
• Electric Charge
– Electric Charge (symbol q or Q) is a property of
objects that participate in electrostatic interactions.
– Electric charge is quantized-you can only change on
object’s charge by increments, not continuously
– Electric Charge is conserved
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The Coulomb



Unit for electric charge is the coulomb
Smallest increment of charge is that of one electron
e- = -1.6 x 10-19 C or
e+=1.6 x 10-19C
Therefore a charge of 2e- can be written 2q or 2e- or in
coulombs 3.2x10-19 C. ALL SAY THE SAME THING!!!
Units of Charge
• The coulomb (selected for use with electric currents) is
actually a very large unit for static electricity. Thus, we often
encounter a need to use the metric prefixes.
1 mC = 1 x 10-6 C
1 nC = 1 x 10-9 C
1 pC = 1 x 10-12 C
Example 1
A metal sphere has a net charge of –2.4 x 10-6 C.
How many excess electrons does the sphere
contain?
GIVEN:
q = -2.4 x 10-6 C
-e = -1.6 x 10-19 C
#electrons = ???
 2.4  10
6
 1 electron 
15
C

1.5

10
electrons

19
  1.6  10 C 
Example 2
If 16 million electrons are removed from a neutral
sphere, what is the charge on the sphere in
coulombs?
1 electron:
e-
10-19
= -1.6 x
C
-19

-1.6
x
10
C
6 q  (16 x 10 e ) 

1e


+ +
+ + +
+ + + +
+ + +
+ +
q = -2.56 x 10-12 C
Since electrons are removed, the charge
remaining on the sphere will be positive.
Final charge on sphere:
q = +2.56 pC
Charge
Opposite charges attract and like charges repel. As a result
negatively charged electrons are attracted to the positive
nucleus.
Despite the great mass difference, the charge on an electron is
exactly equal in magnitude to the charge on a proton, and its
magnitude is denoted by "e."
Conceptual Exercise 14.2
• You pull your sweater and shirt off together, and then pull
them apart. You notice that they attract each other—a
phenomenon called "static" in everyday life. Explain the
mechanism behind this attraction and suggest an
experiment to test your explanation.
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14.3 Conductors and
Nonconductors (dielectrics)
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Conductors
• In metals, some electrons
can move freely
throughout the metal.
– When we bring a
positively charged rod
next to a metal bar, the
free electrons move
closer to the positively
charged rod, leaving
the other side with a
deficiency of electrons.
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Testing experiment
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Testing experiment
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Conductors
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The electroscope
• An electroscope consists of a metal ball attached to a metal rod. A
very lightweight needle-like metal rod is connected on a pivot near
the bottom of the larger rod. Used to study electrostatic interactions
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The electroscope
• The angle of deflection is related to the magnitude of the
electric charge of the electroscope.
• What would happen if I brought a positive rod near top of
the electroscope?
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Dielectrics/Insulators
• Objects that do not have free electrons or any
other charged particles that are free to move
inside. (glass, wood, other nonmetal objects)
• All electrons are tightly bound to their atoms or
molecules
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Dielectrics/Insulators/Nonconducting
Objects
• The presence of electrically charged particles
that can freely move inside conductors explains
how a charged object attracts a neutral metal
object.
• How can we explain the attraction of a neutral
nonmetal object and a charge object (like the
balloon on the wall or the pieces of paper)
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Dielectrics and Polarization
• Plastic, glass, and other nonmetal
materials do not have free electrons or
any other charged particles that are
free to move inside.
• The charge object creates a force that
acts on the tightly bound nucleus that
causes the charged nuclei components
to separate slightly by charge (More
force than the forces keeping the atom
bound together)
• When the atoms are in a polarized state
its called an electric dipole.
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Electric Dipole and Polarization
• Electric Dipole is any object that is overall
electrically neutral but has its negative and positive
charges separated
• Polarization: leads to a small accumulation of
charge on the surface of the object
• Polarization is what causes nonconducting
materials to interact with charged objects
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Polarization of conductors and dielectrics
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Electric properties of materials
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Tip
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Is the human body a conductor or a
dielectric?
• As your hand approaches a
positively charged cup, the free
electrons on the surface of your
hand and arm move toward it.
• Your body is a conductor. We
transfer electrons
• We will talk about electic shock
and sparks in a few minutes
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Grounding
• If the cup has a positive charge, negative electrons
in the ground are attracted toward the cup and
travel from the ground to the cup, causing it to
become neutral.
Earth is a
large
conductor
with infinite
amount of
electrons.
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Grounding
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Discharging by moisture in the air
• If you leave a negatively or
positively charged object
alone for a long time
interval, the object can
become neutral in part
because of the presence
of water vapor in the air.
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Properties of electric charge
• Similar to mass, momentum, and energy,
electric charge is a conserved quantity; it
changes in a predictable way in a nonisolated
system and is constant in isolated systems.
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Law of Conservation of Charge
Like other conservation laws, the law of
conservation of electric charge states that
the net charge (which is basically the sum of
the charge on each proton and electron in a
system) of an isolated system remains
constant.
Quick Overview
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What is Net Charge?
Net charge is the amount of excess charge;
a neutral object has an equal number of
electrons and protons, and therefore, no net
charge.
No Net Charge
Positive Net Charge
How Might an Object Become
Charged???
• Charging by Friction
• Charging by Contact (Insulators and
Conductors)
• Charging by Induction (Conductors Only)
?
Charging by Friction
This is called charging by
friction.
It’s basically the
same
phenomenon
that
occurs when you drag your
feet across a carpet on a dry
day, or rubbed a balloon
through
your
chair.
Electrons, NOT PROTONS,
are, with a little bit of energy,
“scraped”
off,
and
transferred.
Triboelectric Series
The Triboelectric Series is a list of materials, showing which have a greater tendency to
become positive (+) and which have a greater tendency to become negative (−). The list is
a handy tool to determine which combinations of materials create the most static electricity.
1. Higher the material in the
series the more affinity it
has to take electrons.
2. Lower materials tend to
give up electrons.
3. The larger the difference
in position the greater
the transfer of electrons.
Charging by Contact
Also, charging by conduction, it is the process of
giving an object a net electric charge by placing it in
contact with an object that is already charged. It
should be noted that it is nearly always electrons
that are exchanged.
Charging by Induction
It is possible to charge a neutral conductor without contact or
Charging by induction involves transferring charge between
two objects without them touching.
Charging by Induction (grounding wire)
• The earth has an infinite amount of electrons
• The earth will never increase or decrease
charge when indication occurs (The electorn
sink is to big to notice the few electrons
transfered during an inducition process. So
A negatively charged rod is brought near,
but does not touch the sphere. Electrons
within the sphere are repelled by the rod,
and pass through the wire to the ground,
leaving a net positive charge on the
sphere.
The electrons are being pushed
down this wire into the ground.
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Charging by Induction (grounding wire)
While the negatively charged rod remains
near the sphere, the ground is removed. Note
that there can be no more movement of
electrons since the sphere is isolated from the
ground. Electrons cannot jump the gap
between the rod and the sphere or between
the ground and the sphere.
The wire is removed,
disconnecting the
sphere from the ground.
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Charging by Induction (grounding wire)
The rod is then removed. It is
important to note that the charge on
the rod remains constant (negative).
The charge on the sphere is now
positive as it lost electrons to Earth.
Compared to the amount of free
electrons already in Earth, the
earth has gained an insignificant
amount of charge and therefore
the charge on the earth still stays
the same (neutral).
Note: If the ground were left in place, once the initially charged object was
removed, the neutral object will pass its gained charge back to the ground.
Charging by Induction
Charging by Induction
Insulators Can’t Be Charged by
Induction
As you might expect, insulators cannot
become charged by induction because
charged particles are not free to move within
an insulator.
However, if an insulator is in the midst of an
electric field, the individual molecules, while
not able to move freely, may orient
themselves so that there is a polarization of
charge.
What is Charge Polarization??
An unpolarized atom.
With an external electric
field, the center of electron
cloud shifts to the left, or
polarizes.
Charge Polarization
Charge Polarization
Neutral objects may be a attracted to
charged
objects
through
charge
polarization:
Charge Polarization
The Electroscope One More Time!!!
14.4 Coulombs Force Law
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Electric charge
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Coulomb's force law
• In 1785, Charles Coulomb determined the
relationship between distance and magnitude of
charges, and the force between charges.
• The experimental apparatus Coulomb used is
called a torsion balance.
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Coulomb's data
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Coulomb's data
• The data shows: reduce 1 charge by ½ the force
reduces by an ½
• Reduce a charge by ¼ force reduced by ¼
• Increase the distance by 2, the forces is reduced
by ¼.
• Reduce both charges by ½ force reduces by ¼
• What is the relationship!!!!
F ∝ q 1q 2
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and F∝1/r2
Coulomb's law
Like charges repel, opposites attract.
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Tip
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Gravitational and Electric Force
1.
2.
3.
4.
5.
Gravitational force depends on mass of the objects
Electric force depends on the charge of the objects
Gravitational force is always attractive
Electrical force attractive or repulsive
Proportionality constants are much different
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Gravitational and Electric Force
Compare the gravitational force to the electrical force exerted byt the
proton on the electron in an hydrogen atom
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Comparing the magnitude of the electric
force to the gravitational force
• Consider a proton and an electron in a hydrogen atom. They are
separated by about 10–10 m.
• The electric force between the two objects is 2.3 x 10–8 N.
• The gravitational force between the two objects is 1.0 x 10–47 N.
• The electric force between these objects is about 2 x 1039 times
greater than the gravitational force!
• The earth gravitational pull on the e- is 18 orders of magnitude greater
than the gravitation force exerted by the proton but….it’s still 22
orders of magnitude less than the electrical force
• This why Physics confidently ignore gravitational forces when dealing
with atomic size particles.
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Tip
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Solving Electric Force Problems
• Superimposition of Electrical Forces
•
Follow this procedure:
•
1. Assume all charges, other than the one that the initial net force is being
calculated for, are immobile - this will allow the determination of the direction of
the individual initial forces.
•
2. Draw a free body diagram for each charge, using the fact that opposite
charges attract and like charges repel.
•
3. Use Coulomb's Law to find the magnitude of each force.
•
4. Sum the forces, taking into account that they are vectors with direction and
magnitudes. Use the free body diagrams to assign signs to the forces - if they
point to the right, they are positive; if they point to the left, they are negative.
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• Force Labeling Convention
– F12 is the force that Q1 exerts on Q2.
– F13 is the force that Q1 exerts on Q3.
– F23 is the force that Q2 exerts on Q3.
–
–
–
–
Note that by the application of Newton's Third Law:
F12 = - F21
F13 = - F31
F23 = - F32
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• A positive charge Q1 = 25 μC is located at a point x1 = -8 m, a negative
charge Q2 = -10 μC is located at a point x2 = 0 m and a positive charge Q3
= 15 μC is located at a point x3 = 4 m.
• a. Draw free body diagrams for the electric force acting on Q1, Q2 and Q3.
b. Find the magnitude and direction of the net force on Q2.
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Conceptual Exercise 14.3
• Two small aluminum foil balls of equal mass,
A and B, have electric charges +q and +3q,
respectively. If the balls are suspended by
equal-length strings from the same point, will
one string hang at a greater angle from the
vertical than the other? Justify your answer.
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Quantitative Exercise 14.4
• Three identical metal spheres A, B, and C are on
separate insulating stands. You charge sphere
A with charge +q. Then you touch sphere B to
sphere A, and separate them by distance d.
– Write an expression for the electric force that
the spheres exert on each other.
• You now take sphere C, touch it to sphere A, and
then remove sphere C. You then separate
spheres A and B by a distance d/2.
– Write an expression for the magnitude of the
force that spheres A and B exert on each other.
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Quantitative Exercise 14.4
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Example 1
A –5 mC charge is placed 2 mm from a +3 mC charge. Find the
force between the two charges.
Draw and label
givens on figure:
-5 mC
q
-
F
r
+3 mC
q’
+
2 mm
kqq ' (9 x 10
F 2 
r
9 Nm2
C2
)(5 x 10 C)(3 x 10 C
-6
-6
(2 x 10-3m)2
F = 3.38 x 104 N;
Attraction
Note: Signs are used ONLY to determine force direction.
Example 2
Example 4. Three charges, q1 = +8 mC, q2 = +6 mC
and q3 = -4 mC are arranged as shown below. Find the
resultant force on the –4 mC charge due to the others.
+6 mC 3 cm q
3
- -4 mC
q2 +
4 cm
q1
5 cm
+
53.1o
+8 mC
Hint: Draw a free body
diagram
F2
q3
- -4 mC
53.1o
F1
Example 2
kq1q3
F1  2 ;
r1
kq2 q3
F2  2
r2
(9 x 109 )(8 x 10-6 )(4 x 10-6 )
F1 
(0.05 m) 2
(9 x 109 )(6 x 10-6 )(4 x 10-6 )
F2 
(0.03 m) 2
+6 mC 3 cm q
3
- -4 mC
q2 + F2
4 cm F1
q1
F1x = -(115 N) Cos 53.1o = - 69.2 N
+
F2x = -240 N; F2y = 0
F1y = -(115 N) Sin 53.1o = - 92.1 N
Rx = – 69.2 N – 240 N = -309 N
Ry = -69.2 N – 0 = -69.2 N
Resultant Force: R = 317 N, at 77.4 S of W
5 cm
53.1o
+8 mC
Example 14.5
• Metal spheres on insulating stands have the
following electric charges: qA = +2.0 x 10–9 C,
qB = +2.0 x 10–9 C, and qC = –4.0 x 10–9 C. The
spheres are placed at the corners of an equilateral
triangle whose sides have length d = 1.0 m, with qC
at the top of the triangle. What is the magnitude of
the total (net) electric force that spheres A and B
exert on sphere C?
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Summary
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Summary
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Summary
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Summary
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