Students
know the strength of the electric force between two objects increases
with charge and decreases with distance. I/S
In physics, a charge may also be known as an electric charge, electrical
charge, or electrostatic charge and symbolized with either letters
e or q, which represents the quantity of a charge of a single particle
possessing more or fewer electrons than protons. Electric charge is
a fundamental property which determines the electromagnetic interaction
between subatomic particles. Electrically charged particles are affected
by and produce electromagnetic fields. This interaction that occurs
between a moving charge and the electromagnetic field is the foundation
of the electromagnetic force, which is one of the four fundamental
forces.
An electric charge is a trait of a subatomic particle, which becomes
quantized when expressed as a multiple of an elementary charge (e).
In atoms, an electron carries a negative elementary or unit charge;
whereas the proton carries a positive elementary or unit charge. Both
charges are equal and opposite of one another. This is an elemental
physical constant and units of an electric charge are in atomic units.
Charged particles with identical sign repel one another, whilst opposite
sign charged particles attract. This is illustrated quantitatively
in Coulomb’s Law, which states the quantity of the repelling
force is proportional to the product of the two charges, and decreases
proportionality to the square of the distance.
Elementary Charge
When two objects possessing an electric charge are brought near each
other, an electrostatic force is created between them. An electrostatic
force is the resultant of an electrostatic field which surrounds any
object that is charged. Thus, the electric field strength at any given
distance from an object is directly proportional to the amount of
charge on the object. Yet, in close proximity to any object having
a fixed electric charge, the electric field strength dwindles in proportion
to the square of the distance from the object; also known as the inverse
square law.
To get some general information about the inverse square law, go
to
http://hyperphysics.phyastr.gsu.edu/hbase/forces/isq.html
An electrical charge occurs whenever the number of protons in the
nucleus of an atom differs from the number of electrons surrounding
that nucleus. If there are more electrons than protons, the atom will
have a negative charge. If there are fewer electrons than protons,
the atom will have a positive charge. For example, charging something
can be compared to removing bricks from a road and putting them on
a sidewalk: There are exactly as many “holes” in the road
as there are bricks on the sidewalk.
This is alike, but opposite in polarity to the electrical charge carried
by the proton. A particle, atom, or object with a negative charge
encompasses a negative electric polarity; a particle, atom, or object
with a positive charge encompasses a positive electric polarity. Fundamentally,
if electrical charges are of identical polarity, the electrostatic
force is repulsive. If the electrical charges are of opposite polarity,
the electrostatic force is attractive. A positive net force equals
a repulsive force, and a negative net force is attractive. This relation
is known as Coulomb's law.
Example 1: One charge of 2.0 C is 1.5m away from a –3.0 C charge. Determine the force they exert
on each other.
The negative sign just means that one charge is positive, the other is negative, so there is an
attractive force between them. 


For more information about electrical charges, go to
http://library.thinkquest.org/10796/ch11/ch11.htm
The Law of Conservation of Charge says that charge is neither created
nor destroyed. In every event, whether macro to microscopic, the principle
of conservation of charge applies. Any object that is electrically
charged has an excess or deficiency of some whole number of electrons
 electrons cannot be fractioned. Therefore, the charge of an object
is a wholenumber multiple of the charge of the single electron. In
essence, the quantity of charge accepted by an atom is always a multiple
of the elementary charge; an electrical charge carried by a single
electron or a single proton.
Coulomb of Charge
The net charge of an object consisting of atoms is equivalent to the
arithmetic summation, with the consideration of polarity, of the charges
of all the atoms combined. The unit of an electrical charge quantity
in the International System of Units is the Coulomb. One Coulomb (1
C) is equal to approximately 6.24 x 10^{18} elementary charges.
Therefore, an elementary charge is approximately 1.60 x 10^{19} C. One Coulomb is roughly equal to the amount of charge that passes
through a 100W light bulb in one second. In the real world, it is
not uncommon for objects to hold charges of many Coulombs.
Electrical Forces
The interaction between charged objects is a noncontact force, which
diminishes rapidly with distance. Every electrical force involves
at least two charged objects and a distance between these objects.
For example, twolike charged balloons repel each other and the strength
of their repulsive force can be altered by changing three variables.
The first measure of charge on one of the balloons will affect the
strength of the repulsive force. The greater the charge is on a balloon,
the greater its repulsive force. The second measure of charge on the
second balloon will also affect the strength of repulsive force. Gently
rub the two balloons with animal fur, students should notice that
they will repel a bit. Now, rub the two balloons together energetically,
increasing the charge and the repulsive force. Lastly, the distance
between the two balloons will have momentous and apparent effect upon
the repulsive force. The electrical force is noticeably strongest
when the balloons are closest together. Simply stated, decreasing
the distance between the two balloons, greatly increases the electrical
force. The magnitude of the electrical force and the distance between
the two balloons is understood to be inversely related.
To learn more about electrical forces, go to
http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html
Coulomb’s Law
Recall from Newton’s law of gravitation that gravitational force
between two objects of mass m_{1} and mass m_{2} is proportional
to the product of the masses and inversely proportional to the square
of the distance d between them
where G is the universal gravitational
constant. The electrical force between any two objects obeys a similar
inversesquare relationship with distance.
This relationship was discovered by eighteenth century French physicist
Charles Coulomb (1736 – 1806). Coulomb demonstrated that a force
is also proportional to the product of the charges. His work, the
unit of electrical charge is named after him and interestingly one
of the first people to begin designing the metric system.
To learn more about Charles Coulomb, go to
http://wwwhistory.mcs.stand.ac.uk/Biographies/Coulomb.html
Coulomb being familiar with how like charges repel, he observed
using the torsion balance, the spheres on the torsion balance twist
away from the other balls.
By identifying the following: distance between the balls, the force
needed to twist them or torque, and the charges on the balls, he was
able to construct a formula. In equation form, Coulomb's law can be
stated as
which means the electrical force between two charged objects is directly
proportional to the product of the quantity of charge on the objects
and inversely proportional to the square of the separation distance
between the two objects. It provides an accurate portrayal of the
force between two objects when the objects act as point charges.
For example, a charged conducting sphere interacts with other charged
objects in a behavior that eludes its charge to be located at its
center. While the charge is uniformly broadened across the surface
of the sphere, the center of charge can be deemed as the center of
the sphere. The sphere acts as a point charge with its excess charge
located at its center. Since Coulomb's law applies to point charges,
the distance d in the equation is the distance between the centers
of charge for both objects; not the distance between their nearest
surfaces (http://www.glenbrook.k12.il.us/gbssci/Phys/Class/estatics/u8l3b.html).
Coulomb’s Law Constant (k)
and Newton’s Gravitational Force (G)
The proportionality constant k in Coulomb’s Law is
analogous to G in Newton’s Law of Universal Gravitation.
However, instead of being a minute number like G, the electrical
proportionality constant k is a very large number; k = 9.0 x 10^{9} N*m^{2}/C^{2}. Here is a comparison
of Newton’s Law of Universal Gravitation and Coulomb’s
Law.
Contrast this with the gravitational force of attraction between two
masses of 1 kg, each a distance of 1 m apart: 6.67 x 10^{11} N.
This is an exceptionally small force. For the force to be 1 N, two
masses 1 m apart would have to be about 122,000 kilograms each. Gravitational
forces between ordinary objects are significantly too small to be
exposed except in experiments. Electrical forces between ordinary
objects are large enough to be commonly experienced.
Example Problem #1:
Calculate the electrostatic force exerted on an electron by a proton
at a distance of 10^{10}m. Compare this with the gravitational force
between the two. In the light of your comparison, discuss why gravity,
and not electromagnetism, is the fundamental force most apparent to
us on a macroscopic scale.
G: Identify known values in variable form.
(Click Image to Enlarge)
O: Identify the unknown value
A: Substitute and solve
From Coulomb’s law, the force between an electron and a proton
at a distance of 10^{10} m has a magnitude of
(Click Image to Enlarge)
For comparison, the magnitude of the gravitational force between
the same two particles is
(Click Image to Enlarge)
Inverse Square Law
The relationship between electrostatic force and distance can be further
portrayed as an inverse square relationship. By means of careful observations,
an electrostatic force between two point charges may vary inversely
with the square of the distance between two charges. Understanding
this inverse proportionality will allow the students to develop a
better awareness about how to use the equation in terms of as a guide;
a guide towards thinking about how variation in one quantity may affect
another quantity. The inverse square law is a simple recipe for many
algebraic problemsolving.
The inverse square relationship between electrostatic force and separation
distance is illustrated in the table below.
Row 
Separation Distance 
Electrostatic Force 
1 
20.0 cm 
0.1280 N 
2 
40.0 cm 
0.0320 N 
3 
60.0 cm 
0.0142 N 
4 
80.0 cm 
0.0080 N 
5 
100.0 cm 
0.0051 N 


Example Problem #2:
Two charged objects have a repulsive force of .080 N. If the distance
separating the objects is doubled, then what is the new force?
Answer: 0.020 N
Explanation: The electrostatic force is inversely related
to the square of the separation distance. So if d is two times larger,
then F is four times smaller  that is, onefourth the original
value. Onefourth of 0.080 N is 0.020 N.
To learn more about the Inverse Square Law, go to http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/estatics/u8l3c.html
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Content Benchmark P.12.B.3
Students know the strength of the electric force between two objects
increases with charge and decreases with distance. I/S
Common misconceptions associated with this benchmark:
1. Students have the incorrect idea that a charged
object can only affect other charged objects.
The fundamental principle of charge interactions states that a negativelycharged
object will attract its opposite charge, a positivelycharged object.
Oppositelycharged objects will exert an attractive force upon one
another. On the other hand, two objects of like charges will repel
each other. Thus, the interaction between two likecharged objects
is repulsive, whilst the interaction between two oppositelycharged
objects is attractive. Yet, what type of interaction occurs between
a charged object and a neutral object? An object charged whether positively
or negatively will nonetheless have an attractive relationship with
an object that has a net neutral charge. On the macroscopic scale,
the charge may be neutral in an object, but on the microscopic scale
the charge distribution within an object may not be neutral. Therefore,
positivelycharged objects coupled with neutral objects would attract
one another; as well as negativelycharged objects coupled with neutral
objects.
To learn more about this misconception, go to
http://www.glenbrook.k12.il.us/gbssci/phys/class/estatics/u8l1c.html
2. Students incorrectly believe that electric forces
result from “static” or nonmoving elements.
When we introduce student to electrical force, we often use the terms
“static electricity” or “electrostatic force.”
This term may be confusing to students because in common language,
static means nonmoving. However, in electrical force applications,
electrostatics is a term used for studying electric fields and forces
that are not associated with electromotive forces, or more commonly,
electromagnetic forces in closed circuits. Electrostatic forces may
involve movement of charge, as is the case when one gets a jolt when
their finger comes close to a metal door knob on a dry winter day.
But, this type of charge movement is not within a closed circuit,
similar to the alternating current networks that provide commercial
electrical power.
To learn more about misconceptions related to the electrical force,
go to
http://amasci.com/emotor/stmiscon.html#one
3. Students incorrectly assume that gravitational
forces are stronger than electrostatic forces.
Gravitational forces portray similar characteristics to that of electrical
forces; an inverse reliance between two point masses. Gravitational
forces differ from electrostatic forces upon the basis of always being
attractive, never repulsive. Gravitational forces which engage massive
objects such as forces maintaining Earth’s nearly circular orbit
around the Sun or the effects experienced by gravity on ourselves
may easily construe students to create a misconception regarding the
strength between the two forces. Electrical forces may be repulsive,
zero, or attractive depending on the charges of the particles. The
electrical force governs the activity of the electrons in atoms. Yet,
on a macroscopic scale, the gravitational force may exceed the magnitude
of the electrical force. In view of the fact that most macroscopic
objects are neutral, they possess an equal number of protons and electrons.
Therefore, the attractive force which exists between the electrons
in a single body and the protons in another body is canceled by the
repulsive force between the electrons in the both bodies. Yet, if
a student were to stand at arm’s length from someone and each
student had one percent more electrons than protons, the force of
electrostatic repulsion between them would be adequate to lift a weight
equal to that of the entire Earth.
To learn more about the relative strength between the gravitational
and electrostatic forces, go to: http://www.physics.northwestern.edu/Lab/DOWNLOAD/electrostatics.pdf
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Content Benchmark P.12.B.3
Students know the strength of the electric force between two objects increases with charge and decreases with distance. I/S
Sample Test Questions
1^{st} Item Specification: Explain how electric forces change when the distance between the two charges changes and/or when the magnitude of the charges changes.
Depth of Knowledge Level 1
 Which of the following statements is true about the magnitude of force between two objects each holding an electrical charge of +3 x 10^{3} Coulombs?
 The hotter the objects are, the greater the electrical force between them.
 The closer the objects are, the greater the electrical force between them.
 The faster the objects move, the greater the electrical force between them.
 The colder the objects are, the greater the electrical force between them.
 Analyze the diagram below, which shows two electrically charged objects. Use this diagram to answer the following question.
Which of the following would cause a decrease in the magnitude of the electrical force between the two objects?
 Decrease the temperature of the objects.
 Increase the temperature of the objects.
 Decrease the distance between the objects.
 Increase the distance between the objects.
 Analyze the diagram below showing two charged objects. Use this diagram to answer the following question.
Which of the following would cause an increase in the electrical force between the two objects?
 Increase the distance between the two objects.
 Make the charge on one object positive.
 Make one object hotter than the other.
 Increase the charge on one of the objects.
 Which of the following pairs of variables affect the magnitude of the electrical force between two electrically charged objects?
 The kind of charge on the objects and the distance between them.
 The temperature of the charged objects and the distance between them.
 The material that the charged objects are made of and the
distance between them.
 The magnitude of the charge on the objects and the distance between them.
 An electrically charged object is surrounded by an electric field. An object with a like charge is brought into the electric field and the two objects repel. Use the following two diagrams to answer the question below.
Which of the following statements is true about the magnitude of the electric force between two electrically charged objects in Model A compared to those in Model B?
 The magnitude of the force is greater in Model A because the magnitude of
the charges are greater.
 The magnitude of the force is greater in Model B because the magnitude of
the charges are greater.
 The magnitude of the force is lower in Model B because the magnitude of
the charges are greater.
 The magnitude of the force in Models A and B are equal because the
distances between the charges are equal.
 An electrically charged object is surrounded by an electric field. An object with a like charge is brought into the electric field and the two objects repel. Use the following two diagrams to answer the question below.
Which of the following statements is true about the magnitude of the electric force between two electrically charged objects in Model A compared to those in Model B?
 The magnitude of the force is greater in Model B because the magnitude of
the charges is greater.
 The magnitude of the force is greater in Model A because the magnitude of
the charges is greater.
 The magnitude of the force is greater in Model B because the distanc
between the charges is greater.
 The magnitude of the force is greater in Model A because the distance
between the charges is less.
Depth of Knowledge Level 2
 The diagrams below each show two electrically charged objects separated by the distances indicated. Use the two diagrams to answer the question below.
Which of the following statements correctly compares the magnitude of the electrical force between the electrically charged objects in Diagrams I and II?
 The magnitude of the force between the objects in Diagram I is greater than the magnitude of the force between the objects in Diagram II.
 The magnitude of the force between the objects in Diagram II is greater than the magnitude of the force between the objects in Diagram I.
 The magnitude of the force between the objects in Diagram I is equal to the magnitude of the force between the objects in Diagram II.
 There is not enough information to compare the magnitude of the force between the objects in Diagram I and the objects in Diagram II.
 The magnitude of electric force between two electrically charged objects will
 increase as the level of charge on the objects increases and increase as distance between them increases.
 increase as the level of charge on the objects increases and decrease as the distance between them increases.
 decrease as the level of charge on the objects increases and increase as the distance between them increases.
 increase as the level of charge on the objects increases but stay the same as the distance between them increases.
 The four following diagrams below each show two electrically charged objects separated by the distances indicated. In the diagrams, “C” stands for Coulomb, which is a unit of electrical charge. Use the four diagrams to answer the following question.
In which model is the magnitude of the force of attraction between the two objects STRONGEST?
 Diagram I
 Diagram II
 Diagram III
 Diagram IV
 The four diagrams below each show the electrically charged objects separated by the distance indicated. Use the four diagrams to answer the following question.
In the diagrams “C” stands for Coulomb, which is a unit of electrical charge.
Identify the two Diagrams in which the magnitude of the electrical force between objects is EQUAL.
 Diagram I and Diagram II
 Diagram I and Diagram III
 Diagram II and Diagram III
 Diagram III and Diagram IV
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Content Benchmark P.12.B.3
Students know the strength of the electric force between two objects increases with charge and decreases with distance. I/S
Answers to Sample Test Questions
 B, DOK Level 1
 D, DOK Level 1
 D, DOK Level 1
 D, DOK Level 1
 B, DOK Level 2
 D, DOK Level 2
 A, DOK Level 2
 B, DOK Level 2
 A, DOK Level 1
 B, DOK Level 2
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Content Benchmark P.12.B.3
Students know the strength of the electric force between two objects
increases with charge and decreases with distance. I/S
Intervention Strategies and Resources
The following is a list of intervention strategies and resources
that will facilitate student understanding of this benchmark.
1. Electricity and Magnetism – The
Electric Force
This site was created by Jerrie S. Cheek, Educational Technology Center
which provides several illustrations via multimedia animations of
online and offline activities in order to help both teacher and student
to visualize and understand electricity and magnetism.
You can access this interactive site at http://edtech.kennesaw.edu/web/electric.html
2. Introduction to E & M – Interactive
Science Simulations
This introduction to the principles of electricity and magnetism provides
an overview of static and moving charges, magnetism, creating electricity
with magnets, magnetic fields produced by electrical currents, and
a brief introduction to circuits.
To get to this applet, go to http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=29.
Once on the site, click on “Launch Gizmo” in the righthand
corner, and then begin activity.
3. Electricity and Magnetism  The Science
Spot
IPPEX (The Interactive Plasma Physics Education Experience) provides
an educational online site for students to learn about related concepts
pertinent to this benchmark. Concepts such as charged particles, electric
current, resistance, voltage, magnetism and the effects of magnetism.
The site will walk the students through the online module using macromedia’s
shockwave software. It includes vivid graphics along with detailed
explanations of electricity and magnetism. Students will often use
the right arrow in order to navigate their way through the module.
To begin the module, go to http://ippex.pppl.gov/interactive/.
Once on the site click on “Electricity and Magnetism”
and begin the interactive IPPEX module http://ippex.pppl.gov/interactive/electricity/.
4. Static Electricity  42Explore
42explore provides numerous online sites for students to learn more
about electricity. One in particular was developed by BrainPOP.com;
Electricity. Students will need to choose Static Electricity in order
to begin their interactive learning. Students will be able to discover
and learn about electric charges, where they come from, and what they
can attract or repel. They will review the parts of an atom and how
some parts move around as well as what makes a good conductor or insulator
for electrons or electricity. BrainPOP is an educational site that
does require a subscription and offers a free 14 day trial.
The various challenges can be accessed at http://42explore.com/electric.htm
And the BrainPOP – Electricity activity is located at http://www.brainpop.com/search/index.weml?keyword=electricity
5. Coulomb’s Force – Interactive
Science Simulations
This site enhances the understanding of the principles of Coulomb’s
Law by allowing the students to place fixed charges on a twodimensional
grid. Before firing a moving charge, the velocity can be adjusted.
The velocity of the charge will be acted on and manipulated by the
Coulomb forces.
To get to this applet, go to http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=16.
Once on the site, click on “Launch Gizmo” in the righthand
corner, and then begin activity.
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