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Performance 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
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.phy-astr.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
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attractive. A positive net force equals a repulsive force, and a negative net force is
attractive. This relation is known as Coulomb's law.
Figure 1: Electric charges (from http://www.studyphysics.ca/30/charging.pdf)
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 whole-number 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 × 1018 elementary charges.
Therefore, an elementary charge is approximately 1.60 × 10-19 C. One Coulomb is
roughly equal to the amount of charge that passes through a 100-W 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 non-contact force, which diminishes rapidly
with distance. Every electrical force involves at least two charged objects and a distance
between these objects. For example, two-like 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.
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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.
Figure 2: Example Problem (from http://www.studyphysics.ca/30/coulomb.pdf)
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 m1 and mass m2 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
inverse-square 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://www-history.mcs.st-and.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.
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Figure 3: Torsion Balance (from http://www.studyphysics.ca/30/coulomb.pdf)
)
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
Figure 4: Coulomb’s Law (from http://library.thinkquest.org/10796/ch11/ch11.htm)
)
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 × 109 N*m2/C2. Here is a
comparison of Newton’s Law of Universal Gravitation and Coulomb’s Law.
Small Magnitude
Universal Constant
Large Magnitude
Universal Constant
Product of Masses
Attractive or Repulsive
Product of Charges
Only Attractive
Both Are Inverse-Square laws
Figure 5: Comparison (from http://www.studyphysics.ca/30/coulomb.pdf)
)
Contrast this with the gravitational force of attraction between two masses of 1 kg, each a
distance of 1 m apart: 6.67 × 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.
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Example Problem #1:
Calculate the electrostatic force exerted on an electron by a proton at a distance of 10-10m.
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.
mass of the proton = 1.67 × 10-27 kg
mass of the electron = 9.11 × 10-31 kg
d = 10-10 m
Q1 and Q2= +1.60 × 10-19 C
k = 8.99 × 109 N*m2/C2
G = 6.67 × 10-11 N*m2/kg2
O: Identify the unknown value
Fe =?
Fg =?
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
Fe = [(8.99 × 109 N*m2/C2)*(1.60 × 10-19 C)2] / [(10-10 m) 2] = 2.30 × 10-8 N, attractive
For comparison, the magnitude of the gravitational force between the same two particles
is
Fg = [(6.67 × 10-11 N*m2/kg2)*(9.11 × 10-31 kg)* (1.67 × 10-27 kg)]/ [(10-10 m) 2] =
1.01 × 10-47 N, attractive,
The Coulomb force is therefore larger by a factor of:
2.30 × 10-8 N
≈ 2.27 × 1039 N
1.01 ×
10-47
N
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 problem-solving.
The inverse square relationship between electrostatic force and separation distance is
illustrated in the table below.
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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
Figure 5: Inverse Square Law (from
http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l3c.html)
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, one-fourth the
original value. One-fourth 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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Performance 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 negatively-charged object
will attract its opposite charge, a positively-charged object. Oppositely-charged 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 like-charged objects is
repulsive, whilst the interaction between two oppositely-charged 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, positively-charged objects coupled with
neutral objects would attract one another; as well as negatively-charged 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 non-moving. 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
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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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Performance 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. The Q in Coulomb’s law equation stands for _________.
a. mass of a charged object
b. the current of a charged object
c. the distance between the charged objects
d. charge of charged object
2. The symbol r in Coulomb's law equation represents the distance from ___.
a.
b.
c.
d.
A to B
A to D
B to F
C to E
3. An electron and a small charged object are separated by a certain distance
resulting in specific repulsive force. What happens to that repulsive force if
the distance between the electron and the charged object is doubled?
a. The repulsive force will be one-fourth as much
b. The repulsive force will be one-half as much
c. The repulsive force will stay the same.
d. The repulsive force will be twice as much.
4. A small charged object and a proton are separated by a certain distance
resulting in specific attractive force. What happens to that attractive force if
the charge on the small object is doubled?
a. The attractive force will be one-half as much
b. The attractive force will remain the same.
c. The attractive force will be twice as much.
d. The attractive force will be four times as much.
5. Two small charged objects repel each other with a force F when separated by
a distance d. If the charge on one object is reduced to one-fourth of its original
value and the distance between them is reduced to d/2, the force becomes?
a. 2F
b. F
c. F/2
d. F/4
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Performance 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
1.
2.
3.
4.
5.
(d)
(c)
(a)
(c)
(b)
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Performance 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





Static Electricity –
http://www.mos.org/sln/toe/staticmenu.html
What will a Charged Balloon Attract http://www.mos.org/sln/toe/balloon.html
Dancing Paper Bunnies - http://www.mos.org/sln/toe/staticmenu.html
Electrical Safety - http://www.miamisci.org/af/sln/frankenstein/safety.html
The Electric Force http://www.colorado.edu/physics/2000/waves_particles/wavpart2.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&ResourceI
D=29. Once on the site, click on “Launch Gizmo” in the right-hand 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
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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 two-dimensional 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&ResourceI
D=16. Once on the site, click on “Launch Gizmo” in the right-hand corner, and then
begin activity.
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