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 attractive. A positive net force equals a repulsive force, and a negative net force is attractive. This relation is known as Coulomb's law.
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. 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 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.
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 × 109 N*m2/C2. 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 × 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 10-10m. 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 Q1 and Q2= +1.60 × 10-19 C
mass of the electron = 9.11 × 10-31 kg k = 8.99 × 109 N*m2/C2
d = 10-10 m 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:
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.
Row / Separation Distance / Electrostatic Force1 / 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, 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
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 non-moving 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
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.