Electrical Charges, Conservation of Charge, and Transfer of Charge, Static Electricity | Physics

Learning objectives

Teacher Support

The learning objectives in this section will help your students master the following standards

(5) The student knows the nature of forces in the physical world. The student is expected to:
- (C) describe and calculate how the magnitude of the electrical force between two objects depends on their charges and the distance between them; and
- (E) characterize materials as conductors or insulators based on their electrical properties.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled Electric Charge as well as the following standards:

(5) The student knows the nature of forces in the physical world. The student is expected to:
- (C) describe and calculate how the magnitude of the electrical force between two objects depends on their charges and the distance between them; and
- (E) characterize materials as conductors or insulators based on their electrical properties.

Section Key Terms

conduction	conductor	electron	induction
insulator	law of conservation of charge	polarization	proton

Electric Charge

You may know someone who has an electric personality, which usually means that other people are attracted to this person. This saying is based on electric charge, which is a property of matter that causes objects to attract or repel each other. Electric charge comes in two varieties, which we call positive and negative. Like charges repel each other, and unlike charges attract each other. Thus, two positive charges repel each other, as do two negative charges. A positive charge and a negative charge attract each other.

How do we know there are two types of electric charge? When various materials are rubbed together in controlled ways, certain combinations of materials always result in a net charge of one type on one material and a net charge of the opposite type on the other material. By convention, we call one type of charge positive and the other type negative. For example, when glass is rubbed with silk, the glass becomes positively charged and the silk negatively charged. Because the glass and silk have opposite charges, they attract one another like clothes that have rubbed together in a dryer. Two glass rods rubbed with silk in this manner will repel one another, because each rod has positive charge on it. Similarly, two silk cloths rubbed in this manner will repel each other, because both cloths have negative charge. Figure_18_01_Posnegcharg shows how these simple materials can be used to explore the nature of the force between charges.

View original figure (external; image not reproduced in this text edition)

Original figure description: This figure has three parts. Part a: It shows a glass rod suspended from its middle by a string and a nearby silk cloth held from its upper edge by a hand. The glass rod has a series of plus signs, and the silk cloth has many minus signs. There are several faded images of the glass rod and a downward pointing arrow, suggesting the rod's movement toward the cloth. The lower edge of the cloth bends toward the rod. Part b: It shows two glass rods near each other, each with a series of plus signs. One rod is held from one end by a hand, and the other rod is suspended from its middle by a string. There are several faded images of the suspended rod and an upward pointing arrow, suggesting its movement away from the handheld rod. Part c: It shows two silk cloths held by hand near each other, each with a number of minus signs. The lower edges of the cloths curve away from each other.

A glass rod becomes positively charged when rubbed with silk, whereas the silk becomes negatively charged. (a) The glass rod is attracted to the silk, because their charges are opposite. (b) Two similarly charged glass rods repel. (c) Two similarly charged silk cloths repel.

It took scientists a long time to discover what lay behind these two types of charges. The word electric itself comes from the Greek word elektron for amber, because the ancient Greeks noticed that amber, when rubbed by fur, attracts dry straw. Almost 2,000 years later, the English physicist William Gilbert proposed a model that explained the effect of electric charge as being due to a mysterious electrical fluid that would pass from one object to another. This model was debated for several hundred years, but it was finally put to rest in 1897 by the work of the English physicist J. J. Thomson and French physicist Jean Perrin. Along with many others, Thomson and Perrin were studying the mysterious cathode rays that were known at the time to consist of particles smaller than the smallest atom. Perrin showed that cathode rays actually carried negative electrical charge. Later, Thomson’s work led him to declare, “I can see no escape from the conclusion that [cathode rays] are charges of negative electricity carried by particles of matter.”

It took several years of further experiments to confirm Thomson’s interpretation of the experiments, but science had in fact discovered the particle that carries the fundamental unit of negative electrical charge. We now know this particle as the electron.

Atoms, however, were known to be electrically neutral, which means that they carry the same amount of positive and negative charge, so their net charge is zero. Because electrons are negative, some other part of the atom must contain positive charge. Thomson put forth what is called the plum pudding model, in which he described atoms as being made of thousands of electrons swimming around in a nebulous mass of positive charge, as shown by the left-side image of Figure_18_01_pp. His student, Ernest Rutherford, originally believed that this model was correct and used it (along with other models) to try to understand the results of his experiments bombarding gold foils with alpha particles (i.e., helium atoms stripped of their electrons). The results, however, did not confirm Thomson’s model but rather destroyed it! Rutherford found that most of the space occupied by the gold atoms was actually empty and that almost all of the matter of each atom was concentrated into a tiny, extremely dense nucleus, as shown by the right-side image of Figure_18_01_pp. The atomic nucleus was later found to contain particles called protons, each of which carries a unit of positive electric charge.Protons were later found to contain sub particles called quarks, which have fractional electric charge. But that is another story that we leave for subsequent physics courses.

View original figure (external; image not reproduced in this text edition)

Original figure description: This figure has two drawings, side by side. The drawing on the left shows a large blue sphere, one-eighth of which has been cut out. A number of small red spheres are on the surface of the blue sphere and within the cut-away part of the blue sphere. Also, a number of faded red spheres lie within the blue sphere. The drawing on the right shows four ellipses evenly spaced around a common center, with a small blue sphere in each ellipse. Near the top is the word “Electrons,” with two lines connecting that word to two of the blue spheres. The common center contains a clump of four small red spheres and five small gray spheres. Near the top is another word, “Nucleus,” with a line connecting that word to the clump of spheres at the center.

The left drawing shows Thompson’s plum-pudding model, in which the electrons swim around in a nebulous mass of positive charge. The right drawing shows Rutherford’s model, in which the electrons orbit around a tiny, massive nucleus. Note that the size of the nucleus is vastly exaggerated in this drawing. Were it drawn to scale with respect to the size of the electron orbits, the nucleus would not be visible to the naked eye in this drawing. Also, as far as science can currently detect, electrons are point particles, which means that they have no size at all!

Protons and electrons are thus the fundamental particles that carry electric charge. Each proton carries one unit of positive charge, and each electron carries one unit of negative charge. To the best precision that modern technology can provide, the charge carried by a proton is exactly the opposite of that carried by an electron. The SI unit for electric charge is the coulomb (abbreviated as “C”), which is named after the French physicist Charles Augustin de Coulomb, who studied the force between charged objects. The proton carries $+ 1.602 \times 10^{−19} C.$ and the electron carries $−1.602 \times 10^{−19} C,$ . The number n of protons required to make +1.00 C is

n = 1.00 C \times \frac{1 proton}{1.602 \times 10^{- 19} C} = 6.25 \times 10^{18} protons.

The same number of electrons is required to make −1.00 C of electric charge. The fundamental unit of charge is often represented as e. Thus, the charge on a proton is e, and the charge on an electron is −e. Mathematically, $e = + 1.602 \times 10^{−19} C .$

Measuring the Fundamental Electric Charge

The American physicist Robert Millikan (1868–1953) and his student Harvey Fletcher (1884–1981) were the first to make a relatively accurate measurement of the fundamental unit of charge on the electron. They designed what is now a classic experiment performed by students. The Millikan oil-drop experiment is shown in Figure_18_01_Oildrop. The experiment involves some concepts that will be introduced later, but the basic idea is that a fine oil mist is sprayed between two plates that can be charged with a known amount of opposite charge. Some oil drops accumulate some excess negative charge when being sprayed and are attracted to the positive charge of the upper plate and repelled by the negative charge on the lower plate. By tuning the charge on these plates until the weight of the oil drop is balanced by the electric forces, the net charge on the oil drop can be determined quite precisely.

View original figure (external; image not reproduced in this text edition)

Original figure description: This figure is a two-part drawing. One part consists of two circular plates held parallel to each other, with a beam of light shining between them. Each plate has a wire attached to it. The upper plate, with a tiny hole at its center, is marked with a plus sign, and the lower plate is marked with a minus sign. A small spray bottle, labeled “Atomizer,” is held by a hand near and just above the upper plate. The hand squeezes a bulb on the Atomizer, and a spray labeled “Oil” emerges just above the upper plate. The beam of light emerges from a source labeled “Bright light.” The drawing includes a telescope-like device aimed for viewing between the circular plates. The second part of the drawing, located slightly below the first part, shows an edge-on view of the two plates. A downward pointing arrow connects the plates in the first part of the drawing to those in the second part. In the latter drawing, four vertical blue arrows point from the upper to the lower plate, and the arrow on the extreme right is labeled as E. A gray sphere between the two plates is labeled “Oil droplet.” A short red arrow, labeled F subscript E, points from the sphere to the upper plate, and another short red arrow, labeled w, points from the sphere to the lower plate.

The oil-drop experiment involved spraying a fine mist of oil between two metal plates charged with opposite charges. By knowing the mass of the oil droplets and adjusting the electric charge on the plates, the charge on the oil drops can be determined with precision.

Millikan and Fletcher found that the drops would accumulate charge in discrete units of about $−1.59 \times 10^{−19} C,$ which is within 1 percent of the modern value of $−1.60 \times 10^{−19} C.$ Although this difference may seem quite small, it is actually five times greater than the possible error Millikan reported for his results!

Because the charge on the electron is a fundamental constant of nature, determining its precise value is very important for all of science. This created pressure on Millikan and others after him that reveals some equally important aspects of human nature.

First, Millikan took sole credit for the experiment and was awarded the 1923 Nobel Prize in physics for this work, although his student Harvey Fletcher apparently contributed in significant ways to the work. Just before his death in 1981, Fletcher divulged that Millikan coerced him to give Millikan sole credit for the work, in exchange for which Millikan promoted Fletcher’s career at Bell Labs.

Another great scientist, Richard Feynman, points out that many scientists who measured the fundamental charge after Millikan were reluctant to report values that differed much from Millikan’s value. History shows that later measurements slowly crept up from Millikan’s value until settling on the modern value. Why did they not immediately find the error and correct the value, asks Feynman. Apparently, having found a value higher than the much-respected value found by Millikan, scientists would look for possible mistakes that might lower their value to make it agree better with Millikan’s value. This reveals the important psychological weight carried by preconceived notions and shows how hard it is to refute them. Scientists, however devoted to logic and data they may be, are apparently just as vulnerable to this aspect of human nature as everyone else. The lesson here is that, although it is good to be skeptical of new results, you should not discount them just because they do not agree with conventional wisdom. If your reasoning is sound and your data are reliable, the conclusion demanded by the data must be seriously considered, even if that conclusion disagrees with the commonly accepted truth.

Suppose that Millikan observed an oil drop carrying three fundamental units of charge. What would be the net charge on this oil drop?

−4.81 × 10⁻¹⁹ C
−1.602 × 10⁻¹⁹ C
1.602 × 10⁻¹⁹ C
4.81 × 10⁻¹⁹ C

Like and Unlike Charges

This activity investigates the repulsion and attraction caused by static electrical charge.

Adhesive tape
Nonconducting surface, such as a plastic table or chair

Instructions

Procedure for Part (a)

Prepare two pieces of tape about 4 cm long. To make a handle, double over about 0.5 cm at one end so that the sticky side sticks together.
Attach the pieces of tape side by side onto a nonmetallic surface, such as a tabletop or the seat of a chair, as shown in Figure_18_01_scotcha_img(a).
Peel off both pieces of tape and hang them downward, holding them by the handles, as shown in Figure_18_01_scotcha_img(b). If the tape bends upward and sticks to your hand, try using a shorter piece of tape, or simply shake the tape so that it no longer sticks to your hand.
Now slowly bring the two pieces of tape together, as shown in Figure_18_01_scotcha_img(c). What happens?

View original figure (external; image not reproduced in this text edition)

Original figure description: This image has three parts. Part a shows two pieces of sticky tape attached to the edge of an arc-shaped object, with someone's fingers near the end of one tape. Part b shows someone's fingers lifting one tape piece away from the arc-shaped object, while the other tape piece remains attached to the object. Part c shows a left hand and a right hand, each holding a piece of tape from one end. Two short red arrows, each starting from the free end of a piece of tape, point toward each other.

Procedure for Part (b)

Stick one piece of tape on the nonmetallic surface, and stick the second piece of tape on top of the first piece, as shown in Figure_18_01_scotchb_img(a).
Slowly peel off the two pieces by pulling on the handle of the bottom piece.
Gently stroke your finger along the top of the second piece of tape (i.e., the nonsticky side), as shown in Figure_18_01_scotchb_img(b).
Peel the two pieces of tape apart by pulling on their handles, as shown in Figure_18_01_scotchb_img(c).
Slowly bring the two pieces of tape together. What happens?

View original figure (external; image not reproduced in this text edition)

Original figure description: This image has three parts. Part a shows two pieces of sticky tape, with one stuck over the other, and with the lower tape attached to the edge of an arc-shaped object. The two tapes are slightly separated from each other at one end. In part b, someone's hand holds the two pieces of tape from the end where they are separated, while a finger touches the other end. Part c shows two hands pulling the two pieces of tape apart.

In step 4, why did the two pieces of tape repel each other? In step 9, why did they attract each other?

Like charges attract, while unlike charges repel each other.
Like charges repel, while unlike charges attract each other.
Tapes having positive charge repel, while tapes having negative charge attract each other.
Tapes having negative charge repel, while tapes having positive charge attract each other.

Conservation of Charge

Because the fundamental positive and negative units of charge are carried on protons and electrons, we would expect that the total charge cannot change in any system that we define. In other words, although we might be able to move charge around, we cannot create or destroy it. This should be true provided that we do not create or destroy protons or electrons in our system. In the twentieth century, however, scientists learned how to create and destroy electrons and protons, but they found that charge is still conserved. Many experiments and solid theoretical arguments have elevated this idea to the status of a law. The law of conservation of charge says that electrical charge cannot be created or destroyed.

The law of conservation of charge is very useful. It tells us that the net charge in a system is the same before and after any interaction within the system. Of course, we must ensure that no external charge enters the system during the interaction and that no internal charge leaves the system. Mathematically, conservation of charge can be expressed as

q_{i n i t i a l} = q_{f i n a l} .

where $q_{initial}$ is the net charge of the system before the interaction, and $q_{final,}$ is the net charge after the interaction.

What is the missing charge?

Figure_18_01_Conservati shows two spheres that initially have +4 C and +8 C of charge. After an interaction (which could simply be that they touch each other), the blue sphere has +10 C of charge, and the red sphere has an unknown quantity of charge. Use the law of conservation of charge to find the final charge on the red sphere.

Solution

Equating $q_{initial}$ and $q_{final}$ and solving for $q_{red}$ gives

\begin{matrix} q_{initial} & = & q_{final} \\ + 12 C & = & + 10 C + q_{red.} \\ + 2 C & = & q_{red .} \end{matrix}

The red sphere has +2 C of charge.

View original figure (external; image not reproduced in this text edition)

Original figure description: This figure has two rows, one below the other. The upper row is labeled “Before interaction”, and the lower row is labeled “After interaction”. Each row has a blue sphere and a red sphere next to each other. In the upper row, the blue sphere is marked as “plus 4 C” and the red sphere is marked as “plus 8 C”. In the lower row, the blue sphere is marked as “plus 10 C” and the red sphere is marked as “q subscript red = ?”

Two spheres, one blue and one red, initially have +4 C and +8 C of charge, respectively. After the two spheres interact, the blue sphere has a charge of +10 C. The law of conservation of charge allows us to find the final charge

q_{red}

on the red sphere.

Discussion

Like all conservation laws, conservation of charge is an accounting scheme that helps us keep track of electric charge.

Practice Problems

Which equation describes conservation of charge?

q_initial = q_final = constant
q_initial = q_final = 0
q_initial − q_final = 0
q_initial/q_final = constant

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Conductors and Insulators

Materials can be classified depending on whether they allow charge to move. If charge can easily move through a material, such as metals, then these materials are called conductors. This means that charge can be conducted (i.e., move) through the material rather easily. If charge cannot move through a material, such as rubber, then this material is called an insulator.

Most materials are insulators. Their atoms and molecules hold on more tightly to their electrons, so it is difficult for electrons to move between atoms. However, it is not impossible. With enough energy, it is possible to force electrons to move through an insulator. However, the insulator is often physically destroyed in the process. In metals, the outer electrons are loosely bound to their atoms, so not much energy is required to make electrons move through metal. Such metals as copper, silver, and aluminum are good conductors. Insulating materials include plastics, glass, ceramics, and wood.

The conductivity of some materials is intermediate between conductors and insulators. These are called semiconductors. They can be made conductive under the right conditions, which can involve temperature, the purity of the material, and the force applied to push electrons through them. Because we can control whether semiconductors are conductors or insulators, these materials are used extensively in computer chips. The most commonly used semiconductor is silicon. Figure_18_01_classifica shows various materials arranged according to their ability to conduct electrons.

View original figure (external; image not reproduced in this text edition)

Original figure description: Thirteen materials are arranged in a horizontal series, according to their ability to conduct electric charge. The materials, ranging from the least conductive on the left to the most conductive on the right, are: “Dry air”, “Dry wood”, “Rubber8, “Glass”, “Silicon”, “Germanium”, “Sea water”, “Carbon”, “Mercury”, “Iron”, “Aluminum”, “Copper”, and “Silver”. Above the names of the materials is a long, horizontal arrow pointing rightward. The arrow is broken in two places, producing three segments. The left segment, labeled “Insulators”, is above the materials Dry air to Glass; the middle segment, labeled “Semiconductors”, is above Silicon and Germanium; and the right segment, labeled “Conductors”, is above the materials Sea water to Silver. Below the names of the materials are numbers that give the resistivity of each material in ohm-meter.

Materials can be arranged according to their ability to conduct electric charge. The slashes on the arrow mean that there is a very large gap in conducting ability between conductors, semiconductors, and insulators, but the drawing is compressed to fit on the page. The numbers below the materials give their resistivity in Ω•m (which you will learn about below). The resistivity is a measure of how hard it is to make charge move through a given material.

What happens if an excess negative charge is placed on a conducting object? Because like charges repel each other, they will push against each other until they are as far apart as they can get. Because the charge can move in a conductor, it moves to the outer surfaces of the object. Figure_18_01_Conducting(a) shows schematically how an excess negative charge spreads itself evenly over the outer surface of a metal sphere.

What happens if the same is done with an insulating object? The electrons still repel each other, but they are not able to move, because the material is an insulator. Thus, the excess charge stays put and does not distribute itself over the object. Figure_18_01_Conducting(b) shows this situation.

View original figure (external; image not reproduced in this text edition)

Original figure description: This figure has two parts, each consisting of a sphere. In Part a, there are minus signs distributed relatively evenly around the sphere. In Part b, there are minus signs concentrated in the upper right quadrant of the face of the sphere.

(a) A conducting sphere with excess negative charge (i.e., electrons). The electrons repel each other and spread out to cover the outer surface of the sphere. (b) An insulating sphere with excess negative charge. The electrons cannot move, so they remain in their original positions.

Transfer and Separation of Charge

Most objects we deal with are electrically neutral, which means that they have the same amount of positive and negative charge. However, transferring negative charge from one object to another is fairly easy to do. When negative charge is transferred from one object to another, an excess of positive charge is left behind. How do we know that the negative charge is the mobile charge? The positive charge is carried by the proton, which is stuck firmly in the nucleus of atoms, and the atoms are stuck in place in solid materials. Electrons, which carry the negative charge, are much easier to remove from their atoms or molecules and can therefore be transferred more easily.

Electric charge can be transferred in several manners. One of the simplest ways to transfer charge is charging by contact, in which the surfaces of two objects made of different materials are placed in close contact. If one of the materials holds electrons more tightly than the other, then it takes some electrons with it when the materials are separated. Rubbing two surfaces together increases the transfer of electrons, because it creates a closer contact between the materials. It also serves to present fresh material with a full supply of electrons to the other material. Thus, when you walk across a carpet on a dry day, your shoes rub against the carpet, and some electrons are removed from the carpet by your shoes. The result is that you have an excess of negative charge on your shoes. When you then touch a doorknob, some of your excess of electrons transfer to the neutral doorknob, creating a small spark.

Touching the doorknob with your hand demonstrates a second way to transfer electric charge, which is charging by conduction. This transfer happens because like charges repel, and so the excess electrons that you picked up from the carpet want to be as far away from each other as possible. Some of them move to the doorknob, where they will distribute themselves over the outer surface of the metal. Another example of charging by conduction is shown in the top row of Figure_18_01_Transferel. A metal sphere with 100 excess electrons touches a metal sphere with 50 excess electrons, so 25 electrons from the first sphere transfer to the second sphere. Each sphere finishes with 75 excess electrons.

The same reasoning applies to the transfer of positive charge. However, because positive charge essentially cannot move in solids, it is transferred by moving negative charge in the opposite direction. For example, consider the bottom row of Figure_18_01_Transferel. The first metal sphere has 100 excess protons and touches a metal sphere with 50 excess protons, so the second sphere transfers 25 electrons to the first sphere. These 25 extra electrons will electrically cancel 25 protons so that the first metal sphere is left with 75 excess protons. This is shown in the bottom row of Figure_18_01_Transferel. The second metal sphere lost 25 electrons so it has 25 more excess protons, for a total of 75 excess protons. The end result is the same if we consider that the first ball transferred a net positive charge equal to that of 25 protons to the first ball.

View original figure (external; image not reproduced in this text edition)

Original figure description: This figure consists of two rows, and each row is divided into three columns labeled as “Before contact”, “At contact”, and “After contact”. Each column contains two small spheres. First consider the top row: In the “Before contact” column, the left sphere is labeled “100 e superscript minus”, the right sphere is labeled “50 e superscript minus”. In the “At contact” column, the left sphere is labeled “75 e superscript minus”, the right sphere is labeled “50 e superscript minus”. An arrow points from the left sphere to the right one and is labeled “25 e superscript minus”. In the “After contact” column, the left sphere is labeled “75 e superscript minus”, the right sphere is labeled “75 e superscript minus”. Next consider the bottom row: In the “Before contact” column, the left sphere is labeled “100 p superscript plus”, the right sphere is labeled “50 p superscript plus”. In the “At contact” column, the left sphere is labeled “100 p superscript plus”, the right sphere is labeled “75 p superscript plus”. An arrow points from the right sphere to the left one and is labeled “25 e superscript minus”. In the “After contact” column, the left sphere is labeled “75 p superscript plus”, the right sphere is labeled “75 p superscript plus”.

In the top row, a metal sphere with 100 excess electrons transfers 25 electrons to a metal sphere with an excess of 50 electrons. After the transfer, both spheres have 75 excess electrons. In the bottom row, a metal sphere with 100 excess protons receives 25 electrons from a ball with 50 excess protons. After the transfer, both spheres have 75 excess protons.

In this discussion, you may wonder how the excess electrons originally got from your shoes to your hand to create the spark when you touched the doorknob. The answer is that no electrons actually traveled from your shoes to your hands. Instead, because like charges repel each other, the excess electrons on your shoe simply pushed away some of the electrons in your feet. The electrons thus dislodged from your feet moved up into your leg and in turn pushed away some electrons in your leg. This process continued through your whole body until a distribution of excess electrons covered the extremities of your body. Thus your head, your hands, the tip of your nose, and so forth all received their doses of excess electrons that had been pushed out of their normal positions. All this was the result of electrons being pushed out of your feet by the excess electrons on your shoes.

This type of charge separation is called polarization. As soon as the excess electrons leave your shoes (by rubbing off onto the floor or being carried away in humid air), the distribution of electrons in your body returns to normal. Every part of your body is again electrically neutral (i.e., zero excess charge).

The phenomenon of polarization is seen in Figure_18_00_Plasticsli. The child has accumulated excess positive charge by sliding on the slide. This excess charge repels itself and so becomes distributed over the extremities of the child’s body, notably in his hair. As a result, the hair stands on end, because the excess negative charge on each strand repels the excess negative charge on neighboring strands.

Polarization can be used to charge objects. Consider the two metallic spheres shown in Figure_18_01_induction. The spheres are electrically neutral, so they carry the same amounts of positive and negative charge. In the top picture (Figure_18_01_induction(a)), the two spheres are touching, and the positive and negative charge is evenly distributed over the two spheres. We then approach a glass rod that carries an excess positive charge, which can be done by rubbing the glass rod with silk, as shown in Figure_18_01_induction(b). Because opposite charges attract each other, the negative charge is attracted to the glass rod, leaving an excess positive charge on the opposite side of the right sphere. This is an example of charging by induction, whereby a charge is created by approaching a charged object with a second object to create an unbalanced charge in the second object. If we then separate the two spheres, as shown in Figure_18_01_induction(c), the excess charge is stuck on each sphere. The left sphere now has an excess negative charge, and the right sphere has an excess positive charge. Finally, in the bottom picture, the rod is removed, and the opposite charges attract each other, so they move as close together as they can get.

View original figure (external; image not reproduced in this text edition)

Original figure description: This figure has four parts, each consisting of a pair of spheres adjacent to each other. Each sphere is on a short pedestal, and all spheres and pedestals are equal in size. In Parts (a) and (b), the pair of spheres are touching each other, but in Parts (c) and (d), the pair of spheres are slightly separated from each other. In Part (a), there is no charge on either sphere. In Part (b), a rod marked with plus signs is shown close to the left sphere, which in turn has minus signs along its left edge. The right sphere has plus signs along its right edge. Part (c) is similar to Part (b), except for separation between the pair of spheres. In Part (d), minus signs are aligned along the right edge of the left sphere, and plus signs are aligned along the left edge of the right sphere. There is no rod in Part (d).

(a) Two neutral conducting spheres are touching each other, so the charge is evenly spread over both spheres. (b) A positively charged rod approaches, which attracts negative charges, leaving excess positive charge on the right sphere. (c) The spheres are separated. Each sphere now carries an equal magnitude of excess charge. (d) When the positively charged rod is removed, the excess negative charge on the left sphere is attracted to the excess positive charge on the right sphere.

Create a Spark in a Science Fair

Van de Graaff generators are devices that are used not only for serious physics research but also for demonstrating the physics of static electricity at science fairs and in classrooms. Because they deliver relatively little electric current, they can be made safe for use in such environments. The first such generator was built by Robert Van de Graaff in 1931 for use in nuclear physics research. Figure_18_01_VDG shows a simplified sketch of a Van de Graaff generator.

Van de Graaff generators use smooth and pointed surfaces and conductors and insulators to generate large static charges. In the version shown in Figure_18_01_VDG, electrons are “sprayed” from the tips of the lower comb onto a moving belt, which is made of an insulating material like, such as rubber. This technique of charging the belt is akin to charging your shoes with electrons by walking across a carpet. The belt raises the charges up to the upper comb, where they transfer again, akin to your touching the doorknob and transferring your charge to it. Because like charges repel, the excess electrons all rush to the outer surface of the globe, which is made of metal (a conductor). Thus, the comb itself never accumulates too much charge, because any charge it gains is quickly depleted by the charge moving to the outer surface of the globe.

View original figure (external; image not reproduced in this text edition)

Original figure description: This is a diagram in which two small circles are arranged vertically and are labeled “Upper roller” and “Lower roller”. The two circles are connected by a band labeled “Rubber belt”. A comb-shaped structure touches each circle, and these structures are labeled “Upper comb” and “Lower comb”. The upper circle is in the center of a larger circle labeled “Metal sphere”, and the lower circle is enclosed in a rectangle. A bent line connects the upper comb to the larger circle, and another bent line connects the lower comb to the rectangle and to the ground below the rectangle. A series of minus signs, labeled “Electrons”, is accompanied by a series of arrows, suggesting the flow of electrons from within the rectangle and the lower circle to the upper circle and then to the larger circle.

Van de Graaff generators transfer electrons onto a metallic sphere, where the electrons distribute themselves uniformly over the outer surface.

Van de Graaff generators are used to demonstrate many interesting effects caused by static electricity. By touching the globe, a person gains excess charge, so his or her hair stands on end, as shown in Figure_18_01_VDGman. You can also create mini lightning bolts by moving a neutral conductor toward the globe. Another favorite is to pile up aluminum muffin tins on top of the uncharged globe, then turn on the generator. Being made of conducting material, the tins accumulate excess charge. They then repel each other and fly off the globe one by one. A quick Internet search will show many examples of what you can do with a Van de Graaff generator.

View original figure (external; image not reproduced in this text edition)

Original figure description: This is a photograph of a man touching the large sphere of a Van de Graaff generator, causing his hair to stand on end. The picture also shows two observers, one of whom has extended his right arm toward the man touching the generator.

The man touching the Van de Graaff generator has excess charge, which spreads over his hair and repels hair strands from his neighbors. (credit: Jon “ShakataGaNai” Davis)

Why don’t the electrons stay on the rubber belt when they reach the upper comb?

The upper comb has no excess electrons, and the excess electrons in the rubber belt get transferred to the comb by contact.
The upper comb has no excess electrons, and the excess electrons in the rubber belt get transferred to the comb by conduction.
The upper comb has excess electrons, and the excess electrons in the rubber belt get transferred to the comb by conduction.
The upper comb has excess electrons, and the excess electrons in the rubber belt get transferred to the comb by contact.

Balloons and Static Electricity

Original figure description: This simulation allows you to explore concepts of static electricity such as charge transfer, attraction, repulsion, and induced charge.

This simulation allows you to observe negative charge accumulating on a balloon as you rub it against a sweater. You can then observe how two charged balloons interact and how they cause polarization in a wall.

Click the reset button, and start with two balloons. Charge a first balloon by rubbing it on the sweater, and then move it toward the second balloon. Why does the second balloon not move?

The second balloon has an equal number of positive and negative charges.
The second balloon has more positive charges than negative charges.
The second balloon has more negative charges than positive charges.
The second balloon is positively charged and has polarization.

Charging Ink Droplets

Electrically neutral ink droplets in an ink-jet printer pass through an electron beam created by an electron gun, as shown in Figure_18_01_inkdrop. Some electrons are captured by the ink droplet, so that it becomes charged. After passing through the electron beam, the net charge of the ink droplet is $q_{ink drop} = −1 \times 10^{−10} C$ . How many electrons are captured by the ink droplet?

View original figure (external; image not reproduced in this text edition)

Original figure description: Six small purple spheres, each marked as “e superscript minus”, are arranged vertically and labeled as “electrons”. The three lowest spheres are enclosed in a rectangle, the fourth one above them is crossing the upper edge of the rectangle, and the two uppermost spheres are outside the rectangle. An arrow next to the two uppermost spheres is pointing upward, suggesting the direction of movement of the purple spheres. A much larger black sphere, labeled “Ink droplet”, is above and to the left of the column of purple spheres, and an arrow pointing toward the right suggests the direction of movement of the black sphere.

Electrons from an electron gun charge a passing ink droplet.

Solution

The number n of electrons captured by the ink droplet are

n = \frac{q_{ink drop}}{q_{e^{-}}} = \frac{- 1 \times 10^{- 10} C}{- 1.602 \times 10^{- 19} C} = 6 \times 10^{8} .

Discussion

This is almost a billion electrons! It seems like a lot, but it is quite small compared to the number of atoms in an ink droplet, which number about $10^{16} .$ Thus, each extra electron is shared between about $10^{16} / (6 \times 10^{8}) \approx 10^{7}$ atoms.

Practice Problems

How many protons are needed to make 1 nC of charge? 1 nC = 10⁻⁹ C

1.6 × 10⁻²⁸
1.6 × 10⁻¹⁰
3 × 10⁹
6 × 10⁹

Source link

Check Your Understanding

How many types of electric charge exist?

one type
two types
three types
four types

Which are the two main electrical classifications of materials based on how easily charges can move through them?

conductor and insulator
semiconductor and insulator
conductor and superconductor
conductor and semiconductor

True or false—A polarized material must have a nonzero net electric charge.

true
false

Describe the force between two positive point charges that interact.

The force is attractive and acts along the line joining the two point charges.
The force is attractive and acts tangential to the line joining the two point charges.
The force is repulsive and acts along the line joining the two point charges.
The force is repulsive and acts tangential to the line joining the two point charges.

How does a conductor differ from an insulator?

Electric charges move easily in an insulator but not in a conducting material.
Electric charges move easily in a conductor but not in an insulator.
A conductor has a large number of electrons.
More charges are in an insulator than in a conductor.

True or false—Charging an object by polarization requires touching it with an object carrying excess charge.

true
false

Section Summary

Electric charge is a conserved quantity, which means it can be neither created nor destroyed.
Electric charge comes in two varieties, which are called positive and negative.
Charges with the same sign repel each other. Charges with opposite signs attract each other.
Charges can move easily in conducting material. Charges cannot move easily in an insulating material.
Objects can be charged in three ways: by contact, by conduction, and by induction.
Although a polarized object may be neutral, its electrical charge is unbalanced, so one side of the object has excess negative charge and the other side has an equal magnitude of excess positive charge.

Concept Items

Source link

True or false—A liquid can be an insulating material.

true
false

Critical Thinking

If you dive into a pool of seawater through which an equal amount of positively and negatively charged particles is moving, will you receive an electric shock?

Yes, because negatively charged particles are moving.
No, because positively charged particles are moving.
Yes, because positively and negatively charged particles are moving.
No, because equal amounts of positively and negatively charged particles are moving.

True or false—The high-voltage wires that you see connected to tall metal-frame towers are held aloft by insulating connectors, and these wires are wrapped in an insulating material.

true
false

By considering the molecules of an insulator, explain how an insulator can be overall neutral but carry a surface charge when polarized.

Inside the insulator, the oppositely charged ends of the molecules cancel each other.
Inside the insulator, the oppositely charged ends of the molecules do not cancel each other.
The electron distribution in all the molecules shifts in every possible direction, leaving an excess of positive charge on the opposite end of each molecule.
The electron distribution in all the molecules shifts in a given direction, leaving an excess of negative charge on the opposite end of each molecule.

Problems

A dust particle acquires a charge of −13 nC. How many excess electrons does it carry?

20.8 × 10⁻²⁸ electrons
20.8 × ⁻¹⁹ electrons
8.1 × 10¹⁰ electrons
8.1 × 10¹⁹ electrons

Two identical conducting spheres are charged with a net charge of +5.0 q on the first sphere and a net charge of −8.0 q on the second sphere. The spheres are brought together, allowed to touch, and then separated. What is the net charge on each sphere now?

−3.0q
−1.5q
+1.5q
+3.0q

Test Prep Multiple Choice

A neutral hydrogen atom has one proton and one electron. If you remove the electron, what will be the leftover sign of the charge?

negative
positive
zero
neutral

What is the charge on a proton?

+8.99 × 10^–9 C
−8.99 × 10^–9 C
+ 1.60 × 10^–19 C
−1.60 × 10^–19 C

True or false—Carbon is more conductive than pure water.

true
false

True or false—Two insulating objects are polarized. To cancel the polarization, it suffices to touch them together.

true
false

How is the charge of the proton related to the charge of the electron?

The magnitudes of charge of the proton and the electron are equal, but the charge of the proton is positive, whereas the charge of the electron is negative.
The magnitudes of charge of the proton and the electron are unequal, but the charge of the proton is positive, whereas the charge of the electron is negative.
The magnitudes of charge of the proton and the electron are equal, but the charge of the proton is negative, whereas the charge of the electron is positive.
The magnitudes of charge of the proton and the electron are unequal, but the charge of the proton is negative, whereas the charge of the electron is positive.

Test Prep Short Answer

Compare the mass of the electron with the mass of the proton.

The mass of the electron is about 1,000 times that of the proton.
The mass of the proton is about 1,000 times that of the electron.
The mass of the electron is about 1,836 times that of the proton.
The mass of the proton is about 1,836 times that of the electron.

The positive terminal of a battery is connected to one connection of a lightbulb, and the other connection of the lightbulb is connected to the negative terminal of the battery. The battery pushes charge through the circuit but does not become charged itself. Does this violate the law of conservation of charge? Explain.

No, because this is a closed circuit.
No, because this is an open circuit.
Yes, because this is a closed circuit.
Yes, because this is an open circuit.

Source link

The students in your class count off consecutively so each student has a number. The odd-numbered students are told to act as negative charge, and the even-numbered students are told to act as positive charge. How would you organize them to represent a polarized material?

The even-numbered and odd-numbered students will be arranged one after the other.
Two even-numbered will be followed by two odd-numbered, and so on.
Even-numbered students will be asked to come to the front, whereas odd-numbered students will be asked to go to the back of the class.
Half even-numbered and odd-numbered will come to the front, whereas half even-numbered and odd-numbered will go to the back.

An ion of iron contains 56 protons. How many electrons must it contain if its net charge is +5e?

five electrons
51 electrons
56 electrons
61 electrons

Source link

A solid cube carries a charge of +25e. You measure the charge on each face of the cube and find that each face carries +3e of charge. Is the cube made of conducting or insulating material? Explain.

The cube is made of insulating material, because all the charges are on the surface of the cube.
The cube is made of conducting material, because some of the charges are inside the cube.
The cube is made of conducting material, because all the charges are on the surface of the cube.
The cube is made of insulating material, because some of the charges are inside the cube.

You have four neutral conducting spheres and a charging device that allows you to place charge q on any neutral object. You want to charge one sphere with a charge q/2 and the other three with a charge q/6 . How do you proceed?

Charge one sphere with charge q. Touch it simultaneously to the three remaining neutral spheres.
Charge one sphere with charge q. Touch it to one other sphere to produce two spheres with charge $\frac{q}{2}$ . Touch one of these spheres to one other neutral sphere.
Charge one sphere with charge q. Touch it to one other sphere to produce two spheres with charge $\frac{q}{2}$ . Touch one of these spheres simultaneously to the two remaining neutral spheres.
Charge one sphere with charge q. Touch it simultaneously to two other neutral spheres to produce three spheres with charge q/3. Touch one of these spheres to one other neutral sphere.

Test Prep Extended Response

Source link

True or false—Conservation of charge is like balancing a budget.

true
false

True or false—Although wood is an insulator, lightning can travel through a tree to reach Earth.

true
false

True or false—An eccentric inventor attempts to levitate by first placing a large negative charge on himself and then putting a large positive charge on the ceiling of his workshop. Instead, while he attempts to place a large negative charge on himself, his clothes fly off.

true
false

Glossary

conductor: material through which electric charge can easily move, such as metals
electron: subatomic particle that carries one indivisible unit of negative electric charge
induction: creating an unbalanced charge distribution in an object by moving a charged object toward it (but without touching)
insulator: material through which a charge does not move, such as rubber
law of conservation of charge: states that total charge is constant in any process
polarization: separation of charge induced by nearby excess charge
proton: subatomic particle that carries the same magnitude charge as the electron, but its charge is positive

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