Solve for the force in the preceding problem when the

Problem 60E A friend says that the reason one’s hair stands out while touching a charged Van de Graaff generator is simply that the hair strands become charged and are light enough so that the repulsion between strands is visible. Do you agree or disagree?

Problem 1R The three pairs of metal same-size spheres have different charges on their surfaces, as indicated. Each pair is brought together, allowed to touch, and then separated. Rank from greatest to least the total amount of charge on the pairs of spheres after separation.

Problem 1E At the atomic level, what is meant by saying something is electrically charged?

Problem 1P Two point charges are separated by 6 cm. The attractive force between them is 20 N. Find the force between them when they are separated by 12 cm. (Why can you solve this problem without knowing the magnitudes of the charges?)

What term is used for “electricity at rest”?

Problem 2E Why is charge usually transferred by electrons rather than by protons?

Problem 2P Suppose that the charges attracting each other in the preceding problem have equal magnitude. Rearrange Coulomb’s law and show that the magnitude of each charge is 2.8 × 10?6 C (2.8 microcoulombs).

Problem 2RQ Why does the gravitational force between Earth and Moon predominate over electrical forces?

Problem 2R Shown are three separate pairs of point charges. Assume the pairs interact only with each other. Rank the magnitudes of the force between the pairs from largest to smallest.

Problem 3E Why are objects with vast numbers of electrons normally not electrically charged?

Problem 3P Two pellets, each with a charge of 1 microcoulomb (10?6 C), are located 3 cm (0.03 m) apart. Show that the electric force between them is 10N. What would be the mass of an object that would experience this same force in Earth’s gravitational field?

Problem 4P Electronic types neglect the force of gravity on electrons. To see why, compute the force of Earth’s gravity on an electron and compare it with the force exerted on the electron by an electric field of magnitude 10,000 V/m (a relatively small field). The mass and charge of an electron are given on the inside back cover.

Problem 4E Why do clothes often cling together after tumbling in a clothes dryer?

Problem 3RQ What part of an atom is ?positively? charged and what part is ?negatively? charged?

Problem 4RQ How does the charge of one electron compare to that of another electron? How does it compare with the charge of a proton?

Why is dust attracted to a DVD wiped with a dry cloth?

Atomic physicists ignore the effect of gravity within an atom. To see why, calculate and compare the gravitational and electrical forces between an electron and a proton separated by \(10^{-10} \mathrm{~m}\). The charges and masses are given on the inside back cover.

Problem 5RQ What is normally the net charge of an atom?

Problem 7P The potential difference between a storm cloud and the ground is 100 million V. If a charge of 2 C flashes in a bolt from cloud to Earth, what is the change of potential energy of the charge?

Problem 8E When combing your hair, you scuff electrons from your hair onto the comb. Is your hair then positively or negatively charged? How about the comb?

Problem 7RQ What is meant by saying charge is ?conserved?

Problem 8P An energy of 0.1 J is stored in the metal sphere on top of a Van de Graaff generator. A spark carrying 1 microcoulomb (10?6 C) discharges the sphere. Show that the sphere’s potential relative to ground is 1 00,000 V?

Problem 8RQ What is meant by saying charge is ?quantized?

Problem 9E At some automobile toll booths, a thin metal wire protrudes from the road, making contact with cars before they reach the toll collector. What is the purpose of this wire?

Problem 9P Find the voltage change when (a) an electric field does 12 J of work on a 0.0001-C charge; (b) the same electric field does 24 J of work on a 0.0002-C charge.

Problem 9RQ What particle has exactly one quantum unit of charge?

Why are the tires for trucks carrying gasoline and other flammable fluids manufactured to be electrically conducting?

Problem 10P In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates. The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity. That is, when suspended, upward force ?qE? just equaled ?mg?. Millikan accurately measured the charges on many oil drops and found the values to be whole-number multiples of 1.6 × 10?19C—the charge of the electron. For this he won the Nobel Prize. a. If a drop of mass 1.1 × 10?14 kg remains stationary in an electric field of 1.68 × 105 N/C, what is the charge of this drop? b. How many extra electrons are on this particular oil drop (given the presently known charge of the electron)?

How does one coulomb of charge compare with the charge of a single electron?

Problem 11E An electroscope is a simple device consisting of a metal ball that is attached by a conductor to two thin leaves of metal foil protected from air disturbances in a jar, as shown. When the ball is touched by a charged body, the leaves that normally hang straight down spread apart. Why? (Electroscopes ate useful not only as charge detectors but also for measuring the quantity of charge: the more charge transferred to the ball, the more the leaves diverge.)

Problem 11RQ How is Coulomb’s law similar to Newton’s law of gravitation? How is it different?

Problem 12E The leaves of a charged electroscope collapse in time. At higher altitudes, they collapse more rapidly. Why is this true? (?Hint:? The existence of cosmic rays was first indicated by this observation.)

Problem 12RQ Why are metals good conductors both of heat and of electricity?

Problem 13E Is it necessary for a charged body actually to touch the ball of the electroscope for the leaves to diverge? Defend your answer.

Problem 13RQ Why are materials such as glass and rubber good insulators?

Problem 14E Strictly speaking, when an object acquires a positive charge by the transfer of electrons, what happens to its mass? What happens to its mass when it acquires a negative charge? (Think small!)

Problem 14RQ How does a ?semiconductor? differ from a ? onductor? or an? nsulator?

Problem 15E Strictly speaking, will a penny be slightly more massive if it has a negative charge or a positive charge? Explain.

Problem 15RQ What is a transistor composed of, and what are some of its functions?

Problem 16E A crystal of salt consists of electrons and positive ions. How does the net charge of the electrons compare with the net charge of the ions? Explain.

How does the flow of current differ in a superconductor compared with the flow in ordinary conductors?

How can you charge an object negatively with only the help of a positively charged object?

What happens to electrons in any charging process?

Problem 18E It is relatively easy to strip the outer elections from a heavy atom like that of uranium (which then becomes a uranium ion), but it is very difficult to remove the inner electrons. Why do you suppose this is so?

Problem 18RQ Cite an example of something charged by friction.

Problem 19E When one material is rubbed against another, electrons jump readily from one to the other but protons do not. Why is this? (Think in atomic terms.)

Problem 19RQ Cite an example of something charged by contact.

Problem 20E If electrons were positive and protons were negative, would Coulomb’s law be written the same or differently?

Problem 20RQ Give an example of something charged by induction.

Problem 21E What does the inverse-square law tell you about the relationship between force and distance?

Problem 21RQ What is the primary purpose of a lightning rod?

Problem 22E The 5000 billion billion (5 × 1021) freely moving electrons in a penny repel one another. Why don’t they fly out of the penny?

Problem 22RQ How does an electrically ?polarized? object differ from an electrically ?charged? object?

Problem 23RQ What is an electric dipole?

Problem 24E How does the magnitude of electric force compare between a pair of charged particles when they are brought to half their original distance of separation? To one-quarter their original distance? To 4 times their original distance? (What law guides your answers?)

Problem 23E How does the magnitude of electrical force between a pair of charged particles change when the particles are moved half as far apart? One-third as far apart?

Problem 24RQ How is the magnitude of an electric field defined? Its direction?

Problem 25E When you double the distance between a pair of charged particles, what happens to the force between them? Does it depend on the sign of the charges? What law defends your answer?

Problem 25RQ Why is there no electric field at the center of a charged spherical conductor?

Problem 26E When you double the charge on only one of a pair of particles, what effect does this have on the force between them? Does the effect depend on the sign of the charge?

Problem 26RQ When charges mutually repel and distribute themselves on the surface of conductors, what becomes of the electric field inside the conductor?

Problem 27E When you double the charge on both particles in a pair, what effect does this have on the force between them? Does it depend on the sign of the charge?

Problem 27RQ How much energy is given to each coulomb of charge that flows through a 1.5-V battery?

Problem 28E The proportionality constant ?k? in Coulomb’s law is huge in ordinary units, whereas the proportionality constant ?G? in Newton’s law of gravitation is tiny. What does this indicate about the relative strengths of these two forces?

Problem 28RQ A balloon may easily be charged to several thousand volts. Does that mean it has several thousand joules of energy? Explain.

Problem 29E How do electrical field lines indicate the strength of an electric field?

Where is the energy stored in a capacitor?

Problem 30E How is the direction of an electric field indicated with electrical field lines?

Problem 30RQ What is the magnitude of the electric field inside the dome of a charged van de Graaff generator?

Problem 31E Suppose that the strength of the electric field about an isolated point charge has a certain value at a distance of 1 m. How will the electric field strength compare at a distance of 2 m from the point charge? What law guides your answer?

Problem 32E In the phenomenon of superconductivity, what happens to electrical resistance at low temperatures?

Problem 33E Measurements show that there is an electric field surrounding Earth. Its magnitude is about 100 N/C at Earth’s surface, and it points inward toward Earth’s center. From this information, can you state whether Earth is negatively or positively charged?

Why are lightning rods normally at a higher elevation than the buildings they protect?

Problem 35E Why are metal-spiked shoes not a good idea for golfers on a stormy day?

Problem 36E If you are caught outdoors in a thunderstorm, why should you not stand under a tree? Can you think of a reason why you should not stand with your legs far apart? Or why lying down can be dangerous? (?Hint:? Consider electric potential difference.)

Problem 37E If a large enough electric field is applied, even an insulator will conduct an electric current, as is evident in lightning discharges through the air. Explain how this happens, taking into account the opposite charges in an atom and how ionization occurs.

Problem 38E If you rub an inflated balloon against your hair and place it against a door, by what mechanism does it stick? Explain.

How can a charged atom (an ion) attract a neutral atom?

Problem 39E When a car is moved into a painting chamber, a mist of paint is sprayed around its body. When the body is given a sudden electric charge and mist is attracted to it— presto—the car is quickly and uniformly painted. What does the phenomenon of polarization have to do with this?

How will the accelerations of the proton and the electron in the preceding problem compare?

Problem 43E How will the directions of travel compare for the electron and proton in the previous problem?

Problem 41E If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare?

Problem 44E Two pieces of plastic, a full ring and a half ring, have the same radius and charge density. Which electric field at the center has the greater magnitude? Defend your answer.

Problem 45E Why is the magnitude of the electric field zero midway between identical point charges?

Problem 46E Imagine a proton at rest a certain distance from a negatively charged plate. It is released and collides with the plate. Then imagine the similar case of an electron at rest the same distance away from a positively charged plate. In which case will the moving particle have the greater speed when the collision occurs? Why?

Problem 47E A gravitational field vector points toward Earth; an electric field vector points toward an electron. Why do electric field vectors point away from protons?

Problem 48E By what specific means do the bits of fine threads align in the electric fields shown in Figure 22.19?

Problem 49E Suppose that a metal file cabinet is charged. How will the charge concentration at the corners of the cabinet compare with the charge concentration on the flat parts of the cabinet?

Problem 51E When released, what will be the kinetic energy of the 1-C charge of the previous problem if it flies past its starting position?

Problem 50E If you were to expend 10 J of work to push a 1-C charge against an electric field, what would be its change of voltage?

Problem 52E You are not harmed by contact with a charged metal ball, even though its voltage may be very high. Is the reason similar to why you are not harmed by the greater-than-1000°C sparks from a Fourth-of-July sparkler? Defend your answer in terms of the energies that are involved.

Problem 53E What is the voltage at the location of a 0.0001-C charge that has an electric potential energy of 0.5 J (both measured relative to the same reference point)?

Problem 54E Why is it safe to remain inside a car during a lightning storm?

Problem 55E How do the charges on opposing plates of a capacitor compare?

Problem 56E In order to store more energy in a parallel-plate capacitor whose plates differ by a fixed voltage, what change would you make in the plates?

Problem 58E An electron volt, eV, is a unit of energy. Which is larger, a GeV or a MeV?

Problem 57E Why is it dangerous to touch the terminals of a high-voltage capacitor even after the charging circuit is turned off?

Problem 59E Would you feel any electrical effects if you were inside the charged sphere of a Van de Graaff generator? Why or why not?

Problem 6E When you remove your wool suit from the dry cleaner’s garment bag, the bag becomes positively charged. Explain how this occurs.

Problem 7E Plastic wrap becomes electrically charged when pulled from its box. As a result, it is attracted to objects such as food containers. Does the wrap stick better to plastic containers or to metal containers?

Problem 6RQ What is a positive ion? A negative ion?

Problem 6P A droplet of ink in an industrial ink-jet printer carries a charge of 1.6 × 10?10 C and is deflected onto paper by a force of 3.2 × 10?4 N. Show that the strength of the electric field to produce this force is 2 million N/C.

What term is used for “electricity at rest”?

Why does the gravitational force between Earth and the Moon predominate over electrical forces?

Which part of an atom is positively charged, and which part is negatively charged?

How does the charge of one electron compare with the charge of another electron? How does it compare with the charge of a proton?

What is most commonly the net charge of an atom?

What is a positive ion? A negative ion?

What is meant by conservation of charge?

What is meant by saying that charge is quantized?

Name one particle that has exactly one quantum unit of charge.

How does one coulomb of charge compare with the charge of a single electron?

How is Coulomb’s law similar to Newton’s law of gravitation? How is it different?

Why are metals good conductors both of heat and of electricity?

Why are materials such as glass and rubber good insulators?

How does a semiconductor differ from a conductor or an insulator?

What is a transistor composed of, and what are some of its functions?

How does the flow of current differ in a superconductor compared with the flow in ordinary conductors?

What happens to electrons in any charging process?

What kind of charging occurs when you slide your body across a plastic surface?

What kind of charging occurs during thunderstorms?

What is the primary purpose of a lightning rod?

In terms of net charge, how does an electrically polarized object differ from an electrically charged object?

What is an electric dipole?

Give two examples of common force fields.

Give an example of a common electric dipole.

Why is there no electric field at the center of a charged spherical conductor?

When charges mutually repel and distribute themselves on the surface of conductors, what becomes of the electric field inside the conductor?

How much energy is given to each coulomb of charge that flows through a 1.5-V battery?

A balloon may easily be charged to several thousand volts. Does that mean it has several thousand joules of energy? Explain.

Where is the energy stored in a capacitor?

Write a letter to Grandpa and tell him why he’d be safe in a lightning storm if he was inside an automobile.

Two point charges, each with 0.1 C of charge, are 0.1 m apart. Given that \(k=9.0\ \times\ 10^9 \ N\cdot m^2/C^2\) (the proportionality constant for Coulomb’s law), show that the force between the charges is \(9.0\ \times\ 10^9\ N\). Text Transcription: k=9.0 times 10^9 N cdot m^2 /C^2 9.0 times 10^9 N

Solve for the force in the preceding problem when the charges are twice as far apart.

Two point charges are separated by 6 cm. The attractive force between them is 20 N. Find the force between them when they are separated by 12 cm. (Why can you solve this problem without knowing the magnitudes of the charges?)

Suppose that the charges attracting each other in the preceding problem have equal magnitude. Rearrange Coulomb’s law and show that the magnitude of each charge is \(2.8 \times 10^{-6}\ C\) (2.8 microcoulombs). Text Transcription: 2.8 times 10^-6 C

Two pellets, each with a charge of 1 microcoulomb \((10^{-6}\ C)\), are located 3 cm (0.03 m) apart. Show that the electrical force between them is 10 N. What would be the mass of an object that experiences this same force in Earth’s gravitational field? Text Transcription: (10^-6 C)

Electronic types neglect the force of gravity on electrons. To see why, compute the force of Earth’s gravity on an electron and compare it with the force exerted on the electron by an electric field of magnitude 10,000 V/m (a relatively small field). The mass and charge of an electron are given on the inside back cover.

Atomic physicists ignore the effect of gravity within an atom. To see why, calculate and compare the gravitational and electrical forces between an electron and a proton separated by \(10^{-10}\ m\). The charges and masses are given on the inside back cover. Text Transcription: 10^-10 m

A droplet of ink in an industrial ink-jet printer carries a charge of \(1.6 \times 10^{-10}\ C\) and is deflected onto paper by a force of \(3.2 \times 10^{-4}\ N\). Show that the strength of the electric field to produce this force is 2 million N/C. Text Transcription: 1.6 times 10^-10 C 3.2 times 10^-4 N

The potential difference between a storm cloud and the ground is 100 million V. If a charge of 2 C flashes in a bolt from the cloud to Earth, what is the change in the potential energy of the charge?

Energy of 0.1 J is stored in the metal sphere on top of a Van de Graaff generator. A spark carrying 1 microcoulomb \((10^{-6}\ C)\) discharges the sphere. Show that the sphere’s potential relative to ground is 100,000 V. Text Transcription: (10^-6 C)

Find the voltage change when (a) an electric field does 12 J of work on a 0.0001-C charge and (b) the same electric field does 24 J of work on a 0.0002-C charge.

In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates. The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity; that is, when suspended, the upward force qE just equaled mg. Millikan accurately measured the charges on many oil drops and found the values to be whole-number multiples of \(1.6 \times 10^{-19} \mathrm{C}\)—the charge of the electron. For this he won the Nobel Prize. (a) If a drop of mass \(1.1 \times 10^{-14} \mathrm{~kg}\) remains stationary in an electric field of \(1.68 \times 10^{5} \mathrm{~N} / \mathrm{C}\), what is the charge of this drop? (b) How many extra electrons are on this particular oil drop (given the presently known charge of the electron)?

The three pairs of metal, same-size spheres have different charges on their surfaces, as indicated. Each pair is brought together, allowed to touch, and then separated. Rank, from greatest to least, the total amounts of charge on the pairs of spheres after separation.

Shown are three separate pairs of point charges. Assume the pairs interact only with each other. Rank the magnitudes of the forces between the pairs, from largest to smallest.

Why is charge usually transferred by electrons rather than by protons?

At the atomic level, what is meant by saying that something is electrically charged?

Why aren’t objects with vast numbers of electrons normally electrically charged?

Why do clothes often cling together after tumbling in a clothes dryer?

Why is dust attracted to a DVD wiped with a dry cloth?

When combing your hair, you scuff electrons from your hair onto the comb. Is your hair then positively or negatively charged? How about the comb?

At some automobile toll booths, a thin metal wire protrudes from the road, making contact with cars before they reach the toll collector. What is the purpose of this wire?

Why are the tires for trucks carrying gasoline and other flammable fluids manufactured to be electrically conducting?

An electroscope is a simple device consisting of a metal ball that is attached by a conductor to two thin leaves of metal foil protected from air disturbances in a jar, as shown in the sketch. When the ball is touched by a charged body, the leaves that normally hang straight down spread apart. Why? (Electroscopes are useful not only as charge detectors but also for measuring the quantity of charge: The more charge transferred to the ball, the more the leaves diverge.)

The leaves of a charged electroscope collapse in time. At higher altitudes, they collapse more rapidly. Why is this true? (Hint: The existence of cosmic rays was first indicated by this observation.)

Is it necessary for a charged body actually to touch the ball of the electroscope for the leaves to diverge? Defend your answer.

A crystal of salt consists of negative and positive ions. How does the net charge of the negative ions compare with that of the positive ions? Explain.

How can you charge an object negatively with only the help of a positively charged object?

When one material is rubbed against another, electrons jump readily from one to the other but protons do not. Why is this? (Think in atomic terms.)

The 50,000 billion billion \((5\ \times\ 10^{22})\) freely moving electrons in a penny repel one another. Why don’t they fly out of the penny? Text Transcription: (5 times 10^22)

What does the inverse-square law tell you about the relationship between force and distance?

How does the magnitude of the electrical force between a pair of charged particles change when the particles are moved half as far apart? One-third as far apart?

How does the magnitude of the electrical force compare between a pair of charged particles when they are brought to half their original distance of separation? To one-quarter their original distance? To four times their original distance? (What law guides your answers?)

When you double the distance between a pair of charged particles, what happens to the force between them? Does it depend on the sign of the charges? What law defends your answer?

When you double the charge on both particles in a pair, what effect does this have on the force between them? Does it depend on the sign of the charge?

When you double the charge on only one of a pair of particles, what effect does this have on the force between them? Does the effect depend on the sign of the charge?

The proportionality constant k in Coulomb’s law is huge in ordinary units, whereas the proportionality constant G in Newton’s law of gravitation is tiny. What does this indicate about the relative strengths of these two forces?

How do electric field lines indicate the strength of an electric field?

How is the direction of an electric field indicated with electric field lines?

Suppose that the strength of the electric field about an isolated point charge has a certain value at a distance of 1 m. How will the electric field strength compare at a distance of 2 m from the point charge? What law guides your answer?

In the phenomenon of superconductivity, what happens to electrical resistance at low temperatures?

Measurements show that there is an electric field surrounding Earth. Its magnitude is about 100 N/C at Earth’s surface, and it points inward toward Earth’s center. From this information, can you state whether Earth is negatively or positively charged?

Why are lightning rods normally at a higher elevation than the buildings they protect?

Why aren’t metal-spiked shoes a good idea for golfers on a stormy day?

If a large enough electric field is applied, even an insulator will conduct an electric current, as is evident in lightning discharges through the air. Explain how this happens, taking into account the opposite charges in an atom and how ionization occurs.

If you rub an inflated balloon against your hair and place the balloon against a door, what mechanism causes it to stick? Explain.

When a car is moved into a painting chamber, a mist of paint is sprayed around its body. When the body is given a sudden electric charge and mist is attracted to it—presto—the car is quickly and uniformly painted. What does the phenomenon of polarization have to do with this?

If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare?

How can a charged atom (an ion) attract a neutral atom?

How will the accelerations of the proton and the electron in the preceding problem compare?

How will the directions of travel compare for the electron and the proton in the preceding problem?

Imagine a proton at rest a certain distance from a negatively charged plate. It is released and collides with the plate. Then imagine the similar case of an electron at rest the same distance away from a similarly charged but positive plate. In which case will the moving particle have the greater speed when the collision occurs? Why?

Why is the magnitude of the electric field zero midway between identical point charges?

A gravitational field vector points toward Earth; an electric field vector points toward an electron. Why do electric field vectors point away from protons?

Suppose that a metal file cabinet is charged. How does the charge concentration at the corners of the cabinet compare with the charge concentration on the flat parts of the cabinet?

If you expend 10 J of work to push a 1-C charge against an electric field, what is its change of voltage?

When released, what is the kinetic energy of the 1-C charge of the preceding problem if it flies past its starting position?

What is the voltage at the location of a 0.0001-C charge that has an electric potential energy of 0.5 J (both measured relative to the same reference point)?

Why is it safe to remain inside a car during a lightning storm?

How do the charges on opposing plates of a capacitor compare?

In order to store more energy in a parallel-plate capacitor whose plates differ by a fixed voltage, what change should you make in the plates?

Why is it dangerous to touch the terminals of a high-voltage capacitor even after the charging circuit is turned off?

An electron volt (eV) is a unit of energy. Which is larger: a GeV or a MeV?

What is the magnitude of the electric field inside the dome of a charged Van de Graaff generator?

Would you feel any electrical effects if you were inside the charged sphere of a Van de Graaff generator? Why or why not?

A friend says that the reason one’s hair stands out while touching a charged Van de Graaff generator is simply that the hair strands become charged and are light enough so that the repulsion between strands is visible. Do you agree or disagree?

When you remove your wool suit from the dry cleaner’s garment bag, the bag becomes positively charged. Discuss how this occurs.

Plastic wrap becomes electrically charged when pulled from its box. As a result, it is attracted to objects such as food containers. Does the wrap stick better to plastic containers or to metal containers? Discuss.

Strictly speaking, when an object acquires a positive charge by the transfer of electrons, what happens to its mass? Discuss what happens to its mass when it acquires a negative charge. (Think small!)

Strictly speaking, will a penny be slightly more massive if it has a negative charge or a positive charge? Discuss.

It is relatively easy to strip the outer electrons from a heavy atom like that of uranium (which then becomes a uranium ion), but it is very difficult to remove the inner electrons. Discuss why this is so.

If electrons were positive and protons were negative, discuss whether Coulomb’s law would be written the same or differently.

If you are caught outdoors in a thunderstorm, why shouldn’t you stand under a tree? Can you think of a reason why you should not stand with your legs far apart? Or why lying down can be dangerous? (Hint: Consider the electric potential difference.)

Two pieces of plastic, a full ring and a half ring, have the same radius and charge density. Which electric field at the center has the greater magnitude? Discuss and defend your answer.

You are not harmed by contact with a charged metal ball, even though its voltage may be very high. Is the reason similar to why you are not harmed by the hotter than- 1000°C sparks from a fireworks sparkler? Discuss and defend your answer in terms of the energies that are involved.