# 1. Electric field

## Introduction

The photograph shows a Wimshurst generator invented in the 1880s In the eighteenth century there were already electrostatic machines used to generate electrostatic charges by friction; Wimshurst great innovation was the use of electrostatic induction allowing it to accumulate much higher charges by mechanical means. A Wimshurst generator makes use of several electrical principles which will be studied in the following chapters: bottle of Leiden, dielectric strength, etc.

## 1.1. Electrostatic charges

The accumulation of electrostatic charges is a phenomenon present in many everyday situations, especially on days when the air is drier. A case when electrostatic charges are present is when an adherent plastic film is placed on the opening of a plastic bowl and rubbed to make it stick to it, keeping the bottle closed. Rubbing the plastic originates transfer of electric charges between the plastic and the bowl, leaving both with electrostatic charges that produce attractive force. A sheet of acetate also gains electrostatic charges easily, producing attractive force on the sheet of paper that is usually put under the acetate. One can sometimes feel the effect of an electrostatic shock, especially in the summer, while touching a metal object, for instance the car door's handle, or when one shakes someone else's hand. The car or the other person have electrostatic charges and the electric shock is due to the passage of some of those charges through our body (electric current).

An easy way to study the transfer of electrostatic charges is by using adhesive tape. It may also be helpful to use two pencils or pens to hold the tape. Cut about 20 cm of tape and stick it to the surface of a table, leaving a small piece off the table to be able to remove it from the table, letting it hang freely in the air (make sure the free end doesn't touch your fingers or other objects).

While the tape is removed from the table, some electric charges are transferred between the glue and the table; the tape is thus left with an electrostatic charge which it will keep until while it doesn't touch other objects. Repeat the same procedure with a second piece of tape, using the same table. Since the materials are the same in both cases, it is expected that both tapes have the same type of charge. Bring the free ends of both pieces of tape close together, without letting them touch, and observe the repulsive force between charges of the same type (Figure  1.1). Bring the free end of any of the two pieces of tape near other objects without charge, for example the walls, approaching those objects from the tape side that has no glue, to prevent it from getting stuck to the objects. Note that the charged pieces of tape are attracted by the uncharged objects.

Discard the tape already used and prepare two new pieces of tape, but this time stick one on the table and the other on top of the first. Rub the tape on the top and then remove the pieces of tape from the table and simultaneously take the two pieces apart from each other. Since the glue in the tape on the top and the tape in the bottom to which it is stuck are two different materials, one of the two surfaces will pass charges to the other, leaving the two tapes with charges of different types (one of the with lack of charge and the other with excess). In this case an attractive force must be observed between the two pieces of tape, as in Figure  1.2, because the two pieces of tape have charges of different types (this part of the experiment is more difficult because when the tape is peeled off from the roll it already has electric charge, so both pieces of tape have initially charges of the same type, making it difficult to charge them with different types of charge). Notice also that each of the pieces of tape, regardless of the type of charge they have, is attracted by other uncharged objects.

## 1.2. Atomic structure

All matter is composed of atoms. Each atom has a very compact core with two types of particles, protons and neutrons (Figure  1.3 ), surrounded by an electronic cloud formed by another type of particles, much smaller than protons and neutrons, called electrons.

Between two protons or two electrons acts a repulsive force called electric force . Between a proton and an electron there is also an electric force, but it is attractive. The magnitude of the force between two protons, two electron or an electron and a proton is the same, if the distance between the particles is the same in all 3 cases. These particles do not produce any electric forces on the neutrons.

It is concluded that there are two different types of charge, the protons and the electrons and neutrons are not charged.

The electric force acts only between two charged particles; the force is repulsive, the charges of the particles is of the same type or attractive if they are of different types.

A neutral atom (with an equal number of protons and electrons) and non - polarized (electron cloud with the core center) does not produce electric forces on other charged particles. It is accepted as soon as protons and electrons are particles with electrical charges of opposite sign but the same absolute value, having agreed that the electrons have a negative charge and positive charge proton. A set of particles has a charge full equal to the algebraic sum of the individual particles that compose it .

The SI unit used to measure charge is the coulomb , indicated with the letter C. The proton all have the same charge, the charge Elemental :

(1.1)

The electrons also have all the same charge, just like $-e$.

## 1.3. electrization

A very high energy to be able to remove a proton is required, or a neutron, the nucleus of an atom. This only happens inside stars or in the outermost layer of the atmosphere, where hatch cosmic particles with a lot of energy, or in particle accelerators where the energies of the particles are sufficiently high. To extract an electron from a neutral atom much less energy is required, then getting a ion positive full charge equal to$e$. A neutral atom can also attract an additional electron, then getting a negative ion with full charge equal to$-e$.

Where two different objects come into close contact, there is an electron objects pass to another. The object is more likely to lose electrons is then electrified with positive charge ($n$ excess protons) and the object that has less tendency to lose their electrons gets equal charge (in intensity) but negative ($n$excess electrons), as in Figure  1.4 .

In experiments with tape described at the beginning of the chapter, the glue that helps the table and the tape come into close contact, passing electrons from one to the other. If the table and the tape are initially discharged after separation including one is negatively charged and the other with positive charge of the same intensity. The friction is also used as a method to electrify objects, facilitate the passage of electrons from one object to another (Figure  1.4 ).

The different materials can be arranged in a series triboelectric (Table  1.1 ), in which materials at the top of the series are more likely to be positively charged and the materials at the end of the series have a greater tendency to become negatively charged.

 rabbit fur Glass Human hair Over there Lead Silk Aluminum Paper wood Copper Silver Eraser Acetate Foam Vinyl (PVC)

For example, if a glass rod is rubbed with a silk cloth, the bar is positively charged and negatively silk, because the glass is above the tissue in the triboelectric series (see figure  1.4 ). But if the same glass rod is rubbed with a rabbit's skin, the bar is negatively charged and positively charged skin, because the rabbit skin is above the glass in the triboelectric series.

## 1.4. Charge properties

The electrical charge is an intrinsic property of the substance, such as batter . A difference in relation to ground is that there are two types of charges as well as uncharged particles. Two very important properties of electrical charge are your quantization and conservation.

### 1.4.1. charge Quantization

In particle accelerators collisions between particles are produced with very high energy, giving rise to many new particles, different from electrons, protons and neutrons. All known elementary particles always have a charge which is an integer multiple of the elementary charge$e$ ($1.602\times10^{-19}$ W). Thus, the charge from any object is always a multiple integer of the elementary charge.

In electrostatics experiments, produced charges normally correspond to a very large number of elementary charges. In this case it is good approximation to assume that the charge is a continuous variable and not discrete.

### 1.4.2. Conservation of charge

In any case, the initial total charge is equal to the final total charge. In the electron transfer processes between atoms, the result is obvious, but in processes with the creation of new particles is no indication that he had to be. However, in all cases observed in cosmic radiation and particle accelerators, there is conservation of charge; in cases where a particle disintegrates giving rise to other particles, the sum of charges of all particles created is always equal to the charge of the initial particle.

## 1.5. Force between point charges

In the eighteenth century, Benjamin Franklin discovered that the electrical charges distributed on the surface of a metal object can have significant electrical forces on bodies outside the object, without exercising any force on bodies placed inside the same.

In the previous century, as Isaac Newton had shown mathematically that the gravitational force produced by a hollow shell is void inside. This result is a consequence of how the gravitational force between particles decreases with the square of the distance.

Franklin concluded then that the electric force between charged particles should also be proportional to the inverse square of the distance between the particles. Several years after the work of Franklin, Charles Coulomb did experiments to study accurately the intensity of the electrostatic force between two point charges (one charge point is a very small object with electric charge).

The law of Coulomb states that the line of action of the electric force between two point charges$q_1$ and $q_2$ is the line passing through their centers and their intensity ($F$) Is directly proportional to the absolute value of each charge and inversely proportional to the square of the distance between their centers:

(1.2)

at where $d$is the distance between charges (figure  1.5 ) and$q_1$ and $q_2$They are the values of the two charges. The constant Coulomb $k$ is a universal constant with the value:

(1.3)

The electrical forces exerted on the two charges have the same direction and the same module $F$But they are in opposite directions (action and reaction forces). If the signals of the two charges are equal, the forces are repulsive, as in the left side of Figure  1.5 , and its signs are different, forces are attractive, as the right hand la figure  1.5 .

The constant $K$ (Not to be confused with $k$) Without units, it is constant dielectric existing midway between the two charges. The vacuum dielectric constant is 1 and the dielectric constant of air has a value very close to this, so that, if air is the medium existing between the charges can be eliminated$K$equation. Means have different air dielectric constants with values ​​above unity, at which the electric force between point charges is smaller in different media air.

### example 1.1

Consider three positive point charges connected by wires forming a right triangle, as shown in Fig. ( A ) What is the tension in the wire connecting the charges of 7.4 nC and 9.3 nC? ( B ) If the charge of 5.6 nC were removed, the calculated voltage at the point to increased or decreased?

Resolution . ( A ) the forces diagram on the charged particle 7.4 nC (designated particle number 3) is shown in the right figure.

at where $\vec{F}_{13}$ and $\vec{F}_{23}$ Electrostatic forces are produced by the particles 1 and 2, charge 9.3 5.6 nC and nC, respectively, and $\vec{T}_{13}$ and $\vec{T}_{23}$are the voltages on the wires that connect the particle 3 to the two charges. For the particle remains in balance it is necessary that:

Before you do the math, it is convenient to write the value of the constant $k$ the units used in the problem (nC and cm):

Thus, assuming that no air around the charge, the tension in the wire that connects the charges 1 and 3 is:

( B ) The voltage value remained the same, because as we showed in the previous paragraph, in this case,$T_{13}$ not depends on the strength $F_{23}$ produced by particle 5.6 nC.

## 1.6. Electric field

One way to interpret the electrostatic force between two charged particles is to admit that each electric charge creates around a field of forces acting on other charged particles. If we place a particle with charge$q_0$at a point where there is a field power , the result is an electric force$\vec{F}$on the particle; the electric field $\vec{E}$ It is defined as the force on the particle per unit charge:

(1.4)

Thus, the electric field at a point is a vector with the direction and the direction of the electrical force that would feel a positive unit charge placed at that point.

Conversely, a point knowing that there is an electric field $\vec{E}$, One can easily calculate the electric force acting on a particle with charge $q$ placed on this point: $\vec{F} = q\,\vec{E}$. Just know the field to calculate the force; it is not necessary to know what the charges that gave rise to this field. In SI units, the electric field is measured in newtons per coulomb (N / C).

As it turned out, the electric power produced by a positive point charge $Q$ on a second test charge $q_0$ It is always a positive repulsive force whose intensity decreases proportionally with the square of the distance. Thus, the electric field produced by a positive point charge$Q$It is represented by vectors with the radial direction and sense to move away from the charge, as shown on the left side of Figure  1.6 .

A more convenient way to represent this vector field is across the lines of field , and the right side of the figure  1.6 . At each point, the field line passing through this point points in the direction of the electric field vector at that point. The electric field intensity is greater in the regions where the field lines are closer to each other.

To calculate the value of the electric field produced by the point charge $Q$ a point, is placed a test charge $q_0$ at that point and divides the electric power by the charge $q_0$. Using Coulomb's law, obtains the intensity of the electric field produced by the charge$Q$, as

(1.5)

at where $r$ is the distance from the point to the charge $Q$. The charge signal$Q$ It indicates whether the field is repulsive ($Q$ > 0) or attractive ($Q$ <0).

The electric field created by a single point charge is too weak to be observed. The experimentally observed fields are the vector sum of the fields created by many point charges and the resulting field may have curvilinear field lines as in the example in Figure  1.7 .

To calculate the electric field does not point charges, there is a region where charge can be divided into many small regions infinitesimally that point charges can be considered, and the total field is the superposition of fields of all the infinitesimal charge. The sum of fields of several infinitesimal charges leads to full. The study of this method for calculating fields is beyond the scope of this introductory book, but in Appendix B illustrates the calculation of the field for integration in a specific case that will be useful in the following chapter.

### example 1.2

At some point the force over a 5 nC test charge is 2 × 10 -4  N and has the axis direction of$x$. Calculate the electric field at that point. What is the force exerted on an electron that same point?

Resolution . From the force calculated by the field:

The electric force on an electron at that point would be:

## 1.7. Conductors and Insulators

In some materials, such as in metals, the outermost electron of some atoms can be free of the atom and move freely through the material; so there is a "cloud" dense free electrons ( electron conduction), with constant density if the material is homogeneous. Such material is designated driver . A material that is nonconductive if said insulator ; within an insulator, the electrical charges can not move freely.

If a conductor is placed in a region where there electric field as the driving negatively charged electron cloud, moves in the opposite direction to the field lines. The displacement of driving electrons gives rise to negative charge at one end (excess electrons) and positive charge at the other end (lack of electrons). If the total charge of the driver is zero, the absolute value of those charges at the ends is equal. These charges of opposite sign on the driver's opposite ends producing an internal electric field in the opposite direction to the external field and when the accumulated charges in extreme sufficiently high within the driver the two fields cancel each other and the motion of conduction electrons ceases.

Figure  1.8 shows a positively charged rod placed in close proximity to a conductive ball mounted on an insulating support; driving the electron cloud approaching the sphere of the bar leaving a positive charge at the distal region of the bar and the same amount of negative charge in the region closest to the bar. If the support was not insulator, entered the electron conductor support and the positive charges shown in the figure disappeared.

If the bar had a negative charge, rather than positive, the positions of the positive and negative charges in the sphere would be exchanged. Once accumulated opposite signs of charges on sphere of extremes, the total electric field inside the sphere is zero; as such, the field lines do not penetrate the ball and driving electrons within the sphere do not feel any electrical power. In both cases (positive or negatively charged bar), the charges on the surface nearest the ball bar are attracted to the bar, and this attraction is greater than the repulsion of charges on the far surface of the bar. Thus, any external object to charge any signal always produces an attractive force on the conductors with zero total charge.

If the same experiment is performed with an insulating sphere (Fig  1.9 ), no accumulation of charges at the ends; thus, the field inside the sphere is not canceled and all the molecules within it are polarized , in particular, its own electron cloud moves inside, the opposite direction of the field. In this case (positively charged bar), the electronic cloud of molecules is no longer focused on the same point of positive charges, going to be focused on a closest point of the bar; each atom becomes a small dipole electric , which is a system with zero total charge, but with positive and negative charges at different points.

Figure  1.9 shows some dipoles inside the sphere. The side of the dipole that is closest to the charge bar always has the opposite sign to the charge on the bar. Consequently, the resultant force on each dipole is attractive and the overlapping of all these forces causes the ball is attracted to the bar. That is, an insulating material without charge is always drawn by the charge with objects, regardless of the charge signal of these objects.

## 1.8. Electrification by induction

One method used to carry two insulated conductors, being identical charges but with opposite signs, is the method by charge induction illustrated in figure  1:10 .

The two insulated conductors are placed in contact and approaching one a charged object, as shown in Figure  10.1 . The electric field produced by the charged object induces an opposite sign of charge at the nearest driver and a charge of the same sign in the farthest driver. Then, keeping the fixed charged object, they separate the two drivers. Finally, moves away from the charged object, getting the two conductors with opposite charges (equal in absolute value if none of the balls have charge initially). In each driver charges are distributed over the surface due to repulsion between them, but the charges of the two conductors can no longer recombine because there is no contact between them.

In Wimshurst generator, it uses this method to generate charges of opposite signs. The conductors that come into contact are two small diametrically opposite metal blades on an insulator disk, when they pass through two metal brushes attached to a metal bar (figure  01.11 ). The two blades remain in contact only briefly, because the disk rotates.

If the time in which two of the blades of a disk come into contact blade of the opposite disc is charged, this charging will induce charges of opposite sign on the two blades come into contact. These opposite charges induced in two disc regions also induce charges on the opposite record because this record there is also a bar that temporarily connects the diametrically opposed blades.

In each disk, after inducing charges on the opposite disk, charges jump for two collectors connected to two metal cylinders; of the bottles stores positively charged and the other negatively charged. When the charges accumulated in the bottles are lifted up produces an electric discharge between the tips of two bars attached to the bottles, being discharged. This electrical discharge is a small thunder with a very bright spark.

The two discs rotate in opposite directions; brushes that establish contact between blades and the two collectors are placed so that the rotation of each disc, each blade first passes opposite the brush, which exchange charge with the blade in the opposite brush then passes opposite one of the brushes across the disk, inducing opposite charges on the disc blades and then passes across the collector being uncharged and ready to restart the cycle.

At each cycle the induced charges increase, because each blade is induced by the charges of various blades on the opposite disc. To start the process with just one of the blades has acquired some charge, although it is greatly reduced, from the air or by friction with the brushes. The sign of this initial charge determines which of the bottles accumulate positive charge and which negative.

## questions

1. A positively charged bar is placed near a sheet of paper with no charge. The force that the bar has on the paper is then:
1. Attractive.
2. Repulsive.
3. Nula.
4. Attractive or repulsive, as the bar is conductive or insulating.
5. Attractive if the paper is dry or void if it is wet.
2. What distinguishes an electrical conductor to an insulator is:
1. Having more electrons than protons.
2. Having more protons than electrons.
3. Having more electrons than the insulator.
4. Having molecules that deform more easily.
5. Have some particles move from free charge.
3. Three charges are placed on the axis of $x$:
$q_1$ = -6.0 ΜC in $x$ M = -2.0,
$q_2$ = +4.0 ΜC in $x$ = 0,
$q_3$ = -6.0 ΜC in $x$ = +2.0 M.
Determine the intensity of the resulting electric force on$q_3$.
1. 2.4 × 10 -2  N
2. 1.7 × 10 -2  N
3. 0
4. 2.7 × 10 -2  N
5. 3.4 × 10 -2  N
4. Three identical and conducting spheres, isolated, one charge $Q$and the other two uncharged, placed in contact, each touching the other two and then separate itself. Which of the following afrimações correct?
1. All spheres are uncharged.
2. Each of them is charge $Q$.
3. Two of them are charge $Q$/ 2 and other charge -$Q$/2.
4. Each of them is charge $Q$/ 3.
5. One of them is charge $Q$ and other charge -$Q$.
5. A metal ball mounted on a standoff connects ground with a conductive wire and then approaches a plastic bar with a positive charge. The connection of the ground ball is removed and then moves away from the plastic bar. That charge is metallic sphere?
1. Nula.
2. Positive.
3. Negative.
4. Nonzero, but can not know the signal.
5. Positive at one end and negative at the other end.

## Problems

1. A blade acetate, electrified by friction, placed 1 cm above a table on which several pieces of paper, each 0.5 cm. It is observed that some pieces of paper jump, staying glued to acetate. Estimate the acetate charge of the order, assuming that an identical and of opposite sign charge is induced in each piece of paper and knowing that the paper used is 80 g / m 2 .
2. The sum of the values ​​of two point charges $q_1$ and $q_2$ It is $q_1 + q_2$ = 10 μC. When they are apart 3 m apart, the magnitude of the force exerted by each of them on the other is 24 mN. Determine the values ​​of$q_1$ and $q_2$If: ( a ) Both charges are positive. ( B ) One of the charges is positive and the other negative.
3. Knowing that a hydrogen atom the distance between the protons in the nucleus and the electron is 5.3 × 10 -11  m, determine the intensity of the electric field due to the nucleus, at the point where the electron.
4. The electric field in the atmosphere has strength of about 150 N / C and points in the direction and towards the center of the Earth . Calculate the ratio between the weight of an electron and the magnitude of the opposite electric force exerted by the electric field of the atmosphere (the mass of the electron is 9.109 × 10 -31  kg and admit that the acceleration of gravity is 9.8 m / s 2 ).
5. Three point charges are connected by two insulators wires each 2.65 cm (see figure). Calculate the voltage on each wire.
6. Between two oppositely charged parallel plates there is a uniform electric field. An electron released on the surface of the charged plate negatively accelerates uniformly from rest toward the plate charged positively (the weight of the electron can be neglected in comparison to the electric force , and it is assumed that the plates are in a tube under vacuum). Knowing that the distance between the plates is 2.0 cm , and that every electron released on the negative plate reaches the other plate 15 μs later: ( a ) determining the intensity of the electric field (the mass of the electron is 9.109 × 10 -31  kg) ; ( B ) what is the speed at which electrons reach the positive plate?
7. A three-point charging system is in equilibrium (the resulting electrostatic force on each charge is zero). If the values ​​of the two charges are$q$ and 2$q$Separated by a distance $d$, Determine the value and the third charge position.
8. Determine the resulting electrostatic force on each charge represented in the figure and the electric field produced by charges on the 3 point P.

## replies

Questions: 1. A. 2. E. 3. E. 4. D. 5. C.

Problems

1. Order of magnitude of 10 -10  C.
2. ( A ) 6 μC and μC 4 ( b ) 12 μC, and -2 μC.
3. 5.1 × 10 11  N / C.
4. The electrostatic force is 2.7 × 10 12 times greater than the weight.
5. The tension in the wire is 285 μN left side and the right side wire 560 μN.
6. ( A ) 1.1 × 10 -3  N / C ( b ) 2.67 × 10 3  m / s.
7. The third charge is -0343 $q$ and it lies between the other two charges at a distance 0.414 $d$ charge $q$.
8. Originating in charge $q_1$ = -5 NC axis of $x$ toward $q_2$ 9 = nC, and axes of $y$ toward $q_3$ = 7 nC, the forces are:
$\vec{F}_1$ = (1:35$\,\hat{\imath}$ + 3:15$\,\hat{\jmath}$) m
$\vec{F}_2$ = (- 00:12$\,\hat{\imath}$ - 0.71$\,\hat{\jmath}$) m
$\vec{F}_3$ = (- 1:23$\,\hat{\imath}$ - 2:44$\,\hat{\jmath}$) MN
Field in P is: (-0545$\,\hat{\imath}$ - 0.135$\,\hat{\jmath}$) N / μC
Right

Each molecule of the paper is polarized, being the closest bar of negative charges and thus the repulsion of the positive charges of each molecule is smaller than the attraction of the negative charges.

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Wrong

The core role of the atoms (positive) are repelled by the positive charge of the bar, but there are also attractive forces acting on the electrons of atoms.

(Click)

Wrong

The nuclei and electrons of the atoms in the molecules of the paper feel forces in the opposite direction, but the result will not be zero because the molecules are polarized (separation of positive and negative charges) at the bar field.

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Wrong

As the statement says that the bar has a charge, whichever is conductive, it is isolated. The meaning of the bar field lines only depends on the sign of the charges on it and not the type of bar material.

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Wrong

The wet paper is more conductive than dry paper, but both conductors and insulators at the direction of polarization of charges within a neutral material is the same (only depend on the direction of the external electric field).

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Wrong

All neutral materials, whether they are conductors or insulators have the same number of electrons than protons. And all charged materials have electrons or protons excess (depends on the total charge signal). The sign of excess charges do not serve to distinguish insulators conductors.

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Wrong

All neutral materials, whether they are conductors or insulators have the same number of electrons than protons. And all charged materials have electrons or protons excess (depends on the total charge signal). The sign of excess charges do not serve to distinguish insulators conductors.

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Wrong

The number of electrons a material has more to do with the number of atoms and atomic number of each atom. This number does not serve as a criterion to distinguish insulators conductors.

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Wrong

In conducting the excess charges are distributed on the surface, keeping the immune molecules to the effect of the electric field. Thus, the molecules within the driver are not polarized and no matter how easily they are deformed.

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Right

This is the characteristic that defines a driver.

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Wrong

It is necessary to calculate the magnitudes of the forces between the charges q 1 and q 3 and between charges q 2 and q 3 (using Coulomb's law) , and subtracting them, because the two forces are vectors with the same direction over opposite directions.

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Wrong

It is necessary to calculate the magnitudes of the forces between the charges q 1 and q 3 and between charges q 2 and q 3 (using Coulomb's law) , and subtracting them, because the two forces are vectors with the same direction over opposite directions.

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Wrong

The forces produced by the other two charges have opposite directions but do not cancel because they have different modules.

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Wrong

It is necessary to calculate the magnitudes of the forces between the charges q 1 and q 3 and between charges q 2 and q 3 (using Coulomb's law) , and subtracting them, because the two forces are vectors with the same direction over opposite directions.

(Click)

Right

It is calculated the module of the forces between the charges q 1 and q 3 and between charges q 2 and q 3 (using Coulomb's law) , and subtract, because the two forces are vectors with the same direction over opposite directions.

(Click)

Wrong

The final charge can not be null. The charge conservation implies that the sum of charges in order to be equal to the initial charge Q .

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Wrong

As the initial total charging was Q , charge conservation implies that the sum of the charge 3 in order to be equal to the initial charge Q .

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Wrong

If so, the final charge would be Q / 2 + Q / 2 - Q / 2 = Q / 2, which is not equal to the initial total charge, Q .

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Right

The sum of the 3 charges should be equal to the initial charge. The contact balls 3 act as a single conductor, wherein the total charge Q is distributed over its surface. If the spheres are equal for symmetry, the surface of each is equal charging. In chapter 7 it is shown that the spheres have different radii, charges them will not be equal.

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Wrong

The final total charge can not be 0, because the burden of conservation implies that it must be equal to the initial charge Q .

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Wrong

When the bar is approached the driver, negative charges of the land is transferred to the driver. The elimination of grounding causes these charges remain in the driver, without being able to leave.

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Wrong

As the driver is so isolated, the charges that should have already be there when the driver was grounded. If the driver grounded there positive charges, the repulsive force produced in them by the bar to alienate the land, outside the driver.

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Right

When the bar is approximate to the driver, it moved negative charge of the earth for the driver (and positive driver for the land). When away from the bar, these charges can not recombine again, because at the moment there is no connection to the land and, as such, there can be no passage of cargo between Earth and the driver.

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Wrong

When the bar is approached the driver, negative charges of the land is transferred to the driver. If the bar charge was negative, positive charges to the driver would be transferred.

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Wrong

At the end of the bar has already been rejected, so that there is no charge on the driver, regardless of the signal will be distributed across its surface.

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