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Chapter 17 Electric Forces and Fields Section 17-1: Electric Charge • • • • There are two kinds of electric charge. Like charges repel. Opposite or unlike charges attract. Ben Franklin named the two different kinds of charge positive and negative. • Positive and negative charges are said to be opposite because an object with an equal amount of positive and negative charge has no net charge. • • • • • All matter is made up of atoms. Every atom contains even smaller particles. Protons are positive and found in the nucleus. Neutrons are neutral and found in the nucleus. Electrons are negative and move around in the electron cloud surrounding the nucleus. • Protons and neutrons are relatively fixed in the nucleus of the atom, but electrons are easily transferred from one atom to another. • An atom has a net charge of zero when the number of protons equals the number of electrons. • As atoms gain or lose electrons they become negatively or positively charged atoms called ions. • Both a balloon and your hair contain a very large number of neutral atoms. • Charge has a natural tendency to be transferred between unlike materials. • Rubbing the two materials together serves to increase the area of contact and enhance the charge transfer process. • When a balloon is rubbed against your hair, some of your hair’s electrons are transferred to the balloon. • The balloon gains a certain amount of negative charge while your hair loses an equal amount of negative charge and is left with a positive charge. • Only a small portion of the total available charge is transferred from one object to another. • The positive charge on your hair is equal in magnitude to the negative charge on the balloon. • Electric charge is conserved in this process; no charge is created or destroyed. • This principle of conservation of charge is one of the fundamental laws of nature. • In 1909, Robert Millikan (1886-1953) performed an experiment at the University of Chicago in which he observed the motion of tiny oil droplets between two parallel metal plates. • The oil droplets were charged by friction in an atomizer and allowed to pass through a hole in the top plate. • Initially the droplets fell due to their weight. • The top plate was given a positive charge as the droplets fell, and the droplets with a negative charge were attracted back upward toward the positively charged plate. • By turning the charge on this plate on and off, Millikan was able to watch a single oil droplet for many hours as it alternately rose and fell. • After repeating this process for thousands of drops, Millikan found than when an object is charged, its charge is always a multiple of a fundamental unit of charge, symbolized by the letter e. • Charge is said to be quantized meaning that the charge occurs as discrete amounts in nature. • An object may have a charge of ±e, or ±2e, or ±3e, and so on. • Other experiments in Millikan’s time demonstrated that the electron has a charge of –e and the proton has an equal and opposite charge of +e. • The value of e has since been determined to be 1.60219 x 10-19 C, where the coulomb (C) is the SI unit of electric charge. • For calculations, this book will use the approximate value of ±1.60 x 10-19. • 1.0 C is a substantial amount of charge. • When an object is charged by rubbing, a net charge on the order of 1μC. Transfer of Electric Charge • It is convenient to classify substances in terms of their ability to transfer electric charge. • Materials in which electric charges move freely, such as copper and aluminum, are called conductors. • Most metals are conductors. • Materials in which electric charges do not move freely, such as glass, rubber, silk, and plastic, are called insulators. • Semiconductors are a third class of materials characterized by electrical properties that are somewhere between those of insulators and conductors. • In their pure state, semiconductors are insulators. • The carefully controlled addition of specific atoms as impurities can dramatically increase a semiconductor’s ability to conduct electric charge. • Silicon and germanium are two well-known semiconductors that are used in a variety of electronic devices. • Certain metals belong to a fourth class of materials, called superconductors. • Superconductors become perfect conductors when they are at or below a certain temperature called the critical temperature. • Insulators and conductors can both become charged by contact. • When a conductor is connected to Earth by means of a conducting wire or copper pipe, the conductor is said to be grounded. • The earth can be considered an infinite reservoir for electrons because it can accept or supply an unlimited number of electrons. • This is the key to understanding another method of charging a conductor. • Consider a negatively charged rubber rod brought near a neutral (uncharged) conducting sphere that is insulated so that there is no conducting path to ground. • The repulsive force between the electrons in the rod and those in the sphere causes a redistribution of negative charge on the sphere. • As a result, the region of the sphere nearest the negatively charged rod has an excess of positive charge. • If a grounded conducting wire is then connected to the sphere, some of the electrons leave the sphere and travel to earth. • If the wire to the ground is then removed while the negatively charged rod is held in place, the conducting sphere is left with an excess of induced positive charge. • Finally, when the rubber rod is removed from the vicinity of the sphere, the induced positive charge remains on the ungrounded sphere. • The positive charge then becomes uniformly distributed over the outside surface of the ungrounded sphere. • This process is known as induction, and the charge is said to be induced on the sphere. • Induction– the process of charging a conductor by bringing it near another charged object and grounding the conductor. • Charging an object by induction requires no contact with the object inducing the charge but does require contact with a third object, which serves as either a source or a sink of electrons. • A process very similar to charging by induction in conductors takes place in insulators. • In most neutral atoms or molecules, the center of positive charge coincides with the center of negative charge. • In the presence of a charged object, these centers may shift slightly, resulting in more positive charge on one side of a molecule than on the other. • Polarization– when charges on an atom or molecule shift making one side more positive and the other side more negative. • This realignment of charge within individual molecules produces an induced charge on the surface of the insulator. • When an object becomes polarized, it has no net charge but is still able to attract or repel objects due to this realignment of charge. • This is why a plastic comb can attract small pieces of paper that have no net charge. • Like induction, polarization does not require physical contact. Section 17-2: Electric Force • We recall that forces cause a change in motion. • We have electric force. • Electric force is attractive between opposite charges and repulsive between like charges. • What determines how small or large the electric force will be? • The distance between two object affects the magnitude of the electric force between them. • Further, it seems reasonable that the amount of charge on the objects will also affect the magnitude of the electric force. • In the 1780’s, Charles Coulomb conducted a variety of experiments in an attempt to determine the magnitude of the electric force between two charged objects. • Coulomb found that the electric force between two charges is proportional to the product of the two charges. • So, if one charge is doubled, the electric force likewise doubles, and if both charges are doubled, the electric force increases by a factor of four. • Coulomb also found that the electric force is inversely proportional to the square of the distance between the charges. • When the distance between two charges is halved, the force between them increases by a factor of four. • The following equation, known as Coulomb’s law, expresses these conclusions mathematically for two charges separated by a distance, r. • Felectric = kC(q1q2/r2) • The symbol kC, called the Coulomb constant, has SI units of N·m2/C2 because this give N as the unit of electric force. • This book will use the approximate value of 8.99 x 109 N·m2/C2 for kC. • When dealing with Coulomb’s law, remember that force is a vector quantity and must be treated accordingly. • The electric force between two objects always acts along the line between the objects. • Also note that Coulomb’s law applies exactly only to point charges or particles and to spherical distributions of charge. • When applying Coulomb’s law to spherical distributions of charge, use the distance between the centers of the spheres as r. • Electric force is a field force. • Gravitational force is another type of field force. • The mathematical form of the Coulomb force is very similar to that of the gravitational force. • That is, both forces are inversely proportional to the square of the distance of separation. • There are some important differences between electric and gravitational forces. • Electric forces can be either attractive or repulsive. • Gravitational forces are always attractive. • Electric force is significantly stronger than the gravitational force. • Frequently, more than two charges are present, and it is necessary to find the net electric force on one of them. • Coulomb’s law applies even when more than two charges are present. • The resultant force on any single charge equals the vector sum of the individual forces exerted on that charge by all of the other individual charges present. Equilibrium • Objects that are at rest or moving with a constant velocity are said to be in equilibrium. • According to Newton’s 1st Law, the net external force acting on a body in equilibrium must equal zero. • In electrostatic situations, the equilibrium position of a charge is the location at which the net electric force on the charge is zero. • To find this location, you must find the position at which the electric force from one charge is equal and opposite the electric force from another charge. • This can be done by setting the forces (found by Coulomb’s law) equal and then solving for the distance between either charge and the equilibrium position. Section 17-3: The Electric Field • A charged object sets up an electric field in the space around it. • When a second charged object enters this field, forces of an electrical nature arise. • In other words, the second object interacts with the field of the first particle. • To define an electric field more precisely, consider figure 17-10(a), which shows an object with a small positive charge qo, placed near a second object with a larger positive charge, Q. • The strength of the electric field, E, at the location of qo is defined as the magnitude of the electric force acting on q0 divided by the charge of q0: • E = Felectric/qo • Note that this is the electric field at the location of q0 produced by the charge Q, and not the field produced by q0. • Because electric field strength is a ratio of force to charge, the SI units of E are newtons per coulomb (N/C). • The electric field is a vector quantity. • By convention, the direction of E at a point is defined as the direction of the electric force that would be exerted on a small positive charge (called a test charge) placed at that point. • In other words, the direction of E depends on the sign of the charge producing the field. • Consider the positively charged conducting sphere in figure 17-11 (a). • The field in the region surrounding the sphere could be explored by placing a positive test charge, q0, in a variety of places near the sphere. • To find electric field at each point, you would first find the electric force on this charge then divide this force by the magnitude of the test charge. • However, when the magnitude of the test charge is great enough to influence the charge on the conducting sphere, a difficulty with our definition arises. • According to Coulomb’s law, a strong test charge will cause a rearrangement of the charges on the sphere as shown in figure 1711 (b). • As a result, the force exerted on the test charge is different from what the force would be if the movement of charge on the sphere had not taken place. • Furthermore, the strength of the measured electric field is different from what it would be in the absence of the test charge. • To eliminate this problem, we assume that the test charge is small enough to have negligible effect on the location of the charges on the sphere. • To reformulate our equation for electric field strength from a point charge, consider a charge, q, located a distance, r, from a small test charge, q0. • According to Coulomb’s law, the magnitude of the force on the test charge is given by the following equation: • Felectric = kcqq0/r2 • We can substitute this value into our previous equation for electric field strength. • E = Felectric/q0 = kcqq0/r2q0 • Notice that the q0 cancels, and we have a new equation for electric field strength from a point charge. • E = kcq/r2 where q is the charge producing the field. • As stated earlier, electric field, E, is a vector. • If q is positive, the field due to this charge is directed outward radially from q. • If q is negative, the field is directed toward q. • As with electric force, the electric field due to more than one charge is calculated by applying the principle of superposition. • Our new equation for electric field strength points out an important property of electric fields. • As the equation indicates, an electric field at a given point depends only on the charge, q, of the object setting up the field and on the distance, r, from that object to a specific point in space. • As a result, we can say that an electric field exists at any point near a charged body even when there is no test charge at that point. Electric Field Lines • Electric field lines– lines that represent both the magnitude and the direction of the electric field. • This is a convenient aid for visualizing electric field patterns. • Although the electric field lines do not really exist, they offer a useful means of analyzing fields by representing both the strength and direction of the field at different points in space. • With electric field lines, the number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region. • E is stronger where the field lines are close together and weaker when they are far apart. • Figure 17-15 (a) on page 648 shows some representative electric field lines for a positive point charge. • Note that this two-dimensional drawing contains only the field lines that lie in the plane containing the point charge. • The lines are actually directed outward radially from the charge in all directions. • Because a positive test charge placed in this field would be repelled by the positive charge q, the lines are directed away from the positive charge, extending to infinity. • Similarly, the electric field lines for a single negative point charge, which begin at infinity, are directed inward toward the charge, as shown in figure 17-15 (b). • Note that the lines are closer together as they get near the charge, indicating that the strength of the field is increasing. • This is consistent with our equation for electric field strength, which is inversely proportional to the distance squared. Rules for Drawing Electric Field Lines • 1. The lines must begin on positive charges or at infinity for negative charges, and they must terminate on negative charges or at infinity. • 2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. • 3. No two field lines from the same field can cross each other. • Figure 17-16 on page 649 shows the electric field lines for two point charges of equal magnitudes but opposite signs. • This configuration is called an electric dipole. • Electric dipole– charge configuration for two point charges of equal magnitudes but opposite signs. • In this case, the number of lines that begin at the positive charge must equal the number of lines that terminate on the negative charge. • At points very near the charges, the lines are nearly radial. • The high density of lines between the charges indicates a strong electric field in this region. • Figure 17-17 shows the electric field lines in the vicinity of two equal positive point charges. • Again, close to either charge, the lines are nearly radial. • The same number of lines emerges from each charge because the charges are equal in magnitude. • At great distances from the charges, the field approximately equals that of a single point charge of magnitude 2q. • Figure 17-18 is a sketch of the electric field lines associated with a positive charge +2q and a negative charge –q. • In this case, the number of lines leaving the charge +2q is twice the number terminating on the charge –q. • Only half the lines that leave the positive charge end at the negative charge. • The remaining half terminate at infinity. • At distances that are great compared with the separation between the charges, the pattern of electric field lines is equivalent to that of a single charge, +q. Conductors in Electrostatic Equilibrium • A good electric conductor, such as copper, contains charges (electrons) that are not bound to any atoms and are free to move about within the material. • When no net motion of charge is occurring within a conductor, the conductor is said to be in electrostatic equilibrium. • Conductors in electrostatic equilibrium will have the following four properties. Characteristics • 1. The electric field is zero everywhere inside the conductor. • 2. Any excess charge on an isolated conductor resides entirely on the conductor’s outer surface. • 3. The electric field just outside a charged conductor is perpendicular to the conductor’s surface. • 4. On an irregularly shaped conductor, charge tends to accumulate where the radius of curvature of the surface is smallest, that is, at sharp points. • The first property, which states that the electric field is zero inside a conductor in electrostatic equilibrium, can be understood by examining what would happen if this were not true. • If there were an electric field inside a conductor, the free charges would move and a flow of charge, or current, would be created. • If there were a net movement of charge, the conductor would no longer be in electrostatic equilibrium. • The fact that any excess charge resides on the outer surface of the conductor is a direct result of the repulsion between like charges described by Coulomb’s law. • If an excess of charge is placed inside a conductor, the repulsive forces arising between the charges force them as far apart as possible, causing them to quickly migrate to the surface. • If the electric field were not perpendicular to the surface, the electric field would have a component along the surface. • This would cause the free negative charges within the conductor to move. • If the charges moved, a current would be created and there would no longer be electrostatic equilibrium. • E must be perpendicular to the surface. • To understand why charge tends to accumulate at sharp points, consider a conductor that is fairly flat at one end and relatively pointed at the other. • Any excess charge placed on the object moves to its surface. • Figure 17-20 on page 651 shows the forces between two charges at each end of such an object. • When one end of a conductor is sharper than the other, excess charge tends to accumulate at the sharper end, resulting in a larger charge per unit area and a larger repulsive electric force between charges at this end. • At the sharp end, a larger electric field is directed away from the surface. • When the field becomes great enough, the gases of the air around the sharp end of the conductor become ionized and a bluish glow called a corona is seen. • A glow discharge known as St. Elmo’s fire can sometimes be observed at night at the tips of ship masts and at the trailing edges of wing and tail surface of aircraft. • In nuclear physics research, a Van de Graaff generator is often used to generate electric charge. • Some generators are designed to accumulate positive charge. • If protons are introduced into a tube attached to the dome of a Van de Graaff generator, the large electric field of the dome exerts a repulsive force on the protons, causing them to accelerate to energies high enough to initiate nuclear reactions between the protons and various target nuclei. • The Van de Graaff generator is designed to avoid ionizing the air, which would allow charge to “leak off” into the atmosphere. • Figure 17-22 on page 652 shows the basic construction of a Van de Graaff generator. • A motor driven pulley moves a nonconducting belt around a loop. • The pulley and belt are made of different materials, and the friction of the pulley driving the belt causes a separation of charges. • A strong positive charge builds up on the pulley, while the belt becomes negatively charged. • The negative charge spreads over the length of the belt. • Because the positive charge is concentrated on the comparatively small pulley while the corresponding negative charge is spread over the much larger belt, there is a net positive charge in the area around the lower pulley. • A comb of conducting needles is located near where the belt passes over the pulley with its needles very close to, but not touching, the moving belt. • The comb is connected by a wire to ground. • The net positive charge in the area around the pulley attracts negative charge from ground onto the needles of the comb. • The electrostatic attraction of the positive charge is great enough to cause the negative charges to leap off toward the pulley. • The negative charges hit the belt, and the moving belt carries them up. • The negative charges are drawn off the belt by another comb of needles at the top. • These charges distribute themselves over the outer surface of the dome. • A large amount of negative charge can be accumulated on the dome in this manner. • Because the electric field is greatest at sharp points, a sphere is the most effective shape for building up large amounts of charge without producing a corona.