ELECTRIC CHARGE, CONDUCTORS, AND INSULATORS: The fundamental quantity in electrostatics is electric charge.There are two kinds of charge, positive and negative. Charges of the same sign repel each other; charges of opposite sign attract. Charge is conserved; the total charge in an isolated system is constant. All ordinary matter is made of protons, neutrons, and electrons. The positive protons and electrically neutral neutrons in the nucleus of an atom are bound together by the nuclear force; the negative electrons surround the nucleus at distances much greater than the nuclear size. Electric interactions are chieÀy responsible for the structure of atoms, molecules, and solids. Conductors are materials in which charge moves easily; in insulators, charge does not move easily. Most metals are good conductors; most non-metals are insulators. COULOMB¶S LAW: For charges q1 and q2 separated by a distance r , the magnitude of the electric force on either charge is proportional to the product q1q2 and inversely proportional to r 2 . The force on each charge is along the line joining the two charges - repulsive if q1 and q2 have the same sign, attractive if they have opposite signs. In SI units, the unit of electric charge is the coulomb, abbreviated C. When two or more charges each exert a force on a charge, the total force on that charge is the vector sum of the forces exerted by the individual charges. 1 q1q2 F! 4TI o r 2 1 ! 8.988 x109 Nm 2 / C 2 4TI o ELECTRIC FIELD: & Electric field E , a vector quantity, is the force per unit charge exerted on a test charge at any point. The electric field produced by a point charge is directed radially away from or toward the charge. & & F 1 q Ö E! o ! r qo 4TI o r 2 SUPERPOSITION OF ELECTRIC FIELDS: & The electric field E of any combination of charges is the vector sum of the fields caused by the individual charges. To calculate the electric field caused by a continuous distribution of charge, divide the distribution into small elements, calculate the field caused by each element, and then carry out the vector sum, usually by integrating. Charge distributions are described by linear charge density P surface charge density W and volume charge density V . ELECTRIC FIELD LINES: Field lines provide a graphical representation of electric fields. At any point on a & field line, the tangent to the line is in the direction of E at that point. The number of lines per unit area (perpendicular to their direction) is proportional to the & magnitude of E at the point. DISCUSSION QUESTIONS why? (You may want to experiment with your next load of laundry. Q21. All three charges have the same magnitude.9 Suppose the charge shown in Fig. Describe how you could place charges of opposite sign but exactly equal magnitude on the two objects. Will its trajectory follow an electric field line? Again.7 Figure shows some of the electric field lines due to three point charges arranged along the vertical axis. Is it possible that after the spheres touch. Explain why the sphere is first attracted and then repelled. why or why not? then. such as metals. are typically good conductors of heat. If you then stick the sticky side of one to the shiny side of the other and rip them apart. such as wood. they will cling together? Explain. would a charged comb still cause a neutral insulator to become polarized as in Fig. like sediment settling to the bottom of a river? Q21.11 You can use plastic food wrap to cover a container by stretching the material across the top and pressing the overhanging material against the sides. involving transfer of electrons between the strips of tape. the sphere is drawn toward the rod. Q21. When a positively charged glass rod is brought close to the metal sphere. 21. 21.5 An uncharged metal sphere hangs from a nylon thread.) Q21.8? Why or why not? Would the neutral insulator still be attracted to the comb? Again.Q21. What makes it stick? (Hint: The answer involves the electric force. When you bring the spheres close to each other. 21.28b and released (the positive and negative charges shown in the figure are fixed in position). are typically poor conductors of heat. it suddenly flies away from the rod.8 Good electrical conductors.2 Two metal spheres are hanging from nylon threads. In this case. Why? Would you expect more or less clinging if all your clothing were made of the same material (say. Explain why there should be a relationship between electrical conduction and heat conduction in these materials. Will the trajectory of the particle follow an electric field line? Why or why not? Suppose instead that the particle is placed at some point in Fig. But if the sphere touches the rod. Q21. they will attract each other. for this sequence of events.4 Your clothing tends to cling together after going through the dryer. electrical insulators.) Does the food wrap stick to itself with equal Q21. cotton) than if you dried different kinds of clothing together? Again. they tend to attract.10 Two identical metal objects are mounted on insulating stands. discuss all the possible ways that the spheres could be charged. Explain how the fields produced by each individual point charge combine to give a small net field at this point or points. Based on this information alone.3 The electric force between two charged particles becomes weaker with increasing distance. Q21. positively charged particle is then placed at some point in the figure and released.6 The free electrons in a metal are gravitationally attracted toward the earth. Q21. Suppose instead that the electric force were independent of distance. . don¶t they all settle to the bottom of the conductor. why or why not? Explain any differences between your answers for the two different situations. Why. Q21.1 If you peel two strips of transparent tape off the same roll and immediately let them hang near each other. Q21. (a) What are the signs of the three charges? Explain your reasoning. they will repel each other. (b) At what point(s) is the magnitude of the electric field the smallest? Explain your reasoning. A small.28a is fixed in position. Give a plausible explanation. 19 shows the electric field lines near each of these objects.15 A point charge of mass and another point charge of mass are released on a frictionless table.16 A proton is placed in a uniform electric field and then released. 21. why or why not? Q21.12 If you walk across a nylon rug and then touch a large metal object such as a doorknob. Q21.3) we saw that the electric force between two particles is of the order of times as strong as the gravitational force. So why do we readily feel the gravity of the earth but no electrical force from it? Q21. A or B? How do you .22.21 Sufficiently strong electric fields can cause atoms to become positively ionized²that is.) Why are you less likely to get a shock if you touch a small metal object. Figure Q21. Is the air velocity a vector field? Why or why not? Is the air temperature a vector field? Again. Q21. close to A or close to B? How do you know? Q21. such as a paper clip? Q21.tenacity? Why or why not? Does it work with metallic containers? Again. If has an initial acceleration what acceleration of : or Explain. Does the fact that they cross each other violate the statement in Section 21. what will be its initial acceleration: or Explain. Q21.20 Atomic nuclei are made of protons and neutrons. Explain how this can happen. Q21.13 You have a negatively charged object. How can you use it to place a net negative charge on an insulated metal sphere? To place a net positive charge on the sphere? Q21.23 The air temperature and the velocity of the air have different values at different places in the earth¶s atmosphere. to lose one or more electrons. Explain.18 What similarities do electrical forces have with gravitational forces? What are the most significant differences? Q21.1 (Section 21.6 that electric field lines never cross? Explain.22 The electric fields at point due to the positive charges and are shown in Fig. Why does this tend to happen more on dry days than on humid days? (Hint: See Fig.14 When two point charges of equal mass and charge are released on a frictionless table.17 In Example 21. Then an electron is placed at this same point and released. why or why not? Q21. each has an initial acceleration If instead you keep one ¿xed and release the other one. (a) Which object is positive.30. This shows that there must be another kind of interaction in addition to gravitational and electric forces. you may get a spark and a shock.19 Two irregular objects A and B carry charges of opposite sign. Do these two particles experience the same force? The same acceleration? Do they move in the same direction when released? Q21. What determines how strong the field must be to make this happen? Q21. and but the will charge charge charge be the know? (b) Where is the electric field stronger. What will the gold leaf do when the rod is removed in this case? Why? Q17. you may get a spark and a shock. What are the chains for and how do they work? Q17. then perpendicular to it. (a) If a charged rod is brought close to (but does not touch) the ball at the top. what is the net force on it? Will the same thing necessarily be true if the field is not uniform? Q17. Q17.8 Show how it is possible for neutral objects to attract each other electrically. for an entire rotation of Q17. and so on. (b) the hardness of steel. Q17. a fact that. How is this possible? Q17. instead of having its normal vector oriented at just two or three particular angles to the electric field.2 When you walk across a nylon rug and then touch a large metal object.6 Gasoline transport trucks sometimes have chains that hang down and drag on the road at the rear end of the truck. Lightning rods are used in prairie country to protect houses and barns from lightning. consists of a metal tube with a metal ball at the top and a sheet of extremely thin gold leaf fastened at the other end. which is often used in physics demonstrations. so that its normal vector was first parallel to the field.5 How do we know that protons have positive charge and electrons have negative charge. rather than the reverse? Is there anything inherently positive about the proton¶s charge or inherently negative about the electron¶s charge? Q17.3 What similarities does the electrical force have to the gravitational force? What are the most significant differences? Q17. Why does it do this? Q17. Sketch a graph of the resulting electric flux versus time.11 If an electric dipole is placed in a uniform electric field.15 Explain how the electrical force plays an important role in understanding each of the following: (a) the friction force between two objects. Q17.12 Why do electric field lines point away from positive charges and toward negative charges? Q17. and why does it then repel the same ball? Q17.1 Bits of paper are attracted to an electrified comb or rod even though they have no net charge. Explain how we know this.14 A rubber balloon has a single point charge in its interior. Why? (b) What will the gold leaf do when the charged rod is removed? Why? (c) Suppose that the charged rod touches the metal ball for a second or so.4 In a common physics demonstration. and (c) the bonding of amino acids to form proteins.Conceptual Questions Q17. shows that there must be another kind of force in addition to the electrical and gravitational forces. What causes this to happen? Q17. began to rotate continuously.9 Suppose the disk in Example 17. It is then brought close to a small Styrofoam ball. the gold leaf pivots outward. If you then touch the ball with the rod. away from the Metal tube and ball Gold leaf tube.8. (See Fig) The gold leaf is attached in such a way that it can pivot about its upper edge. by itself. Does the electric flux through the balloon depend on whether or not it is fully inflated? Explain your reasoning. it suddenly repels the ball.10 Atomic nuclei are made of protons and neutrons.7 A gold leaf electroscope. Why does it first attract the ball. . then opposite to it.13 A lightning rod is a pointed copper rod mounted on top of a building and welded to a heavy copper cable running down into the ground. the lightning current runs through the copper rather than through the building. a rubber rod is first rubbed vigorously on silk or fur. which it attracts. Is the conductor charged positively.6 A positively charged ball is brought close to an electrically neutral isolated conductor. (a) Is that point to the left of the first two particles.) Q21.5 In Fig. In which situations is there a point to the left of the particles where an electron will be in equilibrium? Q21. a central particle of charge -q is surrounded by two circular rings of charged particles. or between them? (b) Should the third particle be positively or negatively charged? (c) Is the equilibrium stable or unstable? Q21. The charge values are indicated except for the central particle. Q21. or neutral if (a) the ball is first taken away and then the ground connection is removed and (b) the ground connection is first removed and then the ball is taken away? .2 Figure shows three pairs of identical spheres that are to be touched together and then separated. charged negatively. greatest first. a third charged particle can be placed at a certain point such that all three particles are then in equilibrium.4 Figure shows two charged particles on an axis. However. The initial charges on them are indicated. greatest first. Q21.Q21. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consider symmetry. to their right. Rank the pairs according to (a) the magnitude of the charge transferred during touching and (b) the charge left on the positively charged sphere.3 Figure shows four situations in which charged particles are fixed in place on an axis. which has the same charge in all four situations.1 Figure shows four situations in which five charged particles are evenly spaced along an axis. The charges are free to move. Rank the situations according to the magnitude of the net electrostatic force on the central particle. The conductor is then grounded while the ball is kept close.