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Chapter 15 Electric Charge, Forces, and Fields Sections for Chapter 15 Electric Charge Electrostatic Charging Electric Force Electric Field Conductors and Electric Fields Gauss’s Law for Electric Fields What is an “electric charge”? Yeah all that is good, but what is it? 15.1 Electric Charge Electric charge is a fundamental property of matter; electric charges may be positive or negative. The atom consists of a small positive nucleus surrounded by a negative electron cloud. 15.1 Electric Charge Why do protons, electrons, and neutrons have differing charges? Particle Physics Time. 15.1 Electric Charge Proton: Cool! 15.1 Electric Charge Proton: 15.1 Electric Charge Neutron: 15.1 Electric Charge Neutron: 15.1 Electric Charge Electron: 15.1 Electric Charge What’s with the unit for mass? MeV/c2? eV = unit for energy c = speed of light What does this have to do with mass? 15.1 Electric Charge 1 eV = 1.6e-19 J c = 3e8 m/s Mass = E/c2 Mass of electron = 9.1e-31 15.1 Electric Charge SI unit of charge: the coulomb, C. All charges are integer multiples of the charge on the electron: 15.1 Electric Charge Like charges repel; unlike charges attract. 15.1 Electric Charge Charge is conserved: The net charge of an isolated system remains constant. If one object has lost charge, you can be sure another object has gained it. Kind of like: force, mass, energy, momentum, everything. Practice Questions 1. You shuffle across the carpet and develop a net positive charge. a. Do you have a deficiency or an excess of electrons? b. If the charge the carpet acquired has a magnitude of 2.15 nC, how many electrons were transferred? 2. Why don’t we typically exchange protons? 3. What is the net charge on a typical Carbon atom? Nitrogen? Fermium? 15.2 Electrostatic Charging Conductors transmit charges readily. Semiconductors are intermediate; their conductivity can depend on impurities and can be manipulated by external voltages. Insulators do not transmit charge at all. Van de Graaff 15.2 Electrostatic Charging An electroscope may be used to determine if an object is electrically charged. http://en.wikipedia.org/wiki/Triboelectric_effect 15.2 Electrostatic Charging Methods of Charging: • Friction • Conduction • Induction • Polarization 15.2 Electrostatic Charging Charging by friction: This is the process by which you get “charged up” walking across the carpet in the winter. It is also the process that creates “static cling” in your laundry, and makes it possible for you to rub a balloon on your hair and then stick the balloon to the wall. 15.2 Electrostatic Charging An electroscope can be given a net charge by conduction—when it is touched with a charged object, the excess charges flow freely onto the electroscope. 15.2 Electrostatic Charging An electroscope may also be charged by induction, if there is a way of grounding it while charge is being induced. 15.2 Electrostatic Charging Charge may also be moved within an object—without changing its net charge—through a process called polarization. 15.3 Electric Force The force exerted by one charged particle on another is given by: 15.3 Electric Force K is known as the “Coulomb Constant” and is a proportionality constant. Charles-Augustin de Coulomb 1736 – 1806 French physicist for whom the SI unit of charge, coulomb, is named. Noted for his work in the fields of electricity and magnetism k = 9.00x109 N·m2/C2 1. A point charge of +2.5 nC is 0.25 m from a charge of +1.4 nC, what is the electric force on each particle? 2. A point charge of +3.4 nC is 0.50 m from a charge of -2.2 nC, what is the electric force on each particle? 15.3 Electric Force If there are multiple point charges, the force vectors must be added to get the net force. k = 9.00x109 N·m2/C2 Find the net electric force acting upon each of the charges for the following problems: Charge 1: +4.5 nC (0m, 0.3m) Charge 2: +3.0 nC (0m, 0.3m) Charge 3: +2.5 nC (0.4m, 0m) k = 9.00x109 N·m2/C2 Find the net electric force acting upon each of the charges below Charge 1: +2.5 nC (3.0 cm, 0 cm) Charge 2: +1.0 nC (0 cm, 0 cm) Charge 3: +5.5 nC (0 cm, -5.0 cm) 15.4 Electric Field Definition of the electric field: The direction of the field is the direction the force would be on a positive charge. 15.4 Electric Field Charges create electric fields, and these fields in turn exert electric forces on other charges. Electric field of a point charge: 15.4 Electric Field For multiple charges, the total electric field is found using the superposition principle: For a configuration of charges, the total, or net, electric field at any point is the vector sum of the electric fields due to the individual charges. 15.4 Electric Field It is convenient to represent the electric field using electric field lines, or lines of force. These lines are drawn so the field is tangent to the line at every point. 15.4 Electric Field Rules for drawing electric field lines: 1. Closer lines mean a stronger field. 2. The field is tangent to the lines at every point. 3. Field lines start on positive charges and end on negative charges. 4. The number of lines entering or leaving a charge is proportional to the magnitude of the charge. 5. Field lines never cross. 15.4 Electric Field Electric field lines of a dipole: 15.4 Electric Field r = 0.015m Practice! + A +4.5 nC charge is fixed in place. 1) What is the electric field created by this charge 1.5 cm to the right of it? (don’t forget direction!) 2) If a -2.0 nC charge is placed in the above location, what force will it experience? 15.4 Electric Field r = 0.015m Practice! + 1) What is the electric field caused by the -2.0 nC charge 2.0 cm below it? 2) What is the electric field caused by the 4.5 nC charge 2.0 cm below the -2.0 nC charge? 3) What is the overall electric field 2.0 cm below the -2.0 nC charge? r = 0.020m The -2.0 nC charge is now also fixed in place and a +1.5 nC charge is added to the previous system - 15.4 Electric Field Electric field lines due to very large parallel plates: Electric Fields! Exclamation because we’re excited about it 1. You place a charged particle in an electric field and it experiences no net force, which of the following could be true? A. It is far enough from another charge that it is unaffected q ---/ /---? B. It is in-between two charges q---?---q C. It is next to two charges q---q---? D. There is no other charged object ? E. The object placed has no charge q 0 q Bold and underlined because Physics is AWESOME Electric Fields! 2. Thirteen electrons, a proton, and Bilbo Baggins (no charge) set out on a grand adventure. Find the electric field 4.5 cm away from this merry group. 3. A +5.0 nC particle is placed to the left of another charged object and is experiencing a 6.2E9 N force. Find the field acting upon the +5.0 nC particle and determine the charge of the other object. 15.4 Electric Field Electric field lines due to like charges: (a) equal charges; (b) unequal charges. Electric Field Applet 15.5 Conductors and Electric Fields Electric charges are free to move within a conductor; therefore, there cannot be a static field within the conductor: The electric field is zero inside a charged conductor. Excess charges on a conductor will repel each other, and will wind up being as far apart as possible. Any excess charge on an isolated conductor resides entirely on the surface of the conductor. 15.5 Conductors and Electric Fields There cannot be any component of the electric field parallel to the surface of a conductor; otherwise charges would move. The electric field at the surface of a charged conductor is perpendicular to the surface. 15.5 Conductors and Electric Fields The force from neighboring charges is less when the curvature of the surface is large: Excess charge tends to accumulate at sharp points, or locations of highest curvature, on charged conductors. As a result, the electric field is greatest at such locations. 15.6 Gauss’s Law for Electric Fields: A Qualitative Approach Gaussian surface Completely surrounds a point charge and intercepts the same number of field lines regardless of its shape. For a positive charge, the lines exit the surface; for a negative one they enter it. 15.6 Gauss’s Law for Electric Fields: A Qualitative Approach If a greater amount of charge is enclosed, more field lines cross the surface. 15.6 Gauss’s Law for Electric Fields: A Qualitative Approach Here, surface 1 surrounds the positive charge and has lines exiting it. Surface 2 surrounds the negative charge and has lines entering it. Surface 3 does not enclose any charge, and the same number of lines exit as enter. Surface 4 encloses both charges; as they are equal in magnitude, the same number of lines exit the surface as enter it. 15.6 Gauss’s Law for Electric Fields: A Qualitative Approach The underlying physical principle of Gauss’s law: The net number of electric field lines passing through an imaginary closed surface is proportional to the amount of net charge enclosed within that surface. This can be used to show that excess charge on a conductor must reside on the surface. Summary of Chapter 15 Like charges repel; unlike charges attract. Charge is conserved. Electrons move freely inside conductors, but not inside insulators. Objects may be charged electrostatically by friction, conduction, or induction. Polarization is the separation of positive and negative charge within an object. Summary of Chapter 15 Coulomb’s law: The electric field, a vector, is the force per unit charge. Electric fields from multiple charges add by superposition. Electric field lines are used to represent the electric field. A conductor has zero electric field inside and has all excess charge on its surface. Summary of Chapter 15 The electric field is always perpendicular to the surface of a conductor. The charge density and electric field are greatest on a conductor where the curvature is largest. Chapter 15: Overview I. Electric Charge • • II. How to calculate based upon electrons/protons Static charging: friction, conduction, induction, polarization Electric Force • Force between two or more charges Reminder: III. Electric Fields • • Fields define force per unit charge Field lines rules IV. Charged Objects • • Rules of charged conductors Gaussian surfaces Vector Math Equations q = ne F = kq1q2/r2 E = F/q E = kq/r2