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PHYSICS 2415 Suggested strategies: • Read text before lecture • Attend lecture • Do problems! This is where what you learned from reading or from class gets solidified in your mind. Do not beat your head against a brick wall. If, after reasonable effort you’re stumped, go back to the chapter/section • Spread your work out over 4-6 days a week, depending on demands of other classes • Do not work more than ~2 hours or so at one time; then take a real break, at least an hour spent doing something completely different Copyright © 2009 Pearson Education, Inc. Chapter 21 Electric Charge and Electric Field Copyright © 2009 Pearson Education, Inc. Units of Chapter 21 • Static Electricity; Electric Charge and Its Conservation • Electric Charge in the Atom • Insulators and Conductors • Induced Charge; the Electroscope • Coulomb’s Law • The Electric Field • Electric Field Calculations for Continuous Charge Distributions Copyright © 2009 Pearson Education, Inc. Units of Chapter 21 • Field Lines • Electric Fields and Conductors • Motion of a Charged Particle in an Electric Field • Electric Dipoles Copyright © 2009 Pearson Education, Inc. 21-1 Static Electricity; Electric Charge and Its Conservation Objects can be charged by rubbing Copyright © 2009 Pearson Education, Inc. 21-1 Static Electricity; Electric Charge and Its Conservation Charge comes in two types, positive and negative; like charges repel and opposite charges attract. Copyright © 2009 Pearson Education, Inc. ConcepTest 21.1a Electric Charge I Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative ConcepTest 21.1a Electric Charge I Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative The fact that the balls repel each other can tell you only that they have the same charge, but you do not know the sign. So they can be either both positive or both negative. Follow-up: What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral? 21-1 Static Electricity; Electric Charge and Its Conservation Electric charge is conserved – the arithmetic sum of the total charge cannot change in any interaction. Copyright © 2009 Pearson Education, Inc. 21-2 Electric Charge in the Atom Atom: Nucleus (small, massive, positive charge) Electron cloud (large, very low density, negative charge) Copyright © 2009 Pearson Education, Inc. Elementary charge Charge on the electron: e = 1.602 x 10-19 C. Electric charge is quantized in units of the electron charge. Copyright © 2009 Pearson Education, Inc. 21-2 Electric Charge in the Atom Polar molecule: neutral overall, but charge not evenly distributed Copyright © 2009 Pearson Education, Inc. 21-3 Insulators and Conductors Conductor: Insulator: Charge flows freely Almost no charge flows Metals Most other materials Some materials are semiconductors. Copyright © 2009 Pearson Education, Inc. 21-4 Induced Charge; the Electroscope Metal objects can be charged by conduction: Copyright © 2009 Pearson Education, Inc. 21-4 Induced Charge; the Electroscope They can also be charged by induction, either while connected to ground or not: Copyright © 2009 Pearson Education, Inc. 21-4 Induced Charge; the Electroscope Nonconductors won’t become charged by conduction or induction, but will experience charge separation: Copyright © 2009 Pearson Education, Inc. 21-4 Induced Charge; the Electroscope The electroscope can be used for detecting charge. Copyright © 2009 Pearson Education, Inc. 21-4 Induced Charge; the Electroscope The electroscope can be charged either by conduction or by induction. Copyright © 2009 Pearson Education, Inc. 21-4 Induced Charge; the Electroscope The charged electroscope can then be used to determine the sign of an unknown charge. Copyright © 2009 Pearson Education, Inc. ConcepTest 21.2b Conductors II Two neutral conductors are connected 1) 0 0 by a wire and a charged rod is brought 2) + – 3) – + 4) + + 5) – – near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? 0 0 ? ? ConcepTest 21.2b Conductors II Two neutral conductors are connected 1) 0 0 by a wire and a charged rod is brought 2) + – 3) – + 4) + + 5) – – near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? While the conductors are connected, positive 0 0 ? ? charge will flow from the blue to the green ball due to polarization. Once disconnected, the charges will remain on the separate conductors even when the rod is removed. Follow-up: What will happen when the conductors are reconnected with a wire? 21-5 Coulomb’s Law Experiment shows that 1) the electric force between two charges is proportional to the product of the charges and 2) inversely proportional to the distance between them. Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Coulomb’s law: This equation gives the magnitude of the force between two charges. In vector form: Copyright © 2009 Pearson Education, Inc. Q1Q2 F21 k 2 rˆ21 r21 21-5 Coulomb’s Law Unit of charge: coulomb, C. The proportionality constant in Coulomb’s law is then: k = 8.99 x 109 N·m2/C2. Charges produced by rubbing are typically around a microcoulomb: 1 μC = 10-6 C. Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law The proportionality constant k can also be written in terms of ε0, the permittivity of free space: 1C 1C 1N k 2 1m Copyright © 2009 Pearson Education, Inc. 1 statC 1 statC or in cgs units 1dyne 2 1cm 21-5 Coulomb’s Law The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same. Newton’s Third Law applies! Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Example: Three charges in a line. Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 2 (the +3.0 μC in the middle) due to the other two charges. Copyright © 2009 Pearson Education, Inc. ConcepTest 21.4b Electric Force II Two balls with charges +Q and +4Q are separated by 3R. Where should you place another charged ball Q0 on the line between the two charges such that the net force on Q0 will be zero? +4Q +Q 1 2 3 4 2R R 3R 5 ConcepTest 21.4b Electric Force II Two balls with charges +Q and +4Q are separated by 3R. Where should you place another charged ball Q0 on the line between the two charges such that the net force on Q0 will be zero? +4Q +Q 1 2 3 4 5 2R R 3R The force on Q0 due to +Q is: F = k(Q0)(Q)/R2 The force on Q0 due to +4Q is: F = k(Q0)(4Q)/(2R)2 Since +4Q is 4 times bigger than +Q, Q0 needs to be farther from +4Q. In fact, Q0 must be twice as far from +4Q, since the distance is squared in Coulomb’s law. 21-5 Coulomb’s Law Force is a vector quantity: Example: Calculate the net electrostatic force on charge q3 shown in the figure due to the charges q1 and q2. q1 q3 5.00 C q2 2.00 C a 0.100 m Copyright © 2009 Pearson Education, Inc. q1q2 F12 k 2 rˆ12 r12 Coulomb’s Law r r q q q q F k 2 k 2 k q q r r F attractive Copyright © 2009 Pearson Education, Inc. 1 1 r2 r2 0 21-6 The Electric Field The electric field is defined as the force on a small charge, divided by the magnitude of the charge: Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field An electric field surrounds every charge. Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field For a point charge: F Q E r is a vector: E pt k 2 rˆ q r Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field Force on a point charge in an electric field: Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field Example: Calculate the total electric field at point P due to both charges, q and -q. Hint: exploit symmetry! What direction would E point if both charges were equal, not opposite? Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field Problem solving in electrostatics: electric forces and/or electric fields 1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions. 2. Calculate forces using Coulomb’s law. 3. Add forces vectorally to get result. 4. Check your answer! Copyright © 2009 Pearson Education, Inc. ConcepTest 21.9b Superposition II What is the electric field at -2 C 2 -2 C 1 the center of the square? 3 5) E = 0 -2 C 4 -2 C ConcepTest 21.9b Superposition II What is the electric field at -2 C 2 -2 C 1 the center of the square? 3 5) E = 0 -2 C The four E field vectors all point outward from the center of the square toward their respective charges. Because they are all equal, the net E field is zero at the center!! Follow-up: What if the upper two charges were +2 C? What if the right-hand charges were +2 C? 4 -2 C Questions? Copyright © 2009 Pearson Education, Inc.