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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 • Electric Forces in Molecular Biology: DNA • Photocopy Machines and Computer Printers Use Electrostatics 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? ConcepTest 21.1b Electric Charge II From the picture, what can you conclude about the charges? 1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) ConcepTest 21.1b Electric Charge II From the picture, what can you conclude about the charges? 1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) The GREEN and PINK balls must have the same charge, since they repel each other. The YELLOW ball also repels the GREEN, so it must also have the same charge as the GREEN (and the PINK). 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. 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. ConcepTest 21.2a Conductors I A metal ball hangs from the ceiling 1) positive by an insulating thread. The ball is 2) negative attracted to a positive-charged rod 3) neutral held near the ball. The charge of 4) positive or neutral the ball must be: 5) negative or neutral ConcepTest 21.2a Conductors I A metal ball hangs from the ceiling 1) positive by an insulating thread. The ball is 2) negative attracted to a positive-charged rod 3) neutral held near the ball. The charge of 4) positive or neutral the ball must be: 5) negative or neutral Clearly, the ball will be attracted if its charge is negative. However, even if the ball is neutral, the charges in the ball can be separated by induction (polarization), leading to a net attraction. Remember the ball is a conductor! Follow-up: What happens if the metal ball is replaced by a plastic ball? 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 the electric force between two charges is proportional to the product of the charges and 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. Copyright © 2009 Pearson Education, Inc. 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. Copyright © 2009 Pearson Education, Inc. ConcepTest 21.3a Coulomb’s Law I What is the magnitude 1) 1.0 N 2) 1.5 N of the force F2? 3) 2.0 N F1 = 3 N Q Q F2 = ? 4) 3.0 N 5) 6.0 N ConcepTest 21.3a Coulomb’s Law I What is the magnitude 1) 1.0 N 2) 1.5 N of the force F2? 3) 2.0 N F1 = 3 N Q Q F2 = ? 4) 3.0 N 5) 6.0 N The force F2 must have the same magnitude as F1. This is due to the fact that the form of Coulomb’s law is totally symmetric with respect to the two charges involved. The force of one on the other of a pair is the same as the reverse. Note that this sounds suspiciously like Newton’s 3rd law!! ConcepTest 21.3b Coulomb’s Law II F1 = 3 N Q Q F2 = ? 2) 3.0 N If we increase one charge to 4Q, what is the magnitude of F1? F1 = ? 4Q Q 1) 3/4 N F2 = ? 3) 12 N 4) 16 N 5) 48 N ConcepTest 21.3b Coulomb’s Law II F1 = 3 N Q Q F2 = ? 2) 3.0 N If we increase one charge to 4Q, what is the magnitude of F1? F1 = ? 4Q Q 1) 3/4 N F2 = ? 3) 12 N 4) 16 N 5) 48 N Originally we had: F1 = k(Q)(Q)/r2 = 3 N Now we have: F1 = k(4Q)(Q)/r2 which is 4 times bigger than before. Follow-up: Now what is the magnitude of F2? ConcepTest 21.3c Coulomb’s Law III The force between two charges 1) 9F separated by a distance d is F. If 2) 3F the charges are pulled apart to a 3) F distance 3d, what is the force on 4) 1/3F each charge? 5) 1/9F F F Q Q d ? ? Q Q 3d ConcepTest 21.3c Coulomb’s Law III The force between two charges 1) 9F separated by a distance d is F. If 2) 3F the charges are pulled apart to a 3) F distance 3d, what is the force on 4) 1/3F each charge? 5) 1/9F F Originally we had: F Q Q Fbefore = k(Q)(Q)/d2 = F Now we have: Fafter = k(Q)(Q)/(3d)2 = 1/9F d ? ? Q Q 3d Follow-up: What is the force if the original distance is halved? 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 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. 21-5 Coulomb’s Law The proportionality constant k can also be written in terms of ε0, the permittivity of free space: Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Conceptual Example 21-1: Which charge exerts the greater force? Two positive point charges, Q1 = 50 μC and Q2 = 1 μC, are separated by a distance . Which is larger in magnitude, the force that Q1 exerts on Q2 or the force that Q2 exerts on Q1? Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Example 21-2: Three charges in a line. Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μC on the right) due to the other two charges. Copyright © 2009 Pearson Education, Inc. ConcepTest 21.4a Electric Force I Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q0 on the line between the two charges such that the net force on Q0 will be zero? 1) yes, but only if Q0 is positive 2) yes, but only if Q0 is negative 3) yes, independent of the sign (or value) of Q0 4) no, the net force can never be zero +4Q +Q 3R ConcepTest 21.4a Electric Force I Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q0 on the line between the two charges such that the net force on Q0 will be zero? 1) yes, but only if Q0 is positive 2) yes, but only if Q0 is negative 3) yes, independent of the sign (or value) of Q0 4) no, the net force can never be zero A positive charge would be repelled by both charges, so a point where these two repulsive forces cancel +4Q +Q can be found. A negative charge would be attracted by both, and the same argument holds. Follow-up: What happens if both charges are +Q? Where would the F = 0 point be in this case? 3R ConcepTest 21.4c Electric Force III Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q0 anywhere on the line such that the net force on Q0 will be zero? 1) yes, but only if Q0 is positive 2) yes, but only if Q0 is negative 3) yes, independent of the sign (or value) of Q0 4) no, the net force can never be zero – 4Q +Q 3R ConcepTest 21.4c Electric Force III Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q0 anywhere on the line such that the net force on Q0 will be zero? 1) yes, but only if Q0 is positive 2) yes, but only if Q0 is negative 3) yes, independent of the sign (or value) of Q0 4) no, the net force can never be zero A charge (positive or negative) can be placed to the left of the +Q charge, – 4Q +Q such that the repulsive force from the +Q charge cancels the attractive 3R force from –4Q. Follow-up: What happens if one charge is +Q and the other is –Q? 21-5 Coulomb’s Law Example 21-3: Electric force using vector components. Calculate the net electrostatic force on charge Q3 shown in the figure due to the charges Q1 and Q2. Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Conceptual Example 21-4: Make the force on Q3 zero. In the figure, where could you place a fourth charge, Q4 = -50 μC, so that the net force on Q3 would be zero? Copyright © 2009 Pearson Education, Inc. 1 ConcepTest 21.6 Forces in 2D 2 3 Which of the arrows best 4 represents the direction of the net force on charge d +2Q +Q +Q due to the other two charges? d +4Q 5 1 ConcepTest 21.6 Forces in 2D 2 3 Which of the arrows best 4 represents the direction of the net force on charge d +2Q +Q +Q due to the other two d charges? +4Q The charge +2Q repels +Q toward the right. The charge +4Q repels +Q upward, but with a stronger force. Therefore, the net force is up and to +2Q the right, but mostly up. Follow-up: What would happen if the yellow charge were +3Q? +4Q 5 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: Copyright © 2009 Pearson Education, Inc. ConcepTest 21.7 Electric Field You are sitting a certain distance from a point charge, and you measure an electric field of E0. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now? 1) 4E0 2) 2E0 3) E0 4) 1/2E0 5) 1/4E0 ConcepTest 21.7 Electric Field You are sitting a certain distance from a point charge, and you measure an electric field of E0. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now? 1) 4E0 2) 2E0 3) E0 4) 1/2E0 5) 1/4E0 Remember that the electric field is: E = kQ/r2. Doubling the charge puts a factor of 2 in the numerator, but doubling the distance puts a factor of 4 in the denominator, because it is distance squared!! Overall, that gives us a factor of 1/2. Follow-up: If your distance is doubled, what must you do to the charge to maintain the same E field at your new position? 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 21-6: Electric field of a single point charge. Calculate the magnitude and direction of the electric field at a point P which is 30 cm to the right of a point charge Q = -3.0 x 10-6 C. Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field Example 21-7: E at a point between two charges. Two point charges are separated by a distance of 10.0 cm. One has a charge of -25 μC and the other +50 μC. (a) Determine the direction and magnitude of the electric field at a point P between the two charges that is 2.0 cm from the negative charge. (b) If an electron (mass = 9.11 x 10-31 kg) is placed at rest at P and then released, what will be its initial acceleration (direction and magnitude)? Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field Example 21-8: E above two point charges. Calculate the total electric field (a) at point A and (b) at point B in the figure due to both charges, Q1 and Q2. Copyright © 2009 Pearson Education, Inc. ConcepTest 21.9a Superposition I -2 C What is the electric field at 2 1 the center of the square? 3 5) E = 0 -2 C 4 ConcepTest 21.9a Superposition I -2 C What is the electric field at 2 1 the center of the square? 3 5) E = 0 -2 C For the upper charge, the E field vector at the center of the square points toward that charge. For the lower charge, the same thing is true. Then the vector sum of these two E field vectors points to the left. Follow-up: What if the lower charge were +2 C? What if both charges were +2 C? 4 21-6 The Electric Field Problem solving in electrostatics: electric forces and 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 vectorially to get result. 4. Check your answer! Copyright © 2009 Pearson Education, Inc. Summary of Chapter 21 Sec. 1-6 • Two kinds of electric charge – positive and negative. • Charge is conserved. • Charge on electron: e = 1.602 x 10-19 C. • Conductors: electrons free to move. • Insulators: nonconductors. Copyright © 2009 Pearson Education, Inc. Summary of Chapter 21 Sec. 1-6 • Charge is quantized in units of e. • Objects can be charged by conduction or induction. • Coulomb’s law: •Electric field is force per unit charge: Copyright © 2009 Pearson Education, Inc. Summary of Chapter 21 Sec. 1-6 • Electric field of a point charge: Copyright © 2009 Pearson Education, Inc.