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Copyright © 2009 Pearson Education, Inc. Chapter 21 Electric Charge and Electric Field

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Copyright © 2009 Pearson Education, Inc. 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 Units of Chapter 21

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Copyright © 2009 Pearson Education, Inc. 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 Units of Chapter 21

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Copyright © 2009 Pearson Education, Inc. Objects can be charged by rubbing 21 - 1 Static Electricity; Electric Charge and Its Conservation

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Copyright © 2009 Pearson Education, Inc. Charge comes in two types, positive and negative; like charges repel and opposite charges attract. 21 - 1 Static Electricity; Electric Charge and Its Conservation

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ConcepTest 21.1aElectric Charge I ConcepTest 21.1a Electric Charge I 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?

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ConcepTest 21.1aElectric Charge I ConcepTest 21.1a Electric Charge I same charge 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. 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? Follow-up: What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral?

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1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) From the picture, what can you conclude about the charges? ConcepTest 21.1bElectric Charge II ConcepTest 21.1b Electric Charge II

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1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) From the picture, what can you conclude about the charges? 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). ConcepTest 21.1bElectric Charge II ConcepTest 21.1b Electric Charge II

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Copyright © 2009 Pearson Education, Inc. Electric charge is conserved – the arithmetic sum of the total charge cannot change in any interaction. 21 - 1 Static Electricity; Electric Charge and Its Conservation

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Copyright © 2009 Pearson Education, Inc. Atom: Nucleus (small, massive, positive charge) Electron cloud (large, very low density, negative charge) 21 - 2 Electric Charge in the Atom

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Copyright © 2009 Pearson Education, Inc. Polar molecule: neutral overall, but charge not evenly distributed 21 - 2 Electric Charge in the Atom

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Copyright © 2009 Pearson Education, Inc. Conductor: Charge flows freely Metals Insulator: Almost no charge flows Most other materials Some materials are semiconductors. 21-3 Insulators and Conductors

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Copyright © 2009 Pearson Education, Inc. Metal objects can be charged by conduction: 21-4 Induced Charge; the Electroscope

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Copyright © 2009 Pearson Education, Inc. They can also be charged by induction, either while connected to ground or not: 21-4 Induced Charge; the Electroscope

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Copyright © 2009 Pearson Education, Inc. Nonconductors won’t become charged by conduction or induction, but will experience charge separation: 21-4 Induced Charge; the Electroscope

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ConcepTest 21.2aConductors I ConcepTest 21.2a Conductors I 1) positive 2) negative 3) neutral 4) positive or neutral 5) negative or neutral A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be:

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negative neutral induction 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. 1) positive 2) negative 3) neutral 4) positive or neutral 5) negative or neutral A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be: Remember the ball is a conductor! ConcepTest 21.2aConductors I ConcepTest 21.2a Conductors I Follow-up: What happens if the metal ball is replaced by a plastic ball?

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Copyright © 2009 Pearson Education, Inc. The electroscope can be used for detecting charge. 21-4 Induced Charge; the Electroscope

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Copyright © 2009 Pearson Education, Inc. The electroscope can be charged either by conduction or by induction. 21-4 Induced Charge; the Electroscope

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Copyright © 2009 Pearson Education, Inc. The charged electroscope can then be used to determine the sign of an unknown charge. 21-4 Induced Charge; the Electroscope

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Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? ConcepTest 21.2bConductors II ConcepTest 21.2b Conductors II 1)00 2)+– 3)–+ 4)++ 5)– – 0 0 ? ?

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positive charge will flow from the blue to the green ball due to polarization charges will remain on the separate conductors While the conductors are connected, positive 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. Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? ConcepTest 21.2bConductors II ConcepTest 21.2b Conductors II 1)00 2)+– 3)–+ 4)++ 5)– – 0 0 ? ? Follow-up: What will happen when the conductors are reconnected with a wire?

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Copyright © 2009 Pearson Education, Inc. 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. 21-5 Coulomb’s Law

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Copyright © 2009 Pearson Education, Inc. Coulomb’s law: This equation gives the magnitude of the force between two charges. 21-5 Coulomb’s Law

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Copyright © 2009 Pearson Education, Inc. The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same. 21-5 Coulomb’s Law

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Q Q F 1 = 3 N F 2 = ? 1) 1.0 N 2) 1.5 N 3) 2.0 N 4) 3.0 N 5) 6.0 N What is the magnitude of the force F 2 ? ConcepTest 21.3aCoulomb’s Law I ConcepTest 21.3a Coulomb’s Law I

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same magnitude 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!! The force F 2 must have the same magnitude as F 1. 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!! Q Q F 1 = 3 N F 2 = ? 1) 1.0 N 2) 1.5 N 3) 2.0 N 4) 3.0 N 5) 6.0 N What is the magnitude of the force F 2 ? ConcepTest 21.3aCoulomb’s Law I ConcepTest 21.3a Coulomb’s Law I

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ConcepTest 21.3bCoulomb’s Law II ConcepTest 21.3b Coulomb’s Law II 1) 3/4 N 2) 3.0 N 3) 12 N 4) 16 N 5) 48 N If we increase one charge to 4Q, what is the magnitude of F 1 ? 4Q4Q4Q4Q Q F 1 = ? F 2 = ? Q Q F 1 = 3 N F 2 = ?

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ConcepTest 21.3bCoulomb’s Law II ConcepTest 21.3b Coulomb’s Law II Originally we had: F 1 = k(Q)(Q)/r 2 = 3 N Now we have: F 1 = k(4Q)(Q)/r 2 4 times bigger which is 4 times bigger than before. 1) 3/4 N 2) 3.0 N 3) 12 N 4) 16 N 5) 48 N If we increase one charge to 4Q, what is the magnitude of F 1 ? 4Q4Q4Q4Q Q F 1 = ? F 2 = ? Q Q F 1 = 3 N F 2 = ? Follow-up: Now what is the magnitude of F 2 ?

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1) 9F 2) 3F 3) F 4) 1/3F 5) 1/9F The force between two charges separated by a distance d is F. If the charges are pulled apart to a distance 3d, what is the force on each charge? QF QFd Q ? Q ? 3d3d3d3d ConcepTest 21.3cCoulomb’s Law III ConcepTest 21.3c Coulomb’s Law III

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Originally we had: F before = k(Q)(Q)/d 2 = F Now we have: F after = k(Q)(Q)/(3d) 2 = 1/9F 1) 9F 2) 3F 3) F 4) 1/3F 5) 1/9F The force between two charges separated by a distance d is F. If the charges are pulled apart to a distance 3d, what is the force on each charge? QF QFd Q?Q? 3d3d3d3d ConcepTest 21.3cCoulomb’s Law III ConcepTest 21.3c Coulomb’s Law III Follow-up: What is the force if the original distance is halved?

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Copyright © 2009 Pearson Education, Inc. Unit of charge: coulomb, C. The proportionality constant in Coulomb’s law is then: k = 8.99 x 10 9 N·m 2 /C 2. Charges produced by rubbing are typically around a microcoulomb: 1 μC = 10 -6 C. 21-5 Coulomb’s Law

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Copyright © 2009 Pearson Education, Inc. Charge on the electron: e = 1.602 x 10 -19 C. Electric charge is quantized in units of the electron charge. 21-5 Coulomb’s Law

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Copyright © 2009 Pearson Education, Inc. The proportionality constant k can also be written in terms of ε 0, the permittivity of free space: 21-5 Coulomb’s Law

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Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Conceptual Example 21-1: Which charge exerts the greater force? Two positive point charges, Q 1 = 50 μC and Q 2 = 1 μC, are separated by a distance. Which is larger in magnitude, the force that Q 1 exerts on Q 2 or the force that Q 2 exerts on Q 1 ?

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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.

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ConcepTest 21.4aElectric Force I ConcepTest 21.4a Electric Force I Q 0 is positive 1) yes, but only if Q 0 is positive Q 0 is negative 2) yes, but only if Q 0 is negative Q 0 3) yes, independent of the sign (or value) of Q 0 4) no, the net force can never be zero Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 on the line between the two charges such that the net force on Q 0 will be zero? 3R3R +Q+Q +4Q

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ConcepTest 21.4aElectric Force I ConcepTest 21.4a Electric Force I Q 0 is positive 1) yes, but only if Q 0 is positive Q 0 is negative 2) yes, but only if Q 0 is negative Q 0 3) yes, independent of the sign (or value) of Q 0 4) no, the net force can never be zero Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 on the line between the two charges such that the net force on Q 0 will be zero? 3R3R +Q+Q +4Q A positive charge would be repelled by both charges, so a point where these two repulsive forces cancel 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?

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3R3R +Q+Q – – 4Q Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 anywhere on the line such that the net force on Q 0 will be zero? ConcepTest 21.4cElectric Force III ConcepTest 21.4c Electric Force III Q 0 is positive 1) yes, but only if Q 0 is positive Q 0 is negative 2) yes, but only if Q 0 is negative Q 0 3) yes, independent of the sign (or value) of Q 0 4) no, the net force can never be zero

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3R3R +Q+Q – – 4Q to the left A charge (positive or negative) can be placed to the left of the +Q charge, such that the repulsive force from the +Q charge cancels the attractive force from –4Q. Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 anywhere on the line such that the net force on Q 0 will be zero? ConcepTest 21.4cElectric Force III ConcepTest 21.4c Electric Force III Q 0 is positive 1) yes, but only if Q 0 is positive Q 0 is negative 2) yes, but only if Q 0 is negative Q 0 3) yes, independent of the sign (or value) of Q 0 4) no, the net force can never be zero Follow-up: What happens if one charge is +Q and the other is – Q ?

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Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Example 21-3: Electric force using vector components. Calculate the net electrostatic force on charge Q 3 shown in the figure due to the charges Q 1 and Q 2.

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Copyright © 2009 Pearson Education, Inc. 21-5 Coulomb’s Law Conceptual Example 21-4: Make the force on Q 3 zero. In the figure, where could you place a fourth charge, Q 4 = -50 μC, so that the net force on Q 3 would be zero?

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Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges? +2Q +4Q +Q+Q 1 2 3 4 5 d d ConcepTest 21.6Forces in 2D ConcepTest 21.6 Forces in 2D

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net force is up and to the right, but mostly up 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 the right, but mostly up. +2Q +4Q +Q+Q 1 2 3 4 5 d d +2Q+4Q ConcepTest 21.6Forces in 2D ConcepTest 21.6 Forces in 2D Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges? Follow-up: What would happen if the yellow charge were +3Q?

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Copyright © 2009 Pearson Education, Inc. The electric field is defined as the force on a small charge, divided by the magnitude of the charge: 21-6 The Electric Field

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Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field An electric field surrounds every charge.

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Copyright © 2009 Pearson Education, Inc. For a point charge: 21-6 The Electric Field

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4E 0 1) 4E 0 2E 0 2) 2E 0 E 0 3) E 0 1/2E 0 4) 1/2E 0 4E 0 5) 1/4E 0 You are sitting a certain distance from a point charge, and you measure an electric field of E 0. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now? ConcepTest 21.7Electric Field ConcepTest 21.7 Electric Field

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Doubling the chargefactor of 2 doubling the distancefactor of 4 factor of 1/2 Remember that the electric field is: E = kQ/r 2. 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. 4E 0 1) 4E 0 2E 0 2) 2E 0 E 0 3) E 0 1/2E 0 4) 1/2E 0 4E 0 5) 1/4E 0 You are sitting a certain distance from a point charge, and you measure an electric field of E 0. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now? ConcepTest 21.7Electric Field ConcepTest 21.7 Electric Field Follow-up: If your distance is doubled, what must you do to the charge to maintain the same E field at your new position?

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Copyright © 2009 Pearson Education, Inc. Force on a point charge in an electric field: 21-6 The Electric Field

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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.

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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)?

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Copyright © 2009 Pearson Education, Inc. 21-6 The Electric Field Example 21-8: 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, Q 1 and Q 2.

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What is the electric field at the center of the square? 4 3 2 1 -2 C 5) E = 0 ConcepTest 21.9aSuperposition I ConcepTest 21.9a Superposition I

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points to the left 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. What is the electric field at the center of the square? 4 3 2 1 -2 C 5) E = 0 ConcepTest 21.9aSuperposition I ConcepTest 21.9a Superposition I Follow-up: What if the lower charge were +2 C? What if both charges were +2 C?

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Copyright © 2009 Pearson Education, Inc. 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! 21-6 The Electric Field

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Copyright © 2009 Pearson Education, Inc. 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. Summary of Chapter 21 Sec. 1-6

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Copyright © 2009 Pearson Education, Inc. 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: Summary of Chapter 21 Sec. 1-6

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Copyright © 2009 Pearson Education, Inc. Electric field of a point charge: Summary of Chapter 21 Sec. 1-6

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