Date: History of Electricity & Magnetism Chapter 23- part1 Electric Charge and Electric Force • After discovery of lodestone (Fe3O4) itself alignment, 1263 Pierre de Maricourt mapped lodestone to a compass and discovered North and South poles. • In the 1600's William Gilbert, concluded that Earth itself is a giant magnet. • In the 1785, Charles Coulomb confirmed inverse square law form for electric forces. • In 1820 Hans Christian discovered an electric current flowing through a wire can cause a compass needle to deflect, relation between magnetism and electricity. • In 1830 Michael Faraday and Joseph Henry independently discovered that a changing magnetic field produced a current in a coil of wire. • In the 19th century James Clerk Maxwell mathematically unified the electric and magnetic forces. Unified electricity and magnetism • In the late 19th century Pierre Curie discovered that magnets loose their magnetism above a certain temperature. • In the 1900's scientists discover superconductivity. 1/23/19 Electric Charges Content of Chapter • Static Electricity; Electric Charge • Coulomb’s Law • Electric Charge in the Atom • Charge is quantized • Insulators and Conductors • Charge is conserved (a) The two glass rods were each rubbed with a silk cloth and one was suspended by thread. When they are close to each other, they repel each other. • Induced Charge; the Electroscope (b) The plastic rod was rubbed with fur. When brought close to the glass rod, the rods attract each other. The word electromagnetism is the combination of electric and magnetic phenomena. This physics is the root of modern technology. Eg: Lights, computers, TV, telephones, motors and other electronics. And also this field of physics produces several natural behaviors. Eg: lightning and rainbows! Objects can be charged by rubbing!! In physics 1, we learnt about many forces that we can see and feel in day today life. Eg: Friction, gravity, normal, tension and centripetal forces. Now we are going to deal with electric forces acting at atomic level. How does this happened, no contact! Magic??? In this chapter we begin with electrical phenomena and discuss electric charge and electric forces! The concept of force links the study of electromagnetism to previous study. Origin of electroticity? Matter is made up of atoms. + – atom neutron (neutral) + + – Proton (positive charge) + – – electron (negative charge) nucleus If electrons = protons ⇒neutral If electrons > protons ⇒ gaining electrons, negative charge If electrons < protons ⇒ losing electrons, positive charge Electro-negativity Relative electro-negativity ranking for some common materials from electron donating materials (+, glass) to electron accepting materials (-, teflon) +++++ ++++ +++ ++ + Glass Human Hair Rubbing materials does NOT create electric charges. It just transfers electrons from one material to the other. Nylon Silk Fur Aluminum Paper ----------- Cotton Copper Rubber PVC Teflon 1 Date: Electric Charging process Electric Charges • When we rub the glass rod with silk cloth àa small amount of -ve charge moves to the silk by leaving the rod with a small amount of excess +ve charge! • When we hang the rod with a thread à electrically isolate (a) Two charged rods of the same sign repel each other. (b) Two charged rods of opposite signs attract each other. Plus signs indicate a positive net charge, and minus signs indicate a negative net charge. A charge comes in two types, positive and negative; like same charges repel and opposite charges attract! Extra charge is said to be an excess charge! ConcepTest Electric Charge Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? Electric charge is always conserved in an isolated system. • For example, charge is not created in the process of rubbing two objects together. • The electrification is due to a transfer of charge from one object to another. • A glass rod is rubbed with silk. • Electrons are transferred from the glass to the silk. • Each electron adds a negative charge to the silk. • An equal positive charge is left on the rod. ConcepTest a) one is positive, the other is negative b) both are positive c) both are negative d) both are positive or both are negative Electric Charge Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? a) one is positive, the other is negative b) both are positive c) both are negative d) both are positive or both are negative The fact that the balls repel each other only can tell you that they have the same charge, but you do not know the sign. So they can be either both positive or both negative. ConcepTest Electric Charge From the picture, what can you conclude about the charges? ConcepTest Electric Charge a) have opposite charges b) have the same charge c) all have the same charge d) one ball must be neutral (no charge) From the picture, what can you conclude about the charges? a) have opposite charges b) have the same charge c) all have the same charge d) one ball must be neutral (no charge) The GREEN and RED 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 RED). 2 Date: Materials Atomic structure Materials are classified based on their ability to move charges! Atom: • Conductors are materials in which a significant number of electrons are free to move. Examples: metals. Nucleus (small, massive, positive charge) • The charged particles in nonconductors (insulators) are not free to move. Examples: rubber, plastic, glass. Electron cloud (large, very low density, negative charge) Charged Particles. The properties of conductors and insulators are due to the structure and electrical nature of atoms. Atoms consist of positively charged protons, negatively charged electrons, and electrically neutral neutrons. The protons and neutrons are packed tightly together in a central nucleus and do not move. • Semiconductors are materials that are intermediate between conductors and insulators; Examples: silicon and germanium in computer chips. • Superconductors are materials that are perfect conductors, allowing charge to move without any hindrance. Examples: Mercury, diamond Atom is electrically neutral. Rubbing charges objects by moving electrons from one to the other. Charging by Induction Charging Methods Induced Charge. A neutral copper rod is electrically isolated from its surroundings by being suspended on a non-conducting thread. Either end of the copper rod will be attracted by a charged rod. Here, conduction electrons in the copper rod are repelled to the far end of that rod by the negative charge on the plastic rod. Then that negative charge attracts the remaining positive charge on the near end of the copper rod! Although the Copper rod is still neutral, it is said to have an Induced charge, which means that some of its +ve and –ve charges have been separated due to the presence of a nearby charge!! • Metal objects can be charged by conduction: • They can also be charged by induction conduction electrons: When atoms of a conductor like copper come together to form the solid, some of their outermost—and so most loosely held—electrons become free to move within the solid, leaving behind positively charged atoms ( positive ions). We call the mobile electrons as conduction electrons. • Charging by induction requires no contact with the object inducing the charge. Assume we start with a neutral metallic sphere. The sphere has the same number of positive and negative charges • A charged rubber rod is placed near the sphere. It does not touch the sphere. The electrons in the neutral sphere are redistributed. Electrons (-ve) are moving • Nonconductors won’t become charged by conduction or induction, but will experience charge separation: Charging by Induction • The ground wire is removed. There will now be more positive charges. The charges are not uniformly distributed. The positive charge has been induced in the sphere. • The rod is removed. The electrons remaining on the sphere redistribute themselves. There is still a net positive charge on the sphere. The charge is now uniformly distributed. Note the rod lost none of its negative charge during this process. • The sphere is grounded. Some electrons can leave the sphere through the ground wire. Point Charge • The term point charge refers to a particle of zero size that carries an electric charge. The electrical behavior of electrons and protons is well described by modeling them as point charges. • The smallest unit of “free” charge known in nature is the charge of an electron or proton, which has a magnitude of e= 1.602 x 10-19 C. • Charge of any ordinary matter is quantized in \multiples of e. An electron carries one unit of negative charge, −e , while a proton carries one unit of positive charge, +e . In a closed system, the total amount of charge is conserved since charge can neither be created nor destroyed. A charge can, however, be transferred from one body to another. 3 Date: ConcepTest Conductors ConcepTest a) positive A metal ball hangs from the ceiling by A metal ball hangs from the ceiling by b) negative an insulating thread. The ball is an insulating thread. The ball is c) neutral attracted to a positive-charged rod Conductors attracted to a positive-charged rod a) positive b) negative c) neutral held near the ball. The charge of the d) positive or neutral held near the ball. The charge of the d) positive or neutral ball must be: e) negative or neutral ball must be: e) 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 remember the ball is a conductor! attraction. ConcepTest Conductors ConcepTest a) 0 0 b) + – c) – + removed. What are the charges on the d) + + conductors? e) – – 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 0 0 Conductors a) 0 0 b) + – c) – + removed. What are the charges on the d) + + conductors? e) – – 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 While the conductors are connected, 0 0 ? ? negative charge will flow from the green to the blue ball. Once disconnected, the charges will remain on the separate conductors even when the rod is removed. ? ? Lightning kills more than 60 people and one mile every five seconds injures more than 400 people a year in the US about 20,000 C Voltage of up to 1.2x108 volts 4 Date: Coulomb’s Law Coulomb’s Law Coulomb’s law describes the electrostatic force (or electric force) between two charged particles. If the particles have charges q1 and q2, are separated by distance r, and are at rest (or moving only slowly) relative to each other, then the magnitude of the force acting on each due to the other is given by Valid for r>>size of the particles The electrostatic force on particle 1 can be described in terms of a unit vector r along an axis through the two particles, radially away from particle 2. where ε0 = 8.85 ×10-12 C2/N.m2 is the permittivity constant. The ratio 1/4πε0 is often replaced with the electrostatic constant (or Coulomb constant) k=8.99×109 N.m2/C2. Thus k = 1/4πε0 . Unit of charge: coulomb, C and Charge on the electron: e = 1.602 × 10−19 C Example 1 Two charges are separated by a distance r and have a force F on each other. F q1 qq F = k 1 22 r • The electrostatic force vector acting on a charged particle due to a second charged particle is either directly toward the second particle (opposite signs of charge) or directly away from it (same sign of charge). • Multiple Forces: If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. “Principle of superposition” F12=F21, Newton 3rd laws Two charged particles repel each other if they have the same sign of charge, either (a) both positive or (b) both negative. (c) They attract each other if they have opposite signs of charge. ConcepTest Coulomb’s Law a) 1.0 N What is the b) 1.5 N magnitude of the q2 F force F2? F1 = 3N r Q Q c) 2.0 N F2 = ? d) 3.0 N e) 6.0 N If r is doubled then F is : ¼ F If q1 is doubled then F is : 2F If q1 and q2 are doubled and r is halved then F is : 16F Answer: (a) left towards the electron (b) left away from the other proton (c) left ConcepTest Coulomb’s Law a) 1.0 N What is the F1 = 3N Q Q F1 = 3N b) 1.5 N magnitude of the force F2? ConcepTest F2 = ? Q Coulomb’s Law Q F2 = ? a) 3/4 N b) 3.0 N c) 2.0 N If we increase one charge to 4Q, c) 12 N d) 3.0 N what is the magnitude of F1? d) 16 N e) 6.0 N F1 = ? 4Q Q F2 = ? e) 48 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!! 5 Date: ConcepTest F1 = 3N Coulomb’s Law Q Q F2 = ? ConcepTest The force between two charges b) 3.0 N separated by a distance d is F. If If we increase one charge to 4Q, c) 12 N what is the magnitude of F1? d) 16 N F1 = ? 4Q Q F2 = ? Coulomb’s Law a) 3/4 N b) 3 F the charges are pulled apart to a c) F distance 3d, what is the force on d) 1/3 F each charge? e) 48 N e) 1/9 F Originally we had: F Q F1 = k(Q)(Q)/r2 = 3 N Now we have: F Q d ? F1 = k(4Q)(Q)/r2 ? Q Q which is 4 times bigger than before. ConcepTest a) 9 F 3d Coulomb’s Law The force between two charges ConcepTest separated by a distance d is F. If b) 3 F the charges are pulled apart to a c) F distance 3d, what is the force on Electric Force 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? a) 9 F d) 1/3 F each charge? e) 1/9 F F Originally we had: Q Fbefore = k(Q)(Q)/d2 = F Now we have: Q +4Q +Q a) d ? b) c) d) e) 2R R ? Q Fafter = k(Q)(Q)/(3d)2 = 1/9 F F Q 3R 3d ConcepTest Electric Force 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 a) b) c) d) ConcepTest Electric Force 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? e) a) yes, but only if Q0 is positive b) yes, but only if Q0 is negative c) yes, independent of the sign (or value) of Q0 d) no, the net force can never be zero 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 – 4Q +Q 3R Since +4Q is 4 times bigger than +Q, then 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. 6 Date: ConcepTest Electric Force 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? ConcepTest a) yes, but only if Q0 is positive b) yes, but only if Q0 is negative c) yes, independent of the sign (or value) of Q0 d) no, the net force can never be zero a) Forces in 2D b) c) Which of the arrows best d) represents the direction of the net force on charge +Q +2Q d due to the other two charges? +Q e) d +4Q A charge (positive or negative) can be placed to the left of the +Q charge, – 4Q +Q such that the repulsive force from the 3R +Q charge cancels the attractive force from –4Q. ConcepTest A) Forces in 2D B) Charge is Quantized C) Which of the arrows best D) represents the direction of +2Q the net force on charge +Q d due to the other two +Q E) d charges? • Electric charge is quantized (restricted to certain values). • The charge of a particle can be written as ne, where n is a positive or negative integer and e is the elementary charge. Any positive or negative charge q that can be detected can be written as in which e, the elementary charge, has the approximate value +4Q The charge +2Q repels +Q towards the right. The charge +4Q repels +Q upwards, but with a stronger force. Therefore, the net force is up and to +2Q the right, but mostly up. +4Q Charge is Quantized When a physical quantity such as charge can have only discrete values rather than any value, we say that the quantity is quantized. It is possible, for example, to find a particle that has no charge at all or a charge of +10e or -6e, but not a particle with a charge of, say, 3.57e. • The electron and proton are identical in the magnitude of their charge, but very different in mass. • The proton and the neutron are similar in mass, but very different in charge. • Number of protons of the nucleus equals to number of electrons! Charge is Conserved The net electric charge of any isolated system is always conserved. If two charged particles undergo an annihilation process, they have equal and opposite signs of charge. If two charged particles appear as a result of a pair production process, they have equal and opposite signs of charge. Answer: -15e 7 Date: Example: Finding the net force due to two other particles Examples Following figure shows two +ve charged particles fixed in place on x-axis. The charges are q1=1.60x10-19C and q2=3.20x10-19C and the particle separation is R=0.0200m. What are the magnitude and direction of the electrostatic force F12 on particle 1 from particle 2? 1. Where is the resultant force equal to zero? • The magnitudes of the individual forces will be equal. • Directions will be opposite. Take k=8.99×109 N.m2/C2. Thus k = 1/4πε0 . F12=-1.15x10-24N 2. Find electrical Force with Other Forces? • Since they are separated, they exert a repulsive force on each other. • Model each sphere as a particle in equilibrium. • Draw free body diagram 1/23/19 Example: Finding the net force due to two other particles Example: Finding the net force due to two other particles Following figure shows two +ve charged particles fixed in place on x-axis. Now there is a particle 3 lies in between 1 and 2 with charge q3= -3.20x10-19C and is at (3/4)R from particle 1. What is the net electrostatic force F1,net on particle 1 due to particle 2 and 3? Following figure shows two +ve charged particles fixed in place on x-axis. Now the Particle 4 is included with charge are q4=-3.20x10-19C and is at (3/4)R from particle 1 and lies on a line that makes an angle 600 with x-axis. What is the net electrostatic force F1,net on particle 1 due to particle 2 and 4? Take k=8.99×109 N.m2/C2. Thus k = 1/4πε0 . Take k=8.99×109 N.m2/C2. Thus k = 1/4πε0 . F12=-1.15x10-24N from first part F12=-1.15x10-24N from first part F13= 2.05x10-24N F14= 2.05x10-24N =9.00x10-25N F1,net= F12+F13 And direction is X positive 1/23/19 1/23/19 F1,net,x=F12,x +F14,x F1,net,x=-1.25x10-25N F1,net,y=F12,y+F14,y F1,net,y=1.78x10-24N F1,net=Sqrt(F21,net,x+F21,net,y) F1,net= 1.78 x10-24N Θ= tan-1(F1,net,y/F1,net,x)= -86.00 Θ= 94.00 Summary Electric Charge Coulomb’s Law • The strength of a particle’s electrical interaction with objects around it depends on its electric charge, which can be either positive or negative. • The magnitude of the electrical force between two charged particles is proportional to the product of their charges and inversely proportional to the square of their separation distance. Conductors and Insulators • Conductors are materials in which a significant number of electrons are free to move. The charged particles in nonconductors (insulators) are not free to move. Conservation of Charge • . The Elementary Charge • Electric charge is quantized (restricted to certain values). • e is the elementary charge 1. Complete the following statement: When a glass rod is rubbed with silk cloth, the rod becomes positively charged as a) negative charges are transferred from the rod to the silk. b) negative charges are transferred from the silk to the rod. c) positive charges are created on the surface of the rod. d) positive charges are transferred from the silk to the rod. e) positive charges are transferred from the rod to the silk. • The net electric charge of any isolated system is always conserved. 1/23/19 8 Date: 2. Which one of the following statements concerning electrical conductors is false? 2. Which one of the following statements concerning electrical conductors is false? a) Rubber is an excellent electrical conductor. a) Rubber is an excellent electrical conductor. b) A material that is a good electrical conductor has many free electrons that can easily move around inside the material. b) A material that is a good electrical conductor has many free electrons that can easily move around inside the material. c) When a positively-charged object is moved into contact with an electrical conductor, electrons move toward the object. c) When a positively-charged object is moved into contact with an electrical conductor, electrons move toward the object. d) Materials that are good thermal conductors are often good electrical conductors. d) Materials that are good thermal conductors are often good electrical conductors. e) 1/23/19 Most metals are very good electrical conductors. e) 1/23/19 Most metals are very good electrical conductors. 3. Which of the following terms is used to describe a material that does not allow electrons to easily move through it? 3. Which of the following terms is used to describe a material that does not allow electrons to easily move through it? a) conductor a) conductor b) resistor b) resistor c) insulator c) insulator d) transformer d) transformer e) inductor e) inductor 1/23/19 1/23/19 4. A conductor that is initially electrically neutral is touched by a rod that has a net positive charge. Which of the following statements describing the conductor after the rod is removed is true? a) The conductor will have a net positive charge. b) The conductor will electrically neutral. c) The conductor will have a net negative charge. 1/23/19 4. A conductor that is initially electrically neutral is touched by a rod that has a net positive charge. Which of the following statements describing the conductor after the rod is removed is true? a) The conductor will have a net positive charge. b) The conductor will electrically neutral. c) The conductor will have a net negative charge. 1/23/19 9 Date: 5. Silicon is an example of what type of material? 5. Silicon is an example of what type of material? a) metal a) metal b) insulator b) insulator c) semiconductor c) semiconductor d) superconductor d) superconductor e) perfect conductor e) perfect conductor 1/23/19 1/23/19 6. An initially electrically neutral conducting sphere is placed on an insulating stand. A negatively-charged glass rod is brought near, but does not touch the sphere. Without moving the rod, a wire is then attached to the sphere that connects it to earth ground. The rod and wire are then removed simultaneously. What is the final charge on the sphere? 6. An initially electrically neutral conducting sphere is placed on an insulating stand. A negatively-charged glass rod is brought near, but does not touch the sphere. Without moving the rod, a wire is then attached to the sphere that connects it to earth ground. The rod and wire are then removed simultaneously. What is the final charge on the sphere? a) negative a) negative b) positive b) positive c) neutral c) neutral d) It has a fifty percent chance of having a positive charge and a fifty percent chance of having a negative charge. 1/23/19 d) It has a fifty percent chance of having a positive charge and a fifty percent chance of having a negative charge. 1/23/19 7. Three identical conducting spheres on individual insulating stands are initially electrically neutral. The three spheres are arranged so that they are in a line and touching as shown. A negatively-charged conducting rod is brought into contact with sphere A. Subsequently, someone takes sphere C away. Then, someone takes sphere B away. Finally, the rod is taken away. What is the sign of the final charge, if any, of the three spheres? 7. Three identical conducting spheres on individual insulating stands are initially electrically neutral. The three spheres are arranged so that they are in a line and touching as shown. A negatively-charged conducting rod is brought into contact with sphere A. Subsequently, someone takes sphere C away. Then, someone takes sphere B away. Finally, the rod is taken away. What is the sign of the final charge, if any, of the three spheres? B + C - a) b) + - + c) + 0 - d) - + e) - a) A + - 1/23/19 A + B + C - b) + - + c) + 0 - 0 d) - + 0 - e) - - - 1/23/19 10 Date: 8. Three insulating balls are hung from a wooden rod using thread. The three balls are then individually charged via induction. Subsequently, balls A and B are observed to attract each other, while ball C is repelled by ball B. Which one of the following statements concerning this situation is correct? 8. Three insulating balls are hung from a wooden rod using thread. The three balls are then individually charged via induction. Subsequently, balls A and B are observed to attract each other, while ball C is repelled by ball B. Which one of the following statements concerning this situation is correct? a) A and B are charged with charges of opposite signs; and C is charged with charge that has the same sign as B. a) A and B are charged with charges of opposite signs; and C is charged with charge that has the same sign as B. b) A and B are charged with charges of the same sign; and C is electrically neutral. b) A and B are charged with charges of the same sign; and C is electrically neutral. c) A is electrically neutral; and C is charged with charge that has the same sign as B. c) A is electrically neutral; and C is charged with charge that has the same sign as B. d) B is electrically neutral; and C is charged with charge that has the same sign as A. d) B is electrically neutral; and C is charged with charge that has the same sign as A. e) 1/23/19 Choices a and c are both possible configurations. e) 1/23/19 Choices a and c are both possible configurations. 9. Consider the conducting spheres labeled A, B, and C shown in the drawing. The spheres are initially charged as shown on the left, then wires are connected and disconnected in a sequence shown moving toward the right. What is the final charge on sphere A at the end of the sequence? 9. Consider the conducting spheres labeled A, B, and C shown in the drawing. The spheres are initially charged as shown on the left, then wires are connected and disconnected in a sequence shown moving toward the right. What is the final charge on sphere A at the end of the sequence? a) +Q a) +Q b) + Q/2 b) + Q/2 c) + Q/3 c) + Q/3 d) + Q/4 d) + Q/4 e) + Q/8 e) + Q/8 1/23/19 1/23/19 10. Consider the conducting spheres labeled A, B, and C shown in the drawing. The spheres are initially charged as shown on the left, then wires are connected and disconnected in a sequence shown moving toward the right. What is the final charge on sphere C at the end of the sequence? 10. Consider the conducting spheres labeled A, B, and C shown in the drawing. The spheres are initially charged as shown on the left, then wires are connected and disconnected in a sequence shown moving toward the right. What is the final charge on sphere C at the end of the sequence? a) +Q a) +Q b) + Q/2 b) + Q/2 c) + Q/3 c) + Q/3 d) +2Q d) +2Q e) 1/23/19 +3Q e) 1/23/19 +3Q 11 Date: 11. Two objects separated by a distance r are each carrying a charge q. The magnitude of the force exerted on the second object by the first is F. If the first object is removed and replaced with an identical object that carries a charge +4q, what is the magnitude of the electric force on the second object? 11. Two objects separated by a distance r are each carrying a charge q. The magnitude of the force exerted on the second object by the first is F. If the first object is removed and replaced with an identical object that carries a charge +4q, what is the magnitude of the electric force on the second object? a) 4F a) 4F b) 2F b) 2F c) F c) F d) F/2 d) F/2 e) 1/23/19 F/4 e) 1/23/19 F/4 12. Two objects, A with charge +Q and B with charge +4Q, are separated by a distance r. The magnitude of the force exerted on the second object by the first is F. If the first object is moved to a distance 2r from the second object, what is the magnitude of the electric force on the second object? 12. Two objects, A with charge +Q and B with charge +4Q, are separated by a distance r. The magnitude of the force exerted on the second object by the first is F. If the first object is moved to a distance 2r from the second object, what is the magnitude of the electric force on the second object? a) zero newtons a) zero newtons b) 2F b) 2F c) F c) F d) F/2 d) F/2 e) 1/23/19 F/4 e) 1/23/19 F/4 13. Two point charges are stationary and separated by a distance R. Which one of the following pairs of charges would result in the largest repulsive force? 13. Two point charges are stationary and separated by a distance R. Which one of the following pairs of charges would result in the largest repulsive force? a) –2q and +4q a) –2q and +4q b) –3q and -2q b) –3q and -2q c) +3q and -2q c) +3q and -2q d) +2q and +4q d) +2q and +4q e) –3q and -q e) –3q and -q 1/23/19 1/23/19 12 Date: 14. What is the magnitude of the electrostatic force that two electrons separated by 1.0 nm exert on each other? 14. What is the magnitude of the electrostatic force that two electrons separated by 1.0 nm exert on each other? a) 2.3 × 10-10 N a) 2.3 × 10-10 N b) 3.2 × 10-19 N b) 3.2 × 10-19 N c) 4.6 × 10-14 N c) 4.6 × 10-14 N d) 5.2 × 10-6 N d) 5.2 × 10-6 N e) 7.8 × 10-4 N e) 7.8 × 10-4 N 1/23/19 1/23/19 15. A charged particle, labeled A, is located at the midpoint between two other charged particles, labeled B and C, as shown. The sign of the charges on all three particles is the same. When particle A is released, it starts drifting toward B. What can be determined from this behavior? 15. A charged particle, labeled A, is located at the midpoint between two other charged particles, labeled B and C, as shown. The sign of the charges on all three particles is the same. When particle A is released, it starts drifting toward B. What can be determined from this behavior? a) The charge on A is larger than the charge on B. a) The charge on A is larger than the charge on B. b) The charge on A is larger than the charge on C. b) The charge on A is larger than the charge on C. c) The charge on C is larger than the charge on B. c) The charge on C is larger than the charge on B. d) The charge on B is larger than the charge on A. d) The charge on B is larger than the charge on A. e) 1/23/19 The charge on B is larger than the charge on C. e) 1/23/19 The charge on B is larger than the charge on C. 13