Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 12 Solutions

Transcription

1 Concept Check (top) Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 12 Solutions Student Book page 583 Concept Check (botto) The north-seeking needle of a copass is attracted to what is called Earth s agnetic north pole, indicating that there ust be a south agnetic pole at that location. Concept Check (top) Top left Student Book page 586 Top right Botto left Botto right 1

2 Concept Check (botto) Two siilarities: Fields explain action at a distance. They are represented by vector arrows, where the vector s length represents the agnitude of the field and the arrow represents its direction. Fields extend to infinity. Fields can exert forces on objects. Two differences: Gravitational forces can only be attractive, whereas electric and agnetic forces can be attractive or repulsive. Magnetic fields originate fro two separate poles, whereas electric and gravitational fields originate fro the centre of a charge or ass. Skills Practice Student Book page (a) Using the left-hand rule, the thub points in the direction of current and fingers point in the direction of the agnetic field, or clockwise (into the page). (b) Using the left-hand rule, the thub points toward the north end of the agnetic field in the coil. The fingers point out of the page, or counterclockwise. Student Book page 590 Concept Check The filing cabinet has becoe a peranent agnet through prolonged contact with the influence of Earth s agnetic field. If it is a peranent agnet, it will have two poles, as evidenced by the effect of the top and botto of the filing cabinet on a copass. If it was agnetized by the agnetic copass, agnetization would be by induction and the copass needle would point in the sae direction when held near the top and the botto of the cabinet Check and Reflect Student Book page 592 Knowledge 1. The law of agnetis states that like poles repel and unlike poles attract. 2. (a) Yes. Every agnet ust have a north and south pole the poles cannot exist alone. (b) No. A negative or positive charge can exist by itself (e.g., a proton or an electron). 3. Gilbert copared the orientation of agnetized needles on the surface of a spherical piece of lodestone with the north-south orientation of a copass needle on various locations on Earth s surface. 4. (a) In a bar agnet, agnetis is caused by oving charges within the atos. (b) On Earth, agnetis is ost probably caused by oving charges in the olten outer core. 5. Oersted discovered that oving electric charges create agnetic fields. 2

3 6. (a) The agnetic field around a straight current-carrying conductor fors concentric circles around the wire. (b) The agnetic field within a coil of conducting wire carrying a current has a north and south pole and is straight except near the ends of the coil. Applications 7. If you broke a agnet into two pieces, you would have two agnets. 8. The agnetic field around the oving sphere would be circular in a clockwise direction. If the sphere were positively charged, the agnetic field would be circular in a counterclockwise direction. 9. The agnetic field would be straight within the top with the north pole pointing upward at you. The field lines will start curving outside the top with soe ending at the south pole, at the botto. 10. (a) Differences: Gravitational fields have one direction toward the centre of ass, whereas electric fields can have two directions depending on the type of charge. Gravitational fields are created by all asses, whereas electric fields are created only by charged objects. Electric fields are uch stronger and can exert influences that are attractive or repulsive. Siilarities: The agnitudes of electric fields around a point charge and gravitational fields both vary with 1, and they both exert forces that cause action 2 r at a distance. (b) Differences: Gravitational fields have one direction toward the centre of ass, whereas agnetic fields extend fro one pole to another. Gravitational fields are created by all asses, whereas agnetic fields are created only by agnetic objects. Magnetic fields are uch stronger, and they can be attractive or repulsive. Siilarities: The agnitudes of gravitational and agnetic fields vary inversely with distance, and they both exert forces that cause action at a distance. (c) Differences: Electric fields can exist around a single charge, whereas agnetic fields ust have two poles. Electric fields exist whether charges are stationary or oving, whereas all agnetic fields are caused by oving charges. Siilarities: Electric fields and agnetic fields both exert influences that are attractive or repulsive, and they both exert forces that cause action at a distance. 11. (a) As the agnet approaches the unagnetized aterial, the doains in the right orientation for attraction to the pole of the agnet grow at the expense of other doains. The aterial has been agnetized by induction and has becoe a teporary agnet. Attraction occurs. (b) As a agnet strokes a nail, the doains shift in the direction of the stroking. The nail has been agnetized by contact and has becoe a peranent agnet. Attraction occurs. (c) The copass is a tiny agnet. As the copass approaches the etal leg, the doains in the etal leg in the right orientation for attraction to the pole of the copass grow at the expense of other doains. The leg has been agnetized by induction and has becoe a teporary agnet. Attraction occurs. 12. Dropping or heating a bar agnet will return soe or all the doains back to a rando orientation. 3

4 13. The agnetic fields extend fro one pole to the other in both the agnet and Earth and are strongest near the poles. However, the agnetic field of Earth appears to run fro south to north, whereas a bar agnet s agnetic field runs fro north to south. Extensions 14. The agnetic fields at the poles point straight down to the surface, which akes it difficult to get an accurate bearing with a agnetic copass near the poles. 15. No. The lines are parallel to Earth s surface only at the equator. Away fro the equator, the lines gradually begin to dip toward Earth s surface so that, at the poles, the lines point straight down. 16. There is a greater concentration of agnetic field lines within the loop than outside the loop, so the agnetic field is stronger inside the loop. Student Book page 595 Skills Practice 1. (a) The agnetic field points out of the page. (b) The negative charge oves into the page. (c) The positive charge oves into the page. Student Book page 596 Concept Check Coparing the agnetic force with the gravitational force on a oving charge: When a ass or a charge oves perpendicularly through a gravitational or a unifor agnetic field, respectively, the gravitational force causes a ass to accelerate in a parabolic path, whereas the agnetic force on a oving charge causes the charge to accelerate in a circular path. When a ass oves parallel to a gravitational field, it will accelerate in the direction of the field. A charge is unaffected when oving parallel to agnetic fields. Coparing the agnetic force on a oving charge with the electric force due to another nearby charge: When a charge oves perpendicularly through unifor agnetic or electric fields, respectively, the agnetic force on a oving charge causes the charge to accelerate in a circular path, whereas the electric force causes a charge to accelerate in a parabolic path. When a charge oves parallel to an electric field, it will accelerate in the direction of the field. A charge is unaffected when oving parallel to a agnetic field. Exaple 12.1 Practice Probles 1. Given 19 q C 4 B T Student Book page 599 v /s 4

5 agnitude of the agnetic deflecting force on the proton ( F ) To calculate the agnitude of the agnetic deflecting force, use: F qv B ( C)( /s)( T) N The agnitude of the agnetic deflecting force on the proton is N. 2. Given 19 q C 1 B T 5 v /s [30 ] agnitude of the agnetic deflecting force on the ion ( F ) To calculate the agnitude of the agnetic deflecting force, use: F qv B ( C)( /s)(sin 30 )( T) N The agnitude of the agnetic deflecting force on the ion is N. 3. Using the left-hand rule: thub in the direction of the sphere s otion fro west to east fingers in the direction of Earth s agnetic field fro south to north pal downward toward Earth s surface, indicating the direction of deflection The direction of the agnetic deflecting force on the sphere is downward, toward Earth s surface. Exaple 12.2 Practice Probles 1. Given kg 5 B T 19 q C g 9.81 N/kg [down] Student Book page 600 iniu speed required for the electron to reain at the sae height above Earth s surface (v) 5

6 The gravitational force on the electron is Fg g [downward]. The agnetic deflecting force on the electron is F qv B [upward]. To aintain the electron at the sae height, the agnetic deflecting force ust balance the gravitational force: F Fg qv B g v g Bq 31 ( kg ) 9.81 N kg 5 19 ( T)( C) /s The iniu speed required for the electron to reain at the sae height above Earth s surface is /s. 2. Given 19 q C B T 4 v /s kg (a) agnitude of the deflecting force on the ion ( F ) (b) radius of curvature of the otion of the deflected ion (r) (a) To calculate the agnitude of the deflecting force, use: F qv B 19 4 ( C)( /s)(0.150 T) N (b) When the ion is in circular otion within the agnetic field, F Fc. To deterine the radius of the curvature, use: 6

7 qv B r 2 v r v qb 26 4 ( kg)( /s) 19 ( C)(0.150 T) (a) The agnitude of the deflecting force is N. (b) The radius of curvature of the otion of the deflected ion is Student Book page Check and Reflect Knowledge 1. It is called a cathode ray because the rays appeared to originate fro the cathode of a vacuu tube. 2. A agnetic field vector arrow indicates the agnitude and direction of the agnetic field at a particular point. A agnetic field line is a continuous curve (or a straight line), which shows the direction and the shape of the field. 3. The particles will deflect in opposite directions, with the proton aking a larger arc because of its larger ass. 4. A oving charge that enters perpendicular to each unifor field is deflected in a circular path in a agnetic field and in a parabolic path in an electric field. When the oving charge enters parallel to each field, it accelerates along the electric field lines and is unaffected in the agnetic field. Applications 5. (a) No deflection. A charged particle ust travel perpendicular to the external agnetic field to be deflected. (b) The lithiu ion will be deflected downward to the surface of Earth. (c) The lithiu ion will initially be deflected westward along the surface of Earth. 6. (a) Given 19 q C B T 5 v /s (a) agnitude of the deflecting force if the proton enters perpendicular to the agnetic field ( F ) (b) agnitude of the deflecting force if the proton enters the agnetic field at an angle of 35.0 ( F ) 7

8 (a) To calculate the agnitude of the deflecting force, use: F qv B 19 5 ( C)( /s)(0.200 T) N (b) To calculate the agnitude of the deflecting force, use: F qv B 19 5 ( C)( /s)(sin 35.0 )(0.200 T) N (a) The agnitude of the deflecting force if the proton enters perpendicular to the agnetic field is N. (b) The agnitude of the deflecting force if the proton enters the agnetic field at an angle of 35.0 is N. 7. Given g kg 5 B T 6 q C g 9.81 N/kg [down] speed required to aintain the otion of the ball at the sae height ( v ) The gravitational force on the ball is Fg g [downward]. The agnetic deflecting force on the ball is F qv B [upward]. To aintain the speed with the sae horizontal otion, the agnetic deflecting force ust balance the gravitational force: F Fg qv B g v g Bq 5 ( kg )(9.81 N/kg) 5 6 ( T)( C) /s The ball ust be thrown with a speed of /s. 8

9 8. Given 2 B T 5 v /s q C C iniu gravitational force required to aintain the alpha particle at the sae height above Earth s surface ( F g ) Analysis The gravitational force on the alpha particle is Fg g [downward]. The agnetic deflecting force on the alpha particle is F qv B [upward]. To aintain the alpha particle at the sae height, the agnetic deflecting force ust balance the gravitational force: F Fg qv B g To calculate the gravitational force required, use: F qv B g ( C)( /s)( T) N The iniu gravitational force on the alpha particle is N. 9. Given 19 q C B T 6 v /s kg radius of deflection of the electrons in the tube (r) When the electrons are in circular otion within the agnetic field, F Fc. F g is ignored because it is very sall copared with F. 2 v qv B r v r qb 31 6 ( kg)( /s) 19 ( C)( T)

10 The radius of deflection of the electrons in the tube is Given 19 q C 6 v /s kg 6 r agnitude of the agnetic field ( B ) When the electrons are in circular otion within the agnetic field, F Fc. 2 v qv B r v B qr 27 6 ( kg)( /s) 19 6 ( C)( ) T The agnitude of the agnetic field at that point in space is T. Extension 11. It is only at the higher latitudes that the agnetic field lines, which have trapped charged particles fro space, enter the atosphere of Earth. Student Book page 603 Exaple 12.3 Practice Probles 1. Given q 20.0 C 3 t 1.00 s s current (I) q I t 20.0 C s A 4 The current during the lightning strike is A. 10

11 2. Given I 5.00 A t 10.0 s charge (q) q I t q It (5.00 A)(10.0 s) 50.0 C The aount of charge that passes through the appliance is 50.0 C. Student Book page 605 Exaple 12.4 Practice Probles 1. Given l B T I 10.0 A agnitude of the agnetic force on the wire ( F ) To calculate the agnitude of the agnetic force, use: F Il B (10.0 A)(0.500 )(0.200 T) 1.00 N The agnitude of the agnetic force on the wire is 1.00 N. 2. Given l 0.75 B 0.15 T kg iniu current (I) The agnitude of the agnetic force is given by: F Il B The agnitude of the gravitational force is given by: F g g 11

12 To suspend the wire, the agnetic force ust balance the gravitational force: F Fg Il B g g I l B (0.060 kg) 9.81 N/kg (0.75 )(0.15 T) 5.2 A The iniu current required to ake the wire float in the agnetic field is 5.2 A. Student Book page 608 Concept Check The wires are crossed to cancel agnetic fields in a region. Student Book page 609 Concept Check To cause the arature to rotate counterclockwise, reverse the direction of the electric current or switch the peranent agnets. Student Book page Check and Reflect Knowledge 1. The factors that affect the agnetic force on a oving charge through an external agnetic field are the quantity of charge, the agnitude of the agnetic field, and the speed of the charge perpendicular to the agnetic field. 2. The factors that affect the agnetic force on a charge oving through a conducting wire in an external agnetic field are the quantity of current in the conducting wire, the agnitude of the agnetic field, and the length of conducting wire perpendicular to the agnetic field. 3. An apere is the flow of one coulob of charge past a point in a conductor in 1 s. 1 apere 1 coulob/s or 1 C 1 A s 4. (a) A siilarity between otors and generators is that they both consist of an external agnetic field, a rotating loop of wire, and a coutator. (b) A difference is that a siple electric otor uses electricity to produce echanical energy and a siple electric generator uses echanical energy to produce electricity. 5. Faraday and Henry applied the syetry between electricity and agnetis. 12

13 6. The split-ring coutator changes the direction of the current in the coil, every halfrotation of the coil. It also prevents twisting of wires in the external circuit. 7. Electrons in a rotating loop of wire gain energy fro the work done in rotating the coil that initiates electroagnetic induction. Applications 8. According to the left-hand rule for a wire in a agnetic field, the wire should deflect upward (toward the top of the page). 9. To deterine the quantity of charge, use the equation q I t q It 3 ( A)(2.00 s) C 2 The quantity of charge that flows through the circuit in 2.00 s is C. 10. Currents in opposite directions should repel. See Figure 12.31(b) on page 607 of the student book. 11. To calculate the agnitude of the agnetic force, use: F Il B (0.56 A)(0.50 )(0.30 T) N The agnitude of the agnetic force is N. Extension 12. Yes. To convert a generator to a otor, you ust supply current to the loop of wire in the agnetic field and attach an axle to the loop to rotate the loop of the new otor. A split-ring coutator ust also be attached if the supplied current is DC. Student Book page 618 Concept Check When the north pole of the agnet is directed downward, a clockwise current is induced in the tube and a north pole is induced at the top end of the tube. If the south pole of the agnet were directed downward, it would induce a south pole at the top end of the tube and a counterclockwise current Check and Reflect Student Book page 620 Knowledge 1. (a) Students are ost likely to identify exaples fro the text: an electric otor and a loudspeaker. (b) Students are ost likely to identify exaples fro the text: a generator and a transforer. 2. The three basic coponents of an electric otor and generator are the external agnetic field, a rotating loop of conducting wire, and a coutator. 13

14 3. The direction of a agnetically induced current is such as to oppose the cause of the current. Applications 4. (a) You ust supply electric current. (b) As the electric current oves through the agnetic field, the interaction of its agnetic field with the external agnetic field creates a turning effect, resulting in echanical energy fro the device. (c) As the agnetic force oves the wire through the external agnetic field, it cuts agnetic field lines. This effect produces a voltage that induces a current in the wire, which is in a direction opposite to the original flow of charges in the wire. 5. (a) You ust supply echanical energy to turn the wires to cut through an external agnetic field. (b) As the wire oves through the agnetic field, it cuts agnetic field lines, which produces a voltage that induces a current in the wire. (c) The induced current is a flow of charges in the wire, which creates a agnetic field. The interaction of this agnetic field with the external agnetic field creates a agnetic force on the charges and the wire, causing the wire to ove in a direction opposite to its original direction. 6. As you ove a agnet toward a coil of wire, the coil of wire cuts the agnetic field lines. This effect produces a potential difference that induces a current in the coil. The induced current produces a agnetic field. This new agnetic field will always repel the agnetic field of the agnet. 7. The direction of the induced current in the ring is counterclockwise looking at the ring fro the right. Extensions 8. If the current were in the sae direction, then the total current in the wire would be ore than what was originally supplied, which would violate the law of conservation of energy. 9. If the otor is prevented fro rotating, the opposing current that should exist according to Lenz s law is not being produced. Too uch current is now present in the loop, and the loop will overheat. Chapter 12 Review Student Book pages Knowledge 1. (a) Gilbert was the first to suggest the concept of orbs of influence surrounding agnets in attepting to explain action at a distance. This concept was the first notion of a agnetic field. He also established the concept of Earth as a large agnet. (b) Oersted was the first to deonstrate the relationship between electricity and agnetis by showing that oving charges produce agnetic fields. (c) Apère deonstrated that two current-carrying conductors exert agnetic forces on each other. By establishing the variables that affect the agnetic force between two current-carrying conductors, he was able to define a unit of current that we now call the apere. 14

15 (d) Faraday is given credit for establishing the relationship between agnetis and electricity. He was able to deonstrate that oving a conductor through a agnetic field will generate a current in the conductor, thus proving electroagnetic induction. 2. (a) A agnetic field is a region of agnetic influence around a agnet in which other agnets or agnetic substances are affected by agnetic forces. (b) The direction of a agnetic field is the direction of the force on the north pole of a copass placed in the field. 3. A agnetic vector arrow indicates the agnitude and the direction of the agnetic field at a point in the agnetic field. A agnetic field line extends fro the north pole to the south pole of a agnet and only displays direction. The density of the agnetic field lines indicates the agnitude of the field. 4. Two agnetic objects can either attract or repel each other, depending on their orientation to each other. Therefore, there ust be two types of poles. 5. (a) Magnetic field lines run fro the north pole to the south pole on a bar agnet and fro the geographical south pole to the geographical north pole on Earth. (b) A straight current-carrying conductor has circular agnetic field lines around the conductor. In the left diagra below, current direction is left and the agnetic field direction is counterclockwise, viewing fro the right. In the right diagra below, a coil of conducting wire with current in a clockwise direction, viewed fro the right, has a straight agnetic field running to the right through the centre of the coil. 6. The external agnets and the oving charge produce the two agnetic fields that provide the agnetic force of the otor effect. 7. (a) If the charge oves parallel to the external agnetic field lines, it is not deflected. (b) If it oves perpendicular to the external agnetic field lines, the charge will deflect in a circular path. (c) If it enters the agnetic field at an angle, the charge deflects in a circular otion that becoes a helix. 8. A agnetic bottle is fored in the Van Allen belt around Earth where charged particles oscillate back and forth between Earth s agnetic poles. 9. A galvanoeter is a sensitive instruent that can detect very sall currents. An aeter is a galvanoeter designed to easure large currents. 15

16 10. One apere of current exists when 1 C of charge passes a point in a conductor every 1 s. A current of 1 A flows in two parallel, long, straight wires in the sae direction, 7 1 apart, if the wires attract each other with a force of 2 10 N/. 11. In both parts, students answers ay vary, but are likely to be the following: (a) electric otors and eters (b) electric generators and transforers 12. Lenz s law states that the direction of a agnetically induced current is such as to oppose the cause of the current. This eans that whatever you supply into a syste, soething will be produced to hinder what you supply. One exaple is a otor acting as a generator to produce a current that will oppose the direction of the original current in the otor. This affects the operation of both otors and generators. Applications 13. Every charged object does not necessarily have a negative and a positive charge. An electron can exist as a negative charge by itself. A agnetized object ust have a north and a south pole because there is no agnetic onopole. 14. Within the agnet, the direction of the field points fro the south to the north pole so that the field lines for closed loops. 15. (a) During agnetization by induction, the doains in the right orientation for attraction to an external agnet grow at the expense of the other doains, creating a teporary agnet. (b) During agnetization by contact, all doains shift in the direction of the external agnet, creating a peranent agnet. 16. F qv B, so: (a) if the charge is doubled, the force is doubled (b) if the agnetic field is doubled and the speed is halved, the force doesn t change (c) if the ass is doubled, there is no effect on the agnitude of the force 17. In a peranent agnet, all doains within the substance are aligned in one direction. In a teporary agnet, only the doains in the right orientation for attraction to an external agnetic influence grow at the expense of the other doains. No doains shift in the foration of teporary agnets. 18. Hold the copass over the current-carrying wire. You can deterine the direction of the current in the wire by observing the direction of the copass needle and using the left-hand wire-grasp rule. 19. The grape is a diaagnetic substance, which always opposes an external agnetic field. 20. Given 19 q C B T 6 v /s agnitude of the agnetic deflecting force on the electron ( F ) To calculate the agnitude of the agnetic deflecting force, use: 16

17 F qv B 19 6 ( C)( /s)( T) N The agnitude of the agnetic deflecting force on the electron is N. 21. Given 19 q C 2 B T 17 F N 35 (a) speed of the proton at an angle of 35 (v) (b) kinetic energy of the proton in J and ev (E k ) (a) Deterine the speed of the proton: F qv B F v qb N 19 2 ( C)( T) /s Deterine the speed of the proton at 35 : v v sin /s sin /s /s (b) To deterine the kinetic energy of the proton, use: 2 Ek 1 v kg /s J 19 1eV J J 2.77 ev 19 The kinetic energy of the proton is J or 2.77 ev. 17

18 (a) The speed of the proton at 35 to the agnetic field is /s. (b) The kinetic energy of the proton is J or 2.77 ev. 22. Given kg 6 B 50.0 T T 19 q C g 9.81 N/kg speed required to aintain the otion of the alpha particle at the sae height within Earth s agnetic and gravitational fields (v) The gravitational force on the alpha particle is Fg g [downward]. The agnetic deflecting force on the alpha particle is F qv B [upward]. For the alpha particle to aintain its speed at the sae height, the agnetic force ust balance the gravitational force: F Fg qv B g To calculate the speed required, use: g v Bq 27 ( kg ) 9.81 N kg 6 19 ( T)( C) /s The speed that the alpha particle ust aintain to reain at the sae height is /s. 23. Given 19 q C B T 4 v /s (a) agnitude of the agnetic force on the alpha particle perpendicular to the agnetic field ( F ) (b) agnitude of the agnetic force 30.0 o to the agnetic field ( (c) agnitude of the agnetic force parallel to the agnetic field ( (a) To calculate the agnitude of the agnetic force, use: F ) F ) 18

19 F qv B 19 4 ( C)( /s)(0.0300t) N (b) To calculate the agnitude of the agnetic force, use: F qv B 19 4 ( C)( /s)(sin 30.0 )( T) N (c) There will be no force on the alpha particle when it travels parallel to the external agnetic field. (a) The agnitude of the agnetic force on the alpha particle as it enters perpendicular to the agnetic field is N. (b) The agnitude of the agnetic force on the alpha particle as it enters the agnetic field at an angle of 30.0 is N. (c) The particle will experience no deflecting force when it enters parallel to a agnetic field. 24. Given 19 q C 6 v /s kg r 0.25 agnitude of the agnetic field required to bend the electron bea ( B ) When the electrons are in circular otion within the agnetic field: F Fc 2 v qv B r v B qr 31 6 ( kg)( /s) 19 ( C)(0.25 ) T The agnitude of the agnetic field required to bend the electron bea is T. 25. The source of the force of attraction is a agnetic force of attraction between the agnetic fields produced by the currents in each conductor. This force could not be electrostatic attraction because charges flowing in the wires are of the sae sign. So if there is any electrostatic force, it should be a repulsive one rather than an attractive one. 19

20 26. (a) Graph of Magnetic Force vs. Separation Distance 1 (b) The shape of the graph indicates that F 2, since the product of r 2 F is a r constant (~100). 27. Over the poles, the direction of Earth s agnetic field is downward toward the surface. As the plane s wings, which are conductors, cut through the external agnetic field lines, a current is generated in the wings due to the generator effect. The left-hand rule for the generator effect shows that the right wing would have ore electrons. 28. Deterine the agnitude of the agnetic force: F Il B 6 (500 A)(100 )( T) 2.50 N The agnitude of the agnetic force on the wire is 2.50 N. Extensions 29. The glass tube will allow the agnet to fall faster, because the only force on the agnet is the force of gravity. The agnet falling through the copper tube produces a current in the tube, which produces a agnetic field that opposes the otion of the agnet, according to Lenz s Law. 30. The steel balls have becoe agnetized by induction and are attracted to the disk agnet, which ust have like poles on either face. However, the steel balls repel each other because they have like poles facing each other. 20