Peason Physics Level 30 Unit VI Foces and Fields: Unit VI Review Solutions Student Book pages 66 631 Vocabulay 1. ampee: the flow of 1 C of chage past a point in a conducto in 1 s chage migation: movement of electons in a neutal object whee one side of the object becomes positive and the othe side becomes negative; caused by induction chage shift: movement of electons in an atom whee one side of an atom becomes positive and the othe side becomes negative; caused by induction chaging by induction: pocess of chaging an object by fist polaizing it by induction and then etaining the chage by gounding commutato: a mechanism fo maintaining a popely polaized connection to the moving coil in a moto o geneato; a split metal ing conduction: pocess of chaging an object though the diect tansfe of electons when a chaged object touches a neutal object conducto: mateial in which electons in the outemost egions of the atom ae fee to move 18 coulomb (C): the SI unit fo electic chage, equivalent to the chage on 6.5 10 electons o potons Coulomb s law: magnitude of the foce of electostatic attaction o epulsion ( F e ) is: diectly popotional to the poduct of the two chages q 1 and q : Fe qq 1 invesely popotional to the squae of the distance between thei centes : 1 Fe If these ae the only vaiables that detemine the electostatic foce, then: qq 1 Fe cuent: quantity of chage that flows though a wie in a given unit of time domain: a egion of mateial in which the magnetic fields of most of the atoms ae aligned electic field line: line epesenting the electic field aound a chage o chages; each line shows diection; the density of the lines indicates the magnitude of the electic field electic potential: the electic potential enegy stoed pe unit chage at a given point in an electic field; symbol is V electic potential diffeence: change in electic potential expeienced by a chage moving between two points in an electic field electic potential enegy: enegy stoed in a system of two chages a cetain distance apat 1 Copyight 009 Peason Education Canada
electomagnet: a magnet having its magnetic field poduced by electic cuent flowing though a coil of wie electomagnetic induction: poduction of electicity by magnetism electon volt: the change in enegy of an electon when it moves though a potential diffeence of 1 V electostatics: study of electic chages at est feomagnetic: having magnetic popeties, like those of ion field: a thee-dimensional egion of influence suounding an object geneato effect (electomagnetic induction): poduction of an electic cuent by moving a conducto though a magnetic field gounding: the pocess of tansfeing chage to and fom Eath induction: movement of chage caused by an extenal chaged object insulato: mateial in which the electons ae tightly bound to the nucleus and ae not fee to move within the substance law of consevation of chage: the net chage of an isolated system is conseved law of magnetism: like magnetic ends epel and unlike ends attact each othe Lenz s law: the diection of a magnetically induced cuent is such as to oppose the cause of the cuent magnetic field: a thee-dimensional egion of magnetic influence suounding a magnet, in which othe magnets ae affected by magnetic foces moto effect foce: the deflecting foce acting on a chaged paticle moving in a magnetic field net chage: the sum of all electic chages in the system plasma: highly ionized gas containing nealy equal numbes of fee electons and positive ions semiconducto: a mateial that is a good conducto in cetain situations, and a good insulato in othe situations solenoid: an electomagnet that opeates a mechanical device souce chage: chage that poduces an electic field supeconducto: a conducto that has no measuable esistance at vey low tempeatues test chage: chage with a magnitude small enough that it does not distub the chage on the souce chage and thus change its electic field Knowledge Chapte 10. The atoms of silve do not hold onto thei oute electons as tightly as atoms of ubbe do. Theefoe, silve has moe fee electons, which makes the silve a bette conducto than ubbe. 3. Mateials that ae supeconductos can tansmit cuent with no measuable esistance, and theefoe no measuable loss of enegy to heat. Using these mateials in technology inceases the efficiency of all components opeating on electical enegy. 4. This method of chaging objects is called chaging by induction with the gounding step. The final chage on the metal ball is a net positive chage. Copyight 009 Peason Education Canada
5. (a) A similaity between the two pocedues is that both involve contact between two objects. A diffeence is that chaging by fiction involves moe suface contact between the two objects. (b) Duing induction, a chage shift occus when electons meely move to the othe side of thei atoms in an insulato, thus polaizing the atoms. A chage migation occus when electons move to the othe side of a conducto, thus polaizing the conducto. 6. (a) The ebonite will be negative and the fu will be positive. This pocedue is chaging by fiction. When the od is held nea the sphee, the sphee becomes polaized. This method is chaging by induction. (b) The glass od will be positive, the silk will be negative, and the sphee will be positive. In the ubbing pocess, the od and the silk become chaged by fiction. When the od touches the sphee, the sphee becomes similaly positively chaged by conduction. 7. The othe object must have an equal but net positive chage, accoding to the law of consevation of chages. The net chage of the system is zeo because no chages have been ceated. 8. (a) Fe q1q 1 (b) Fe (c) F e is attactive if both chages ae diffeent, and it is epulsive if both chages ae the same. Chapte 11 9. The net vecto field at a point is equal to the vecto sum of individual vectos acting at the point. 10. The test chage must be small enough so that it does not distub the position of any othe chage in the system. 11. (a) a negative point chage (b) a positive chage and a negative point chage in the same egion (c) a negatively chaged cone-shaped object 3 Copyight 009 Peason Education Canada
1. At any point within a chaged object, the vecto sum of the electic fields acting at that point will always equal zeo. 13. If an object becomes chaged, epulsive electostatic foces cause the chages to accumulate on the outside suface of the object. The vecto sum of electic fields within the object is always zeo, so the inteio of the object is shielded fom any net electic field. Thee is neve any net chage o electic field within a conducting object. The same effect is impossible with gavitational fields because gavitational foces can neve be epulsive. 14. 15. The zeo efeence point fo electic potential enegy aound any chage is chosen at infinity. Fo all chages, the values of the electic potential enegy may be positive o negative, depending on the type of chage placed in the field. Howeve, the values of the electic potential enegy decease as distance fom the chage inceases. 16. If the distance between the plates deceases, then the value of the electic field must 1 incease, because E. d q1 17. (a) The magnitude of the electic field would be E k, and the diection is away fom the positive chage. (b) The electic potential enegy of anothe chage placed at this point is equal to the wok done to move the chage against the electic field to this point: Ep W. (c) The electic potential at this point depends on how much electic potential enegy E is stoed pe unit chage: p V. q 18. The electic potential enegy of a chage at a point in an electic field is equal to the wok done to move the chage against the electic field to this point: Ep W. This elationship is govened by the law of consevation of enegy. Chapte 1 19. (a) Similaities: Both consist of magnetic field lines. The magnitude of the magnetic fields deceases with distance fom the magnets. (b) Diffeences: In a ba magnet, the magnetic field lines un fom the noth pole to the south pole, wheeas on Eath, the magnetic field lines un fom the geogaphical south pole to the geogaphical noth pole. Students may also add that the magnetic field lines aound a ba magnet fom simila pattens on eithe 4 Copyight 009 Peason Education Canada
side, wheeas on Eath, the magnetic field lines ae compessed on the side facing the Sun and stetched out on the side away fom the Sun. 0. Magnetic effects ae caused by domains, which have a noth and a south egion on eithe side o end. As long as thee ae two sides o ends, thee must be two poles. This popety is simila to a coin. It must have a head and a tail. One pole cannot exist by itself. 1. Two simple demonstation techniques to outline the magnetic field suounding a magnet ae spinkling ion filings aound the magnet and placing compasses aound the magnet.. A chage moving pependicula to a magnetic field will expeience a foce causing it to follow a cicula path. This motion is acceleated motion in which the diection is always changing but the magnitude of the motion emains constant. In ode fo the magnitude of the motion to incease, the foce must be in the same diection as the motion of the chage. 3. In the diagam below, the chage expeiencing the deflecting foce is negative. 4. The diection of the magnetic field is downwad, into the pape. 5. The magnetic field aound the dat is in the shape of concentic cicles aound the dat and its diection is counteclockwise. 6. The magnetic foce depends on the amount of chage, the speed of the chage pependicula to the magnetic field, and the magnitude of the extenal magnetic field. 7. Both effects involve an extenal magnetic field and a moving chage within this magnetic field. Howeve, the pinciple of the moto effect is that electicity poduces magnetism, and the pinciple of the geneato effect is that magnetism poduces electicity. 8. (a) In a moto, a cuent must be supplied to povide the magnetic foce to otate the loop of wie. As the loop of wie otates, it cuts magnetic field lines. This effect geneates a cuent in the opposite diection to the supplied cuent, which inhibits the opeation of the moto, as pedicted by Lenz s law. 5 Copyight 009 Peason Education Canada
(b) In a geneato, a foce must be applied to otate a loop of wie though an extenal magnetic field, thus geneating a cuent in the loop. Howeve, as the geneated cuent flows though the loop, it ceates a magnetic foce, which opposes the oiginal foce supplied to otate the loop. This inhibits the opeation of the geneato, as pedicted by Lenz s law. Applications 9. The negative chages on the conducto will distibute equally on the outside suface of the conducto due to the electostatic epulsive foces. The negative chages on the insulato will emain on the outside suface of the insulato at the point of contact. 30. As wate molecules in the clouds collide, a tansfe of electons occus. Some doplets become negatively chaged, wheeas othes ae positively chaged though this pocess of chaging by fiction. The positive wate vapou molecules ise to the top of the cloud, and the negative wate vapou molecules condense into wate doplets and dop to the bottom of the cloud. The negatively chaged bottom of the cloud then causes chage migation on Eath s suface and the pat of the suface closest to the cloud becomes positively chaged by induction. When a steame fom the suface meets a leade fom the clouds, a lightning dischage occus, sending negative chages to the suface though this path. This is a type of chaging by conduction. 31. (a) To chage a neutal electoscope positively using a negatively chaged od, you must use the pocess of chaging by induction with the gounding step. (b) To chage a neutal electoscope negatively using a negatively chaged od, you must use the pocess of chaging by conduction. 3. As the od is bought nea the thead, electons in the thead ae epelled to the othe side of the atoms. This pocess is chage shift due to induction. The atoms of the thead ae now polaized. Attaction between the negative od and the positive side of the atoms is geate than epulsion of the negative od and the negative electons. Attaction occus, and the od attacts the thead. Upon contact, electons fom the od tansfe to the thead, chaging the thead negatively by contact. Both the thead and the od ae negatively chaged, so epulsion occus. 33. (a) You ae being chaged by conduction because you ae actually touching the sphee. (b) Yes, howeve, the chage will flow though you to the gound as a shock. 34. (a) As the od is bought nea the ball, electons in the ball ae epelled to the othe side of the atoms. This is chage shift due to induction. The atoms of the ball ae now polaized. Attaction between the negative od and the positive side of the atoms is geate than epulsion of the negative od and the negative electons. The od attacts the ball. (b) On contact, electons fom the od tansfe to the ball, chaging the ball negatively by contact. Both the ball and the od ae negatively chaged, and epulsion occus. 35. The compass will deflect counteclockwise and point in a westwad diection, as defined by the left-hand wie gasp ule. 6 Copyight 009 Peason Education Canada
36. (a) (b) The foce that balances the gavitational foce is the vetical component of the tension foce. The foce that balances the electostatic foce is the hoizontal component of the tension foce. 37. Selenium is a semiconducto that becomes a conducto when exposed to light and an insulato in the dak. This popety is essential in the opeation of a photocopie. 38. Chage shift occus in an insulato when electons meely move to the othe side of each atom, thus causing the atoms to become polaized. Chage migation occus in a conducto when electons tansfe to the othe side of the conducto, thus causing the conducto to become polaized. 39. Given (a) V = 0.70 V d = 5.0 10 9 m q = +1.6 10 19 C Requied (a) magnitude of the electic field between the outside and the inside of the membane E (b) the amount of wok necessay to move the sodium ion (W) (a) To calculate the magnitude of the electic field, use: V E d 0.70 V 9 5.0 10 m 8 1.410 V/m (b) In a consevative system, Ep W. E To calculate the electic potential enegy, use the equation p V. q ΔE p = Vq = (0.70 V)( 1.6 10 19 C) = 1.1 10 19 J 7 Copyight 009 Peason Education Canada
Paaphase (a) The magnitude of the electic field between the outside and the inside of the membane is 1.4 10 8 V/m. (b) The wok necessay to move the sodium ion is 1.1 10 19 J. 40. Similaities Newton s law of The gavitational foce: univesal vaies with 1 ; gavitation acts at a distance. Coulomb s law of The electostatic foce: electostatics vaies with 1 ; acts at a distance. 41. Given 19 q1 1.6010 C 19 q 1.6010 C 11 F 3.50 10 N e Requied the distance between the two electons () To calculate the distance, use: qq 1 Fe k Diffeences is much smalle than the electostatic foce; can only be attactive. is much lage than the gavitational foce; can be attactive o epulsive. kq q F 1 e 8.99 10 9 9 N m 19 C 19 (1.60 10 C )(1.60 10 C ) 11 (3.50 10 N ).56 10 m Paaphase The distance between the two electons is.56 10 9 m. 4. Given q 3.00 10 C 0.00 m Requied electostatic foce acting on the two sphees afte they touch ( F e ) When the two sphees touched, the chage was equally divided between them, so each sphee now has a chage of 1.50 10 C. 8 Copyight 009 Peason Education Canada
Accoding to Newton s thid law, the electostatic foces exeted by the two chages on each othe ae the same in magnitude but opposite in diection. Thus, it is only necessay to calculate the magnitude of the foces. To calculate the magnitude of the electostatic foce between two chages, use: qq 1 Fe k 9 N m 8.99 10 (1.50 10 C )(1.50 10 C ) C (0.00 m ) 7 5.06 10 N Paaphase The magnitude of the electostatic foce acting on the two sphees is 5.06 10 7 N. Since both chages ae negative, the electostatic foce is epulsive. 43. (a) (b) (c) The intensity of the electic field will be geatest at the points of the footballshaped object. (d) The intensity of the electic field is geatest at the point of the lightning od compaed to othe sufaces on Eath. The electic chages fom the clouds will move to the egion with the geatest electic field intensity the lightning od. 44. (a) As the ca is tavelling along the suface of Eath, its antenna, which is a conducto, is cutting the magnetic field lines of Eath, which un paallel to the suface of Eath. A voltage is poduced in the antenna, which in tun induces a cuent in the antenna, as a esult of the geneato effect. (b) Since magnetic noth is at the south pole and the ca tavels east, the diection of the cuent in the antenna is downwad. 45. To detemine the stength of the electic field, use: Fe E q 5 3.0 10 N 6.0 10 C 15 N/C The stength of the electic field is 15 N/C. 9 Copyight 009 Peason Education Canada
46. Given q = +1.60 10 19 C V =.0 10 4 V m = 1.67 10 7 kg Requied kinetic enegy gained by the poton ( E ) maximum speed of the poton at the negative plate (v) The initial electic potential enegy of the poton at the positive plate is: kf E pi = Vq Since it is at est, its initial kinetic enegy is: E k = 0 J i The final electic potential enegy of the poton at the negative plate is: E p = 0 J f Since this is a consevative system, a loss of electic potential enegy is conveted to a gain of kinetic enegy, accoding to the law of consevation of enegy: E E E E p k p k i i f f Vq 0J 0J E E Vq k f k f 4 19.0 10 V1.60 10 C 15 3. 10 J To solve fo the speed of the poton, use: 1 Ek mv Ek v m 15 3. 10 J 7 1.67 10 kg 6.0 10 m/s Paaphase 15 The kinetic enegy gained by the poton is 3. 10 J and its maximum speed at the negative plate is.0 10 6 m/s. 47. Given 6 q1 4.0010 C 6 q 3.0010 C 6 q3.00 10 C q 1 to q 0.500 m Requied position of the thid chage so that the net electostatic foce on it is zeo ( q3to q ) 1 The distance of q 3 fom q 1 is q3to q. 1 The distance of q fom q 3 is ( 0.500 m q 3to q ). 1 10 Copyight 009 Peason Education Canada
The electostatic foce of q 1 on q 3 is an attactive foce to the left and is a negative vecto quantity: F1. The electostatic foce of q on q 3 is an attactive foce to the ight and is a positive vecto quantity: F3. The negative and the positive signs fo the chages ae used only to detemine if the electostatic foce is attactive o epulsive. Since the two electostatic foces ae foce vectos along the same line, the net foce can be detemined by adding the vectos. Conside to the ight of the fist chage to be positive. F F F net 13 3 9 8.99 10 N m 6 6 9 (4.0010 C )(.00 10 C ) 8.99 10 N m 6 6 C (3.00 10 C )(.00 10 C ) 0 C ( ) (0.500 m ) q 3to q 1 q3toq1 q3to q1 0.68 m Paaphase The net electostatic foce on the thid chage is 0 N when it is placed 0.68 m to the ight of the fist chage. 48. To calculate the magnitude of the chage, use: Ep V q Ep q V 1.4 J 4.5 10 V 5 5.0 10 C The magnitude of the chage is 5.0 10 5 C. 49. Given l 0.30 m B 0.50 T F 0.11 N m Requied cuent in the wie (I) To detemine the cuent in the wie, use the equation: Fm Il B Fm I l B 0.11 N (0.30 m)(0.50 T) 0.73 A 11 Copyight 009 Peason Education Canada
Paaphase The cuent in the wie is 0.73 A. 50. Given 6 q1 3.0 10 C 5 q 1.510 C q 1 to q 0.50 m Requied (a) net electic field at a point midway between the two chages ( E net ) (b) the electostatic foce acting on the two chages ( F e ) (a) The electic field ceated by q 1 at point P, midway between the two chages, is to the left. The electic field ceated by q at point P, midway between the two chages, is to the left. The distance between each chage and point P is: 0.50 m 0.5 m Since the two electic field vectos ae along the same line, the net electic field can be detemined by adding the individual field vectos. Enet E q 1 + E q Conside left to be positive. Enet Eq E 1 q kq kq 1 Ptoq1 Ptoq 9 N m 6 9 N m 5 8.9910 (3.010 C ) C 8.9910 (1.5 10 C ) C (0.5 m ) (0.5 m ) 5 6 4.310 N/C.16 10 N/C 6.6 10 N/C (b) Accoding to Newton s thid law, the electostatic foces exeted by the two chages on each othe ae the same in magnitude but opposite in diection. Thus, it is only necessay to calculate the magnitudes of the foces. To calculate the magnitude of the electostatic foce acting on the two chages, use: qq 1 Fe k 9 N m 8.9910 C 1.6 N 6 5 (3.0 10 C )(1.5 10 C ) (0.50 m ) 1 Copyight 009 Peason Education Canada
The chages ae opposite, so the foce is attactive. Paaphase (a) The net electic field at a point midway between the two chages is.6 10 6 N/C [left]. (b) The electostatic foce acting on the two chages is 1.6 N. Since one chage is negative and the othe is positive, the electostatic foce is attactive. 51. (a) The ball of the geneato acquies a negative chage as the belt of the geneato ubs against the metal combs in the geneato. Electon tansfe occus between the belt and the comb, and the electons accumulate on the outside suface of the ball. This pocess is chaging by fiction. (b) When you touch the ball, the chage tansfes to you as a shock. This pocess is chaging by conduction. (c) The shaft of the wie is a pointed suface. Chages tend to accumulate at a point and then the electons leak into the ai and ionize ai molecules. This pocess is the same as a lightning od. The shaft of wie dains the chages fom the ball of the geneato, thus you will not feel a shock when you touch the ball. (d) As the plane tavels though Eath s magnetic field, a cuent is geneated by the metal wings, which ae conductos. To pevent a dangeous chage buildup, the metal stips dain the chage into the ai, simila to the metal wie on the geneato in pat (c) above. 5. Given m 0.015 kg 8 q1 1.510 C 8 q.510 C 1.0 cm 0.010 m Requied a fee-body diagam showing all the foces magnitude of the electostatic foce of epulsion acting on the two chages ( Daw a fee-body diagam of the foces and distances. F e ) Accoding to Newton s thid law, the electostatic foces exeted by the two chages on each othe ae the same in magnitude but opposite in diection. Thus, it is only necessay to calculate the magnitude of the foces. Detemine the foce of gavitational attaction on the mass: 13 Copyight 009 Peason Education Canada
F g mg (0.015 kg)(9.81 N/kg) 0.147 N Detemine the magnitude of d y : d y (0.75 m) (0.010 m) 0.75 m Detemine the electostatic foce on the two chages, using the fee-body diagam: Fe dx F d g y Fg dx Fe d y (0.147 N)(0.010 m ) (0.75 m ) 3.0 10 N Paaphase The magnitude of the epulsive electostatic foce acting on the two chages is.0 10 3 N. 53. Given 6 E 3.0010 N/C V = 500 V Requied minimum distance between the chaged plates ( d ) To calculate the minimum distance between the plates, use: 14 Copyight 009 Peason Education Canada
V E d V d E 500 V 6 3.0010 N/C 4 1.6710 m Paaphase 4 The minimum distance between the chaged plates is1.67 10 m. 54. Given 19 q 1.60 10 C q e p e p 11 19 1.60 10 C 5.9 10 m 31 m 9.11 10 kg m 7 1.67 10 kg Requied (a) magnitude of the gavitational foce of attaction between the two masses ( F g ) (b) magnitude of the electical foce of attaction between the two chages ( F e ) F e (c) how much geate the electical foce is than the gavitational foce F g (a) To calculate the magnitude of the gavitational foce, use: m m e p F G g 11 N m 31 6.67 10 7 (9.11 10 kg )(1.67 10 kg ) kg 11 (5.9 10 m ) 47 3.63 10 N (b) To calculate the magnitude of the electostatic foce, use: q q e p Fe k 9 N m 19 19 8.99 10 (1.60 10 C )(1.60 10 C ) C 11 (5.9 10 m ) 8 8. 10 N (c) The atio of the electostatic foce to the gavitational foce is: 15 Copyight 009 Peason Education Canada
F 8 e 8. 10 N 47 3.63 10 N g 39 F.7 10 Paaphase (a) The gavitational foce of attaction between the two masses is 3.63 10 47 N. (b) The electical foce of attaction between the two chages is 8. 10 8 N. (c) The electical foce is.7 10 39 times geate than the gavitational foce. 55. (a) The alpha paticle and the poton ae positively chaged and deflect in a cicula ac in one diection, wheeas the electon is negatively chaged and deflects in a cicula ac in the othe diection, as detemined by the ight- and left-hand ules, espectively. Since the alpha paticle has twice the chage, thee is twice the foce causing it to deflect. The alpha paticle also has almost fou times the mass of the poton, so the alpha paticle will deflect in a lage ac than the poton, fom the equation mv. qb (b) The alpha paticle and the poton deflect in a paabolic ac, eventually tavelling in the diection of the electic field, wheeas the electon will deflect in a paabolic ac, eventually tavelling against the diection of the electic field. (c) All thee chages will deflect in a paabolic ac, eventually tavelling in the diection of the gavitational field. 56. (a) Rub the ebonite od with the fu. The od will now be negatively chaged. If the od touches the electoscope, electon tansfe occus, and the electoscope is now negatively chaged by conduction. (b) Rub the glass od with silk. The od is now positively chaged. If this od is held nea a neutal electoscope, electons in the electoscope ae attacted to the ball of the electoscope, and the leaves divege with a positive chage. Gounding the electoscope moves electons into the scope fom the gound to neutalize the appaent suplus of positive chage on the leaves. When the gound is emoved and then the od, the electoscope will have a esidual negative chage by induction. 57. Given 6 m.0010 kg 4 B.00 10 T [N] 19 q 6.40 10 C Requied speed (v) at which the magnitudes of the magnetic foce and the gavitational foce ae equal chage of the paticle The gavitational foce on the chage has a magnitude of Fg mg and is diected downwad. The magnetic foce on the chage has a magnitude of Fm qv B and must be diected upwad. 16 Copyight 009 Peason Education Canada
F net = F m F g But the magnetic deflecting foce and the gavitational foce balance, so Theefoe, Fm Fg qv B mg v mg Bq F net = 0. 6 N (.0010 kg ) 9.81 kg 4 19 (.0010 T)(6.4010 C) 3 1.5310 m/s If the magnetic foce is upwad, the diection of the magnetic field is nothwad, and the diection of the motion of the chage is east, then the chage on the paticle must be positive, accoding to the ight-hand ule. Paaphase The positive chage will tavel in a staight line if its speed is1.53 10 3 m/s. 58. Given 19 q 3.010 C B 3.30 T 6 v 3.0010 m/s 7 m 6.6510 kg Requied (a) magnitude of the deflecting foce on the helium ion F m (b) adius of the deflecting ac () (a) Detemine the magnitude of the deflecting foce: F qv B m 19 6 (3.010 C)(3.0010 m/s)(3.30 T) 1 3.17 10 N (b) The magnetic foce on the helium ion has a magnitude of Fm qv B and it is the centipetal foce causing the alpha paticle to deflect in a cicula ac. mv Since Fm Fc, whee Fc, 17 Copyight 009 Peason Education Canada
mv qv B mv qb 7 6 (6.6510 kg)(3.00 10 m/s) 19 (3.0 10 C)(3.30 T) 1.8910 m Paaphase 1 (a) The magnitude of the deflecting foce on the helium ion is 3.17 10 N. (b) The helium ion will deflect in a cicula ac with a adius of1.89 10 m. 59. Given 6 qa 3.50 10 C 6 qb.44 10 C 6 qc 1.00 10 C AB 4.35 cm 0.0435 m Requied (a) net electostatic foce on sphee C midway between chages A and B ( F net ) (b) net electostatic foce on sphee C.50 cm ight of chage B ( F net ) (c) net electostatic foce on sphee C.50 cm down fom chage B ( F net ) (a) The distance fom q A to q C is: 0.0435 AC 0.0175 m So the distance fom q B to q C is: BC 0.0175 m The electostatic foce of q A on q C is a epulsive foce to the ight, and is a positive vecto quantity: F AC. The electostatic foce of q B on q C is an attactive foce to the ight, and is a positive vecto quantity: F BC. The negative and the positive signs fo the chages ae used only to detemine if the electostatic foce is attactive o epulsive. Since the two electostatic foces ae foce vectos along the same line, the net foce can be detemined by adding the vectos. F F F net AC + BC 18 Copyight 009 Peason Education Canada
F F F net AC BC 9 N m 6 6 8.99 10 (3.50 10 C )(1.00 10 C ) 8.9910 C (0.0175 m ) 66.51 N + 46.37 N 113 N 9 N m C 6 6 (.44 10 C )(1.00 10 C ) (0.0175 m ) (b) AC 0.0435m 0.050 m 0.0685m BC 0.050 m The electostatic foce of q A on q C is a epulsive foce to the ight, and is a positive vecto quantity: F AC. The electostatic foce of q B on q C is an attactive foce to the left, and is a negative vecto quantity: F BC. The negative and the positive signs fo the chages ae only used to detemine if the electostatic foce is attactive o epulsive. Since the two electostatic foces ae foce vectos along the same line, the net foce can be detemined by adding the vectos. Conside ight to be positive. F F F net AC + BC F F F (c) net AC BC 9 N m 6 6 8.99 10 (3.50 10 C )(1.00 10 C ) 8.99 10 C (0.0685 m ) 6.706 N 35.10 N 8.4 N 9 N m C 6 6 (.44 10 C )(1.00 10 C ) (0.050 m ) The electostatic foce of q A on q C is a epulsive foce ( AC F ) on a line fom chage A away fom chage C. 19 Copyight 009 Peason Education Canada
The electostatic foce of q B on q C is an attactive foce ( F BC ) diectly up fom chage C towad chage B. The negative and the positive signs fo the chages ae used only to detemine if the electostatic foce is attactive o epulsive. Since the two electostatic foces on chage C ae foce vectos that ae at an angle, use the component method to detemine the net foce. Daw a fee body diagam of the electostatic foces on chage C: Detemine the distance between chages A and C by using the Pythagoean theoem: AC (0.0435 m) (0.050 m) 0.05017 m Detemine the electostatic foce of chage A on chage C (epulsion away fom A): qaqc F k AC AC 9 N m 6 6 8.99 10 (3.5010 C )(1.00 10 C ) C (5.017 10 m ) 1.50 N Detemine the electostatic foce of chage B on chage C (attaction towad B): qq B C F k BC BC 9 N m 8.99 10 C 35.10 N 6 6 (.44 10 C )(1.00 10 C ) (0.050 m ) Use tigonomety to detemine the angle 1 fo the diection of F AC : 0 Copyight 009 Peason Education Canada
0.0435 m tan1 0.050 m 1 60.11 Resolve F AC into x and y components: FAC (1.50 N)(sin 60.11 ) x 10.84 N FAC (1.50 N)(cos 60.11 ) y 6.9 N The electostatic foce of chage B on chage C has only a y component: FBC 0 N x FBC 35.10 N y Add the x and y components: F net x = 0 N + 10.84 N = 10.84 N F net y = 35.10 N + ( 6.9 N) = 8.87 N Then detemine the magnitude of the foce, using the Pythagoean theoem: Fnet (10.84 N) (8.87 N) 30.8 N Use tigonomety to detemine the diection of the net electostatic foce on chage C. 1 Copyight 009 Peason Education Canada
Detemine the angle : 8.87 N tan 10.84 N 69.4 The diection of the net foce is 69.4. Paaphase (a) The net electostatic foce on sphee C midway between chages A and B is 113 N [ight]. (b) The net electostatic foce on sphee C.50 cm ight of chage B is 8.4 N [left]. (c) The net electostatic foce on sphee C.50 cm down fom chage B is 30.8 N [69.4 ]. 60. Given q = 1.6 10 19 C m = 3.3 10 7 kg v = 8.0 10 5 m/s Requied potential diffeence equied to acceleate the deuteon (V) The initial electic potential enegy of the deuteon at the positive plate is: E p i = Vq Since it is at est, its initial kinetic enegy is: E k i = 0 J The final electic potential enegy of the deuteon at the negative plate is: E p f = 0 J Since this system is consevative, a loss of electic potential enegy is conveted to a gain of kinetic enegy, accoding to the law of consevation of enegy: Copyight 009 Peason Education Canada
Ep E i k E i p E f kf Vq 0J 0J 1 mv 1 mv V q 7 5 1 3.3 10 kg 8.0 10 m/s 19 1.6 10 C 3 6.6 10 V Paaphase The potential diffeence equied to acceleate the deuteon is 6.6 10 3 V. 61. Given 6 E 7.8110 N/C d = 3.0 mm = 3.0 10 3 m q = 1.60 10 19 C m = 9.11 10 31 kg B 1.50 T Requied (a) voltage between the plates (V) (b) maximum speed of the electon between the plates (v) (c) magnetic foce on the electon F m (d) motion of the electon though the electic field and though the magnetic field (a) To calculate voltage between the plates, use the equation: V E d V E d 6 3 (7.8110 N/C)(3.0 10 m) 4.499 10 V (b) This system is consevative. You can use kinetic enegy of the electon to find its speed. The initial electic potential enegy of the sphee at the positive plate is E p i = Vq. Since the sphee was at est, its initial kinetic enegy, E k, is 0 J. i The final electic potential enegy of the sphee at the negative plate is E p f = 0 J. Accoding to the law of consevation of enegy, 3 Copyight 009 Peason Education Canada
E E E E Vq + 0 J 0 J + E E Vq p k p k i i f f k f k f 4 19 (.499 10 V)( 1.60 10 C) 15 3.999 10 J Since E 1 k mv, 15 (3.999 10 J) v 31 9.1110 kg 7 9.36910 m/s (c) Detemine the magnitude of the magnetic deflecting foce: F qv B m 19 7 (1.6010 C)(9.369 10 m/s)(1.50 T) 11.4910 N (d) As the electon tavels though the electic field, paallel to the electic field lines, the electon acceleates in a paabolic path in a diection opposite to the diection of the electic field (i.e., towad the positive plate). As the electon entes the magnetic field, it deflects in a cicula ac. Paaphase (a) The voltage between the plates is.50 10 4 V. (b) The speed of the electon at the positive plate is 9.37 10 7 m/s. (c) The magnitude of the magnetic foce on the electon is.5 10 11 N. 6. (a) As the noth pole of the magnet appoaches the coil, the wies in the coil cut the magnetic field lines of the magnet, which geneates a voltage in the coils though electomagnetic induction. An induced cuent in the coil will then egiste a eading in the galvanomete. (b) The induced cuent in the coil of wie, geneated by the movement of the magnet though the coils, tavels though the coil in a cicula diection. This cicula chage movement poduces a seconday magnetic field, simila to the field poduced by a ba magnet. The diection of this seconday magnetic field will be such as to oppose the initial motion of the magnet. If the noth pole of the magnet is appoaching the coil, cuent in the coil will be in a diection to poduce a noth pole at that end of the coil to oppose the motion of the appoaching magnet, i.e., clockwise. (c) As the magnet is pulled away fom the coil, a simila voltage is poduced, though electomagnetic induction, as the voltage poduced in pat (a). The diection of the induced cuent will be in the opposite diection, compaed to the cuent in pat (a), i.e., counteclockwise. (d) The diection of the induced cuent in the coil will be such as to poduce a magnetic field with a south pole at that end of the coil to oppose the motion of the noth pole of the magnet away fom the coil. 4 Copyight 009 Peason Education Canada
Extensions 63. The metal casing shields the sensitive inne electical components fom outside electical intefeence. 64. The metal ca body is simila to a hollow metal conducto, so chages accumulate on the outside suface of the ca. The inside cannot have a chage, so the net electic field inside the ca must be zeo. 65. Black holes ae caused by the temendous gavitational foces attacting masses into an extemely dense cente. The foces cannot be electical o magnetic because these foces cannot act on objects with no chage o no magnetic popeties. 66. Electical dischage fom the wokes could damage sensitive electonic equipment. 67. Chaged paticles fom the Sun ae tapped by Eath s magnetic field and move in a helical path along Eath s magnetic field lines towad the noth pole due to the magnetic foce. As the magnetic field lines of Eath s magnetic field each the poles, they dip towad Eath s suface. The magnetic deflecting foce on the chaged paticles now has a component that is opposite to the motion of the paticles. This causes the chaged paticles to deflect and move in a helical path along the magnetic field lines towad Eath s south pole, whee the pocess epeats. The paticles ae now tapped in a magnetic bottle. 68. These belts tap high-enegy chaged paticles fom space. A spacecaft enteing these egions would expeience seious damage to sensitive electonic equipment. 69. (a) When a chaged paticle tavels pependicula to gavitational o electic fields, it acceleates in a paabolic path. When a chaged paticle tavels pependicula to a magnetic field, it acceleates in a cicula path. (b) When a chaged paticle tavels paallel to and in the same diection as gavitational o electic fields, it acceleates along the gavitational o electic field lines. When a chaged paticle tavels paallel to and in the same diection as a magnetic field, it expeiences no foce and tavels in unifom motion. 70. Pointed objects have a moe intense electic field than neaby ounded objects, and thus ae moe likely to attact lightning stikes. 71. Initially, the magnetic domains of the steel beam ae aanged in a andom patten. Ove an extended peiod of time, the influence of the magnetic field of Eath causes the domains of the steel beam to line up along the magnetic field lines of Eath s magnetic field. The steel beams will become pemanent magnets though the pocess of magnetization by contact. This effect cannot happen with a wood beam because the motion of chages, in the atoms of wood, does not ceate stong enough magnetic fields to ceate magnetic domains. 7. The small distance between the feet of the bid, in contact with the same wie, and the insulation of the wie, do not allow a high enough potential diffeence to sustain a sufficient cuent to ham the bid. The potential diffeence between two adjacent wies, howeve, may poduce a high enough potential diffeence to ham the bid. 73. Magnetic field lines un along Eath s suface fom the south pole to the noth pole. Only at the equato do the magnetic field lines un paallel to the suface of Eath. At the magnetic poles, the magnetic field lines point pependiculaly downwad towad the suface of Eath. The angle of the magnetic field lines and the suface of Eath is called the dip angle. 5 Copyight 009 Peason Education Canada
A diectional compass cannot be used nea the poles because the magnetic field lines will point downwad and cannot affect a diectional compass, which is held in a position paallel to the suface of Eath. The angle between magnetic noth of the magnetic field of Eath and tue geogaphic noth is called the angle of declination. A diectional compass will point to magnetic noth, so angula coections must be made to locate tue geogaphic noth. 74. No. An electon at est does not poduce the magnetic field necessay to be influenced by an extenal magnetic field to poduce the moto effect foce equied to move the electon. 75. The changing magnetic field poduced nea a high-voltage powe line will poduce magnetic field lines that vibate back and foth. If a loop of wie is held in this vibating magnetic field, the wie of the loop will cut these magnetic field lines, thus poducing a voltage in the loop that, in tun, induces a cuent in the loop. This cuent can be egisteed in the galvanomete. 76. The ow of magnetite cystals can detect the magnetic field lines of Eath s magnetic field, enabling the bacteium to navigate, in pope diections. To test this hypothesis, place the bacteium nea the stonge magnetic field of a ba magnet, and obseve if the movement of the bacteium changes. Skills Pactice 77. Similaities listed in the ovelapping pats of the Venn diagam: 1 Both ae vecto fields. Both vay with. Both can exet attactive and epulsive foces. Both ae vey stong foces. Diffeences listed in the electic field cicle of the Venn diagam: An electic field oiginates fom one chage and extends in staight lines to infinity o oiginates fom infinity to the chage. Diffeences listed in the magnetic field cicle of the Venn diagam: A magnetic field extends fom one pole and cuves to anothe. 78. Students answes will vay but will likely take the following appoaches: fo a gavitational field an expeiment to see which way a test mass will tavel if placed in the field fo an electic field an expeiment to see which way a positive test chage will tavel if placed in the field fo a magnetic field an expeiment to see which way the noth pole of a small compass needle will point 79. Students answes will vay but thei concept maps should cove the following steps: Detemine the electostatic foce of the othe two chages on one chage. Detemine the angles of each electostatic foce on the chage. Detemine the x and y components of each foce. Detemine the sum of the x components and the sum of the y components. Daw vecto diagams of these sums. Detemine the esultant foce and the angle using tigonomety. 6 Copyight 009 Peason Education Canada
80. Students answes will vay but the expeiment could be simila to Pat B of 10-3 Inquiy Lab on page 56. 81. (a) (b) 1 B (c) To staighten the gaph, plot B as a function of 1. (d) (e) Invese of the distance fom the wie 1 1 m Magnetic field ( B (T)) 10.0 6.8 5.00 3.14 3.33.09.50 1.57.00 1.6 7 Copyight 009 Peason Education Canada
(f) slope = ise un 6.3 T 1 10.00 m 0.63 T m Since slope = ise un, B 1 B I B B I (0.63 T m) 5.00 A 0.79 T m/a B (g) I (6.8 T)(0.100 m) 5.00 A 0.789 T m/a Self-assessment Students' answes in this section will vay geatly depending on thei expeiences, depth of undestanding, and the depth of the eseach that they do into each of the topics. 8 Copyight 009 Peason Education Canada