CHAPTER 16: Electric Charge and Electric Field. Answers to Questions

Transcription

1 CHAPTR : ectic Chage an ectic ie Answes t uestins. A pastic ue is suspene by a thea an then ubbe with a cth. As iscusse in sectin -, the ue is negativey chage. Bing the chage cmb cse t the ue. If the ue is epee by the cmb, then the cmb is negativey chage. If the ue is attacte by the cmb, then the cmb is psitivey chage.. The cthing gets chage by fictina cntact in the tumbing mtin f the ye. The ai insie the ye is y, an s the cthes can sustain a eativey age static chage. That chage bject wi then paize yu cthing, an be attacte t yu eectstaticay. 3. Wate is a pa mecue it has a psitive egin an a negative egin. Thus it is easiy attacte t sme the chage bject, ie an in eectn in the ai. 4. The psitivey chage sighty paizes the mecues in the pape. The negative chages in the pape ae sighty attacte t the pat f the pape csest t the, whie the psitive chages in the pape ae sighty epee fm the pat f the pape csest t the. Since the ppsite chages ae nw cse tgethe an the ie chages ae nw fathe apat, thee is a net attactin between the an the pape. 5. The pastic ue has gaine sme eectns fm the cth an thus has a net negative chage. This chage paizes the chage n the piece f pape, awing psitives sighty cse an epeing negatives sighty futhe away. This paizatin esuts in a net attactive fce n the piece f pape. A sma amunt f chage is abe t ceate enugh eectic fce t be stnge than gavity, an s the pape can be ifte. On a humi ay this is me ifficut because the wate mecues in the ai ae pa. Thse pa wate mecues ae abe t attact sme factin f the fee chages away fm the pastic ue. Thus the ue has a smae chage, the pape is ess paize, an thee is nt enugh eectic fce t pic up the pape.. The net chage n the cnuct is the unbaance chage, excess chage afte neutaity has been estabishe. The net chage is the sum f a f the psitive an negative chages in the cnuct. If a neuta cnuct has exta eectns ae t it, then the net chage is negative. If a neuta cnuct has eectns emve fm it, then the net chage is psitive. If a neuta cnuct has the same amunt f psitive an negative chage, then the net chage is ze. ee chages in a cnuct efe t thse eectns (usuay pe atm) that ae s sey attacte t the nuceus that they ae fee t be mve aun in the cnuct by an extena eectic fce. Neuta cnucts have these fee eectns. 7. each atm in a cnuct, ny a sma numbe f its eectns ae fee t mve. exampe, evey atm f cppe has 9 eectns, but ny fm each atm ae fee t mve easiy. As, nt even a f the fee eectns mve. As eectns mve twa a egin, causing an excess f negative chage, that egin then exets a age epusive fce n the eectns, peventing them fm a gatheing in ne pace. 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

2 Chapte ectic Chage an ectic ie 8. The fce f gavity puing wn n the eaves, tening t etun them t the vetica psitin. 9. The magnitue f the cnstant in Newtn s aw is vey sma, whie the magnitue f the cnstant in Cumb s aw is quite age. Newtn s aw says the gavitatina fce is pptina t the puct f the tw masses, whie Cumb s aw says the eectica fce is pptina t the puct f the tw chages. Newtn s aw ny puces attactive fces, since thee is ny ne in f gavitatina mass. Cumb s aw puces bth attactive an epusive fces, since thee ae tw ins f eectica chage. 0. the gavitatina fce, we n t ntice it because the fce is vey wea, ue t the vey sma vaue f G, the gavitatina cnstant, an the sma vaue f inay masses. the eectic fce, we n t ntice it because inay bjects ae eecticay neuta t a vey high egee. We ntice u weight (the fce f gavity) ue t the huge mass f the ath, maing a significant gavity fce. We ntice the eectic fce when bjects have a static chage (ie static cing fm the cthes ye), ceating a etectabe eectic fce.. The eectic fce is cnsevative. Yu can ste enegy in it, an get the enegy bac. exampe, mving a psitive chage cse t anthe statinay psitive chage taes w (simia t ifting an bject in the ath s gavitatina fie), but if the psitive chage is then eease, it wi gain inetic enegy an mve away fm the ste enegy catin (ie pping an bject in the ath s gavitatina fie). Anthe agument is that the mathematica fm f Cumb s aw is ientica t that f Newtn s aw f univesa gavitatin. We nw that gavity is cnsevative, an s we wu assume that the eectic fce is as cnsevative. Thee ae the inicatins as we. If yu mve a chage aun in an eectic fie, eventuay etuning t the stating psitin, the net w ne wi be 0 J. The w ne in mving a chage aun in an eectic fie is path inepenent a that mattes is the stating an ening catins. A f these ae inicatins f a cnsevative fce.. The chage pastic ue has a negative chage esiing n its suface. That chage paizes the chage in the neuta pape, pucing a net attactive fce. When the piece f pape then tuches the ue, the pape can get chage by cntact with the ue, gaining a net negative chage. Then, since ie chages epe, the pape is epee by the cmb. 3. The test chage ceates its wn eectic fie, an s the measue eectic fie is the sum f the igina eectic fie pus the fie f the test chage. By maing the test chage sma, the fie that it causes is sma, an s the actua measue eectic fie is nt much iffeent than the igina fie t measue. 4. A negative test chage cu be use. pupses f efining iectins, the eectic fie might then be efine as the OPPOSIT f the fce n the test chage, ivie by the test chage. quatin (-3) might be change t q, q Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

3 Gianci Physics: Pincipes with Appicatins, th itin. The eectic fie is stngest t the ight f the psitive chage, because the iniviua fies fm the psitive chage an negative chage bth ae in the same iectin (t the ight) at that pint, s they a t mae a stnge fie. The eectic fie is weaest t the eft f the psitive chage, because the iniviua fies fm the psitive chage an negative chage ae in ppsite iectins at that pint, an s they patiay cance each the. Anthe inicatin is the spacing f the fie ines. The fie ines ae cse t each the t the ight f the psitive chage, an futhe apat t the eft f the psitive chage. 7. At pint A, the net fce n a psitive test chage wu be wn an t the eft, paae t the neaby eectic fie ines. At pint B, the net fce n a psitive test chage wu be up an t the ight, paae t the neaby eectic fie ines. At pint C, the net fce n a psitive test chage wu be 0. In e f eceasing fie stength, the pints wu be ee A, B, C. 8. ectic fie ines shw the iectin f the fce n a test chage pace at a given catin. The eectic fce has a unique iectin at each pint. If tw fie ines css, it wu inicate that the eectic fce is pinting in tw iectins at nce, which is nt pssibe. 9. m ue : A test chage wu be eithe attacte iecty twas epee iecty away fm a pint chage, epening n the sign f the pint chage. S the fie ines must be iecte eithe aiay twas aiay away fm the pint chage. m ue : The magnitue f the fie ue t the pint chage ny epens n the istance fm the pint chage. Thus the ensity f the fie ines must be the same at any catin aun the pint chage, f a given istance fm the pint chage. m ue 3: If the pint chage is psitive, the fie ines wi iginate fm the catin f the pint chage. If the pint chage is negative, the fie ines wi en at the catin f the pint chage. Base n ues an, the ines ae aia an thei ensity is cnstant f a given istance. This is equivaent t saying that the ines must be symmeticay space aun the pint chage. 0. If the tw chages ae f ppsite sign, then 0 at a pint cse t the weae chage, an n the ppsite sie f the weae chage fm the stnge chage. The fies ue t the tw chages ae f ppsite iectin at such a pint. If the istance between the tw chages is, then the pint at which 0 is.4 away fm the weae chage, an 3.4 away fm the stnge chage. If the tw chages ae the same sign, then 0 at a pint between the tw chages, cse t the weae chage. The pint is 4% f the istance fm the weae chage t the stnge chage.. We assume that thee ae n the fces (ie gavity) acting n the test chage. The iectin f the eectic fie ine gives the iectin f the fce n the test chage. The acceeatin is aways paae t the fce by Newtn s n aw, an s the acceeatin ies ang the fie ine. If the patice is at est initiay an then eease, the initia vecity wi as pint ang the fie ine, an the patice wi stat t mve ang the fie ine. Hweve, nce the patice has a vecity, it wi nt fw the fie ine uness the ine is staight. The fie ine gives the iectin f the acceeatin, the iectin f the change in vecity. 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 3

4 Chapte ectic Chage an ectic ie. Since the ine f chage is infinitey ng, it has n pefee eft ight iectin. Thus by symmety, the ines must pint aiay ut away fm the cente f the ine. A sie view an an en view ae shwn f a ine f psitive chage. As seen fm the en view, the fie is nt unifm. As yu mve futhe away fm the ine f chage, the fie ines get futhe apat, inicating that the fie gets weae as yu mve away fm the ine f chage. 3. Just because the eectic fux thugh a cse suface is ze, the fie nee nt be ze n the suface. exampe, cnsie a cse suface nea an isate pint chage, an the suface es nt encse the chage. Thee wi be eectic fie ines passing thugh the suface, but the tta eectic fux thugh the suface wi be ze since the suface es nt encse any chage. The same numbe f fie ines wi ente the vume encse by the suface as eave the vume encse by the suface. On the cntay, if 0 at a pints n the suface, then thee ae n eectic fie ines passing thugh the suface, an s the fux thugh the suface is ze. 4. The eectic fux epens ny n the chage encse by the gaussian suface, nt n the shape f the suface. wi be the same f the cube as f the sphee. Sutins t Pbems. Use Cumb s aw t cacuate the magnitue f the fce C N m C 3.47 N 3 N m. Use the chage pe eectn t fin the numbe f eectns. eectn C.87 0 eectns C 3. Use Cumb s aw t cacuate the magnitue f the fce C.0 0 C N m C.7 0 N.5 0 m 4. Use Cumb s aw t cacuate the magnitue f the fce C N m C 9. N m 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 4

5 Gianci Physics: Pincipes with Appicatins, th itin 5. Use Cumb s aw t cacuate the magnitue f the fce C C N m C N m. Since the magnitue f the fce is invesey pptina t the squae f the sepaatin istance,, if the istance is mutipie by a fact f /8, the fce wi be mutipie by a fact f N.0 N 0 7. Since the magnitue f the fce is invesey pptina t the squae f the sepaatin istance,, if the fce is tipe, the istance has been euce by a fact f cm 4.88 cm Use the chage pe eectn an the mass pe eectn. eectn C eectns C g. 0 e.4 0 g e 9. Cnvet the g f H O t mes, then t atms, then t eectns. Oxygen has 8 eectns pe atm, an hygen has eectn pe atm. 3 9 me H O.0 0 mec. 0 e.0 0 C.0 g H O.0 g H O.8 0 g me mec. e C 0. Tae the ati f the eectic fce ivie by the gavitatina fce N m C.0 0 C m m G Gm m.7 0 N m g 9. 0 g.7 0 g G 39 The eectic fce is abut.3 0 times stnge than the gavitatina fce f the given scenai.. (a) Let ne f the chages be q, an then the the chage is T chages is x x q q T q q q q T T T, whee 0 x. A gaph f T T q. The fce between the. If we et x q, then f x x x between the imits f 0 an T 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 5

6 Chapte ectic Chage an ectic ie shws that the maximum ccus at x 0.5, q 0.5. Bth chages ae haf f the tta, T an the actua maximize fce is 0.5. T (b) If ne f the chages has a f the chage, an the the has n chage, then the fce between them wi be 0, which is the minimum pssibe fce.. Let the ight be the psitive iectin n the ine f chages. Use the fact that ie chages epe an unie chages attact t etemine the iectin f the fces. In the fwing expessins, N m C. 75 C 48 C 75 C 85 C m 0.70m 75 C 48 C 48 C 85 C m 0.35m 85 C 75 C 85 C 48 C m 0.35m 47. N.5 0 N 53.5 N 5. 0 N 4.3 N 4. 0 N 3. The fces n each chage ie ang a ine cnnecting the chages. Let the vaiabe epesent the ength f a sie f the tiange, an et the vaiabe epesent the chage at each cne. Since the tiange is equiatea, each ange is 0. cs0, sin 0 x y cs 0, sin 0 3 3x 3 y 0 sin 0 3 x x 3x y y 3 y.0 0 C 9 x y N m C 83.7 N 0.50 m The iectin f is in the y-iectin. As ntice that it ies ang the bisect f the ppsite sie f the tiange. Thus the fce n the we eft chage is f magnitue 83.7 N, an wi pint 30 bew the x axis. inay, the fce n the we ight chage is f magnitue 83.7 N, an 3 3 wi pint 30 bew the x axis. 4. Detemine the fce n the uppe ight chage, an then use the symmety f the cnfiguatin t etemine the fce n the the thee chages. The fce at the uppe ight cne f the squae is the vect sum f the fces ue t the the thee chages. Let the vaiabe epesent the 0.00 m ength f a sie f the squae, an et the vaiabe epesent the.00 mc chage at each cne Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

7 Gianci Physics: Pincipes with Appicatins, th itin, 0 4 4x 4y 4 4 cs45, 4 4 x 4 y 0, 43 43x 43 y A the x an y cmpnents tgethe t fin the tta fce, nting that. 4x 4 y x 4x 4 x 43x 4 y 4 4x 4 y C N m C.9 0 N 0.00 m tan 45 4 y 4 x abve the x-iectin. each chage, the net fce wi be the magnitue etemine abve, an wi ie ang the ine fm the cente f the squae ut twas the chage. 5. Detemine the fce n the uppe ight chage, an then the symmety f the cnfiguatin says that the fce n the we eft chage is the ppsite f the fce n the uppe ight chage. Liewise, etemine the fce n the we ight chage, an then the symmety f the cnfiguatin says that the fce n the uppe eft chage is the ppsite f the fce n the we ight chage. The fce at the uppe ight cne f the squae is the vect sum f the fces ue t the the thee chages. Let the vaiabe epesent the 0.00 m ength f a sie f the squae, an et the vaiabe epesent the.00 mc chage at each cne., 0 4 4x 4y 4 4 cs45, 4 4 x 4 y 0, 43 43x 43 y A the x an y cmpnents tgethe t fin the tta fce, nting that. 4x 4 y x 4x 4x 43x 4 y x 4 y Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 7

8 Chapte ectic Chage an ectic ie C N m C N 0.00 m tan 5 4 y 4x fm the x-iectin, exacty twas the cente f the squae. 7 each chage, the net fce wi be the magnitue f.9 0 N an each net fce wi ie ang the ine fm the chage inwas twas the cente f the squae.. Tae the we eft han cne f the squae t be the igin f cinates. ach chage wi have a hiznta fce n it ue t ne chage, a vetica fce n it ue t ne chage, an a iagna fce n it ue t ne chage. in the cmpnents f each fce, a the cmpnents, fin the magnitue f the net fce, an the iectin f the net fce. At the cncusin f the pbem is a iagam shwing the net fce n each f the tw chages. 4 (a) : cs x 3 4 sin y (b) y 0. tan tan x y x : cs x sin y y 4.8 tan tan x 3y x The fces n each chage ie ang a ine cnnecting the chages. Let the vaiabe epesent the ength f a sie f the tiange. Since the tiange is equiatea, each ange is 0. ist cacuate the magnitue f each iniviua fce Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 8

9 Gianci Physics: Pincipes with Appicatins, th itin C C N m C N C.0 0 C N m C N 3.0 m.0 m C.0 0 C N m C 0.99 N m Nw cacuate the net fce n each chage an the iectin f that net fce, using cmpnents. x x 3x y y 3 y N cs N cs N N sin N sin N y 0.30 N tan tan 5 x y x x 3x y y 3 y x N N N cs N N N sin N y 0. N tan tan 39 x y 3x 3x 3 x 3 y 3y 3 y x.79 0 N N N cs N.47 0 N N sin N 3 y 0. N tan tan x 3 y 3 0 3x.97 0 N.47 0 N 8. Since the fce is epusive, bth chages must be the same sign. Since the tta chage is psitive, bth chages must be psitive. Let the tta chage be. Then if ne chage is f magnitue q, then the the chage must be f magnitue q. Wite a Cumb s aw expessin f ne f the chages. q q q q 0 q C 50 0 C 4.8 N.0 m N m C C, C q C, C Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 9

10 Chapte ectic Chage an ectic ie 9. The negative chages wi epe each the, an s the thi chage must put an ppsite fce n each f the igina chages. Cnsieatin f the vaius pssibe cnfiguatins eas t the cncusin that the thi chage must be psitive an must be between the the tw chages. See the iagam f the efinitin f vaiabes. each negative chage, equate the magnitues f the tw fces n the chage. As nte that 0 x eft: x x ight: x 0.3 x x 3 3 x 3 x Thus the chage shu be f magnitue 0.40, an a istance 0.37 fm twas x x Assume that the negative chage is = 8.5 cm t the ight f the psitive chage, n the x-axis. T expeience n net fce, the 4.7 C 3.5 C thi chage must be cse t the smae magnitue chage + (the negative chage). The thi chage cannt be between the x chages, because it wu expeience a fce fm each chage in the same iectin, an s the net fce cu nt be ze. An the thi chage must be n the ine jining the the tw chages, s that the tw fces n the thi chage ae ang the same ine. See the iagam. quate the magnitues f the tw fces n the thi chage, an sve f x > 0. x x x x 8.5cm C C C cm. (a) If the fce is epusive, bth chages must be psitive since the tta chage is psitive. Ca the tta chage N.0 m C C N m C C,. 0 C 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 0

11 Gianci Physics: Pincipes with Appicatins, th itin (b) If the fce is attactive, then the chages ae f ppsite sign. The vaue use f must then be negative. Othe than that, the sutin meth is the same as f pat (a) N.0 m C C N m C C, C. The sphees can be teate as pint chages since they ae spheica, an s Cumb s aw may be use t eate the amunt f chage t the fce f attactin. ach sphee wi have a magnitue f chage, since that amunt was emve fm ne sphee an ae t the the, being initiay unchage..7 0 N 0. m N m C 9 eectn C.0 0 eectns C 3. Use q. 3 t cacuate the fce. 9 q.0 0 C 30 N C east N west q 4. Use q. 3 t cacuate the eectic fie. q N suth C 5. Use q. 3 t cacuate the eectic fie. 8.4 Nwn N C up q C N C suth. Use q. 4a t cacuate the eectic fie ue t a pint chage C N m C N C up.00 0 m Nte that the eectic fie pints away fm the psitive chage. 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

12 Chapte ectic Chage an ectic ie 7. Assuming the eectic fce is the ny fce n the eectn, then Newtn s n aw may be use t fin the acceeatin. 9 q.0 0 C 4 ma q a net N C.3 0 m s m 9. 0 g Since the chage is negative, the iectin f the acceeatin is ppsite t the fie. 8. The eectic fie ue t the negative chage wi pint twa the negative chage, an the eectic fie ue t the psitive chage wi pint away fm the psitive chage. Thus bth fies pint in the same iectin, twas the negative chage, an s can be ae. 4 / / N m C m 9 The iectin is twas the negative chage C C N C Assuming the eectic fce is the ny fce n the eectn, then Newtn s n aw may be use t fin the eectic fie stength. ma q net ma q.7 0 g m s C 0.0 N C 0.N C 3. Since the eectn acceeates fm est twas the nth, the net fce n it must be t the nth. Assuming the eectic fce is the ny fce n the eectn, then Newtn s n aw may be use t fin the eectic fie. m ma q a q g net C 0 5 m s nth.54 0 N C suth 3. The fie ue t the negative chage wi pint twas the negative chage, an the fie ue t the psitive chage wi pint twas the negative chage. Thus the magnitues f the tw fies can be ae tgethe t fin the chages. 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

13 Gianci Physics: Pincipes with Appicatins, th itin N C.0 0 m C net 9 / N m C 33. The fie at the cente ue t the tw negative chages n ppsite cnes (we ight an uppe eft in the iagam) wi cance each the, an s ny the psitive chage an the ppsite negative chage nee t be cnsiee. The fie ue t the negative chage wi pint iecty twa it, an the fie ue t the psitive chage wi pint iecty away fm it. Accingy, the tw fies ae in the same iectin an can be ae agebaicay C N m C N C at m C 7.0 C 34. The fie at the uppe ight cne f the squae is the vect sum f the fies ue t the the thee chages. Let the vaiabe epesent the.0 m ength f a sie f the squae, an et the vaiabe epesent the chage at each f the thee ccupie cnes., 0 x y cs45, x y , 3 3x y A the x an y cmpnents tgethe t fin the tta eectic fie, nting that x. y x x x 3x y x y C N m C N C.00m tan 45 y x fm the x-iectin Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 3

14 Chapte ectic Chage an ectic ie 35. Chse the ightwa iectin t be psitive. Then the fie ue t + wi be psitive, an the fie ue t wi be negative. 4xa x a x a x a x a x a The negative sign means the fie pints t the eft. 3. the net fie t be ze at pint P, the magnitues f the fies ceate by an must be equa. As, the istance x wi be taen as psitive t the eft f. That is the ny egin whee the tta fie ue t the tw chages can be ze. Let the vaiabe epesent the cm istance, an nte that. x x x cm 9cm 37. (a) The fie ue t the chage at A wi pint staight wnwa, an the fie ue t the chage at B wi pint ang the ine fm A t the igin, 30 bew the negative x axis. 0, A Ax Ax 3 cs30 B Bx x y sin 30 By Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the x Ax Bx y Ay By y 3 tan tan tan tan 3 40 x 3 3 (b) Nw evese the iectin f 0, A Ax Ax A 3 cs30, sin 30 B Bx By 3 x Ax Bx y Ay By B A A B

15 Gianci Physics: Pincipes with Appicatins, th itin x y tan tan tan 330 x 3 3 y 38. In each case, fin the vect sum f the fie cause by the chage n the eft an the fie eft cause by the chage n the ight ight Pint A: m the symmety f the gemety, in cacuating the eectic fie at pint A ny the vetica cmpnents f the fies nee t be cnsiee. The hiznta cmpnents wi cance each the. 5.0 tan. 0.0 A 5.0 cm 0.0 cm 0.8 m C sin N m C sin N C m Pint B: Nw the pint is nt symmeticay pace, an s hiznta an vetica cmpnents f each iniviua fie nee t be cacuate t fin the esutant eectic fie eft tan 45 eft tan eft 5.0 cm 5.0 cm m ight 9 A ight eft A eft ight eft ight eft ight 5.0 cm 5.0 cm 0.58m cs cs x eft x ight x eft ight eft ight 9 cs45 cs N m C C.5 0 N C m 0.58m sin sin y eft y ight y eft ight eft ight B 7 y x y B 9 sin45 sin N m C C N C m 0.58m. 0 N C tan 5 x 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 5

16 Chapte ectic Chage an ectic ie The esuts ae cnsistent with igue -3b. In the figue, the fie at Pint A pints staight up, matching the cacuatins. The fie at Pint B shu be t the ight an vetica, matching the cacuatins. inay, the fie ines ae cse tgethe at Pint B than at Pint A, inicating that the fie is stnge thee, matching the cacuatins. 39. Bth chages must be f the same sign s that the eectic fies ceate by the tw chages ppse each the, an s can a t ze. The magnitues f the tw eectic fies must be equa m the iagam, we see that the x cmpnents f the tw fies wi cance each the at the pint P. Thus the net eectic fie wi be in the negative y-iectin, an wi be twice the y-cmpnent f eithe eectic fie vect. a sin sin net x a x a / a x a x a x a a 3/ in the negative y iectin 4. We assume that gavity can be igne, which is pven in pat (b). (a) The eectn wi acceeate t the ight. The magnitue f the acceeatin can be fun fm setting the net fce equa t the eectic fce n the eectn. The acceeatin is cnstant, s cnstant acceeatin eatinships can be use. q ma q a net m q v v a x v a x x 0 m C.45 0 N C.0 0 m m s g (b) The vaue f the acceeatin cause by the eectic fie is cmpae t g. 9 4 q.0 0 C.45 0 N C 5 a.55 0 m s 3 m 9. 0 g 5 a.55 0 m s g 9.80m s The acceeatin ue t gavity can be igne cmpae t the acceeatin cause by the eectic fie. 4. (a) The eectn wi expeience a fce in the ppsite iectin t the eectic fie. Since the eectn is t be bught t est, the eectic fie must be in the same iectin as the initia vecity f the eectn, an s is t the ight. 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

17 Gianci Physics: Pincipes with Appicatins, th itin (b) Since the fie is unifm, the eectn wi expeience a cnstant fce, an theefe have a cnstant acceeatin. Use cnstant acceeatin eatinships t fin the fie stength. q q q ma a v v a x v x 0 0 m m g m s m v v mv q x q x.0 0 C m.4 0 N C 43. Use Gauss s aw t etemine the encse chage. enc N m C C N m.8 0 C enc 44. (a) (b) (c) A N C.8 0 m 59 N m C A cs N C cs m 4 N m C A cs (a) Use Gauss s aw t etemine the eectic fux..0 0 C enc 5. 0 N m C C N m (b) Since thee is n chage encse by suface A, (a) Assuming that thee is n chage cntaine within the cube, then the net fux thugh the cube is 0. A f the fie ines that ente the cube as eave the cube. (b) Thee ae fu faces that have n fux thugh them, because nne f the fie ines pass thugh thse faces. In the iagam shwn, the eft face has a psitive fux an the ight face has the ppsite amunt f negative fux. eft ight A.50 0 N C N C 0 the 47. quatin -0 appies. A A C N m 30 N C.0m.5 0 C 48. The eectic fie can be cacuate by q. -4a, an that can be sve f the chage N C m N m C 9 This cespns t abut be negative C 8 0 eectns. Since the fie pints twa the ba, the chage must 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 7

18 Chapte ectic Chage an ectic ie 49. See xampe - f a etaie iscussin eate t this pbem. (a) Insie a si meta sphee the eectic fie is 0. (b) Insie a si meta sphee the eectic fie is 0. (c) Outsie a si meta sphee the eectic fie is the same as if a the chage wee cncentate at the cente as a pint chage C N m C N C 3.0m () Same easning as in pat (c) C N m C N C.00m (e) The answes wu be n iffeent f a thin meta she. 50. See igue -33 in the text f aitina insight int this pbem. (a) Insie the she, the fie is that f the pint chage,. (b) Thee is n fie insie the cnucting mateia: 0. (c) Outsie the she, the fie is that f the pint chage,. () The she es nt affect the fie ue t ane, except in the she mateia, whee the fie is 0. The chage es affect the she it paizes it. Thee wi be an inuce chage f unifmy istibute ve the insie suface f the she, an an inuce chage f + unifmy istibute ve the utsie suface f the she. 5. (a) The net fce between the thymine an aenine is ue t the fwing fces. 0.4e 0.e 0.08e O H attactin: OH.80A.80A O N epusin: N N epusin: H N attactin: 0.4e 0.e 0.08e ON.80A.80A 0.e 0.e 0.04e NN 3.00A 3.00A 0.e 0.e 0.04e HN.00A.00A A-T OH ON NN HN m e 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 8

19 Gianci Physics: Pincipes with Appicatins, th itin N m C.0 0 C N 4. 0 N m (b) The net fce between the cytsine an guanine is ue t the fwing fces. 0.4e 0.e 0.08e O H attactin: ( f these) OH.90A.90A O N epusin: H N attactin: N N epusin: 0.4e 0.e 0.08e ( f these) ON.90A.90A 0.e 0.e 0.04e HN.00A.00A 0.e 0.e 0.04e NN 3.00A 3.00A m C-G OH ON NN HN N m C.0 0 C N 7. 0 N m (c) 0 pais f mecues, we assume that haf ae A-T pais an haf ae C-G pais. We 5 aveage the abve esuts an mutipy by N 7. 0 N net A-T C-G N 0 N e 5. Set the magnitue f the eectic fce equa t the magnitue f the fce f gavity an sve f the istance. e mg G e mg N m C C 5.08m g 9.80 m s 53. Cacuate the tta chage n a eectns in 3.0 g f cppe, an then cmpae the 38 C t that vaue. 3 9 me.0 0 atms 9 e.0 0 C Tta eectn chage 3.0g 3.5g me atms e C 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 9

20 Chapte ectic Chage an ectic ie 38 0 C actin st C Since the gavity fce is wnwa, the eectic fce must be upwa. Since the chage is psitive, the eectic fie must as be upwa. quate the magnitues f the tw fces an sve f the eectic fie. q mg mg.7 0 g 9.80 m s 7 G 9 q.0 0 C 55. Use q. -4a t cacuate the magnitue f the eectic chage n the ath. 50 N C.38 0 m N m C C N C, up Since the eectic fie is pinting twas the ath s cente, the chage must be negative. 5. (a) m pbem 55, we nw that the eectic fie is pinte twas the ath s cente. Thus an eectn in such a fie wu expeience an upwas fce f magnitue e. The fce f gavity n the eectn wi be negigibe cmpae t the eectic fce. e ma a e m C 50 N C g m s. 0 m s, up (b) A ptn in the fie wu expeience a wnwas fce f magnitue gavity n the ptn wi be negigibe cmpae t the eectic fce. e ma a e m (c) the eectn: the ptn: C 50 N C g a g a g.38 0 m s 9.80m s m s 9.80m s m s.4 0 m s, wn e. The fce f 57. the pet t emain statinay, the magnitue f the eectic fce n the pet must be the same as the weight f the pet. The mass f the pet is fun fm its vume times the ensity f wate. Let n be the numbe f excess eectns n the wate pet. 4 3 q mg ne g n g m.00 0 g m 9.80 m s 9 3e C 50 N C eectns 58. Thee ae fu fces t cacuate. Ca the ightwa iectin the psitive iectin. The vaue f 9 9 is N m C an the vaue f e is.0 0 C. 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 0

21 Gianci Physics: Pincipes with Appicatins, th itin net CH CN OH ON N.4 0 N 0.40e 0.0e 0 m The eectic fce must be a aia fce in e f the eectn t mve in a cicua bit. mv aia bit bit C 9 0 bit 3 mv N m C. 0 m 9. 0 g. 0 m s 0. Set the Cumb eectica fce equa t the Newtnian gavitatina fce n ne f the bies (the Mn). M M Mn ath G G bit bit GM Mn M ath N m g g g N m C C. (a) The eectn wi expeience a fce in the ppsite iectin t the eectic fie. Thus the acceeatin is in the ppsite iectin t the initia vecity. The fce is cnstant, an s cnstant acceeatin equatins appy. T fin the stpping istance, set the fina vecity t 0. e e ma a v v a x 0 m x g.5 0 m s a e.0 0 C.4 0 N C v v mv 0.5m (b) T etun t the stating pint, the vecity wi evese. Use that t fin the time t etun. v v at t 0 v v v v mv a a q g.5 0 m s C.4 0 N C s. Because f the invese squae natue f the eectic fie, any catin whee the fie is ze must be cse t the weae chage. As, in between the tw chages, the fies ue t the tw chages ae paae t each the an cannt cance. Thus the ny paces whee the fie can be ze ae cse t the weae chage, but nt between them. In the iagam, this means that x must be psitive Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

22 Chapte ectic Chage an ectic ie C C C.0m.m fm,.m fm 3. The sphee wi sciate sinusiay abut the equiibium pint, with an ampitue f 5.0 cm. The angua fequency f the sphee is given by m N m 0.800g.5a s. The istance f the sphee fm the tabe is given by cs.5t m. Use this istance an the chage t give the eectic fie vaue at the tabetp. That eectic fie wi pint upwas at a times, twas the negative sphee N m C C cs.5t m cs.5t N C cs.5t 7 N C, upwas 4. The wies fm tw sies f an equiatea tiange, an s the tw chages ae sepaate by a istance 78 cm an ae iecty hiznta fm each the. Thus the eectic fce n each chage is hiznta. m the fee-by iagam f ne f the sphees, wite the net fce in bth the hiznta an vetica iectins an sve f the eectic fce. Then wite the eectic fce by Cumb s aw, an equate the tw expessins f the eectic fce t fin the chage. mg cs mg 0 y T T cs mg sin 0 sin sin mg tan x T T cs mg tan mg tan 4 0 g 9.80 m s tan m.04 0 C. 0 C N m C T mg 5. The eectic fie at the suface f the pea is given by quatin (-4a). Sve that equatin f the chage N C m N m C This cespns t abut 3 biin eectns C. Thee wi be a ightwa fce n ue t, given by Cumb s aw. Thee wi be a eftwa fce n ue t the eectic fie ceate by the paae pates. Let ight be the psitive iectin. x 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the

23 Gianci Physics: Pincipes with Appicatins, th itin.7 0 C.8 0 C N m C.7 0 C N C 0.34m 0.45 N, ight 7. Since the eectic fie exets a fce n the chage in the same iectin as the eectic fie, the chage is psitive. Use the fee-by iagam t wite the equiibium equatins f bth the hiznta an vetica iectins, an use thse equatins t fin the magnitue f the chage. 43 cs sin 0 sin x T T mg cs mg 0 mg tan y T T cs mg tan.0 0 g 9.80 m s tan N C mg T C 43cm L 55cm 8. The weight f the mass is ny abut N. Since the tensin in the sting is me than that, thee must be a wnwa eectic fce n the psitive chage, which means that the eectic fie must be pinte wn. Use the fee-by iagam t wite an expessin f the magnitue f the eectic fie. mg 0 mg T T T mg 5.7 N 0.0g 9.80m s C N C mg T 9. T fin the numbe f eectns, cnvet the mass t mes, the mes t atms, an then mutipy by the numbe f eectns in an atm t fin the tta eectns. Then cnvet t chage. 5 g A 5 g A C 3 9 me A.0 0 atms 3 eectns.0 0 C.7 0 g me mecue eectn The net chage f the ba is 0C, since thee ae equa numbes f ptns an eectns. 70. (a) The fce f sphee B n sphee A is given by Cumb s aw., away fm B AB R (b) The esut f tuching sphee B t unchage sphee C is that the chage n B is shae between the tw sphees, an s the chage n B is euce t. Again use Cumb s aw. R AB R, away fm B 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 3

24 Chapte ectic Chage an ectic ie (c) The esut f tuching sphee A t sphee C is that the chage n the tw sphees is shae, an s the chage n A is euce t 3 4. Again use Cumb s aw , away fm B R 8R AB 7. On the x-axis, the eectic fie can ny be ze at a catin cse t the smae magnitue chage. Thus the fie wi neve be ze t the eft f the mipint between the tw chages. As, in between the tw chages, the fie ue t bth chages wi pint t the eft, an s the tta fie cannt be ze. Thus the ny pace n the x-axis whee the fie can be ze is t the ight f the negative chage, an s x must be psitive. Cacuate the fie at pint P an set it equa t ze. x x 0 x x x.4 The fie cannt be ze at any pints ff the x-axis. any pint ff the x-axis, the eectic fies ue t the tw chages wi nt be ang the same ine, an s they can neve cmbine t give The eectic fie wi put a fce f magnitue n each chage. The istance f each chage fm the pivt pint is L L, an s the tque cause by each fce is. Bth tques wi ten t mae the tate cunteccwise L in the iagam, an s the net tque is L. net 73. A negative chage must be pace at the cente f the squae. Let 8.0 C be the chage at each cne, et -q be the magnitue f negative chage in the cente, an et 9.cm be the sie ength f the squae. By the symmety f the pbem, if we mae the net fce n ne f the cne chages be ze, the net fce n each the cne chage wi as be ze., 0 4 4x 4y 4 4 cs45, 4 4 x 4 y 0, 43 43x 43 y q q q cs 45 The net fce in each iectin shu be ze. 4q 4qx 4qy q C q x 4 4 S the chage t be pace is q 7. 0 C. 4q q Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 4

25 Gianci Physics: Pincipes with Appicatins, th itin This is an unstabe equiibium. If the cente chage wee sighty ispace, say twas the ight, then it wu be cse t the ight chages than the eft, an wu be attacte me t the ight. Liewise the psitive chages n the ight sie f the squae wu be cse t it an wu be attacte me t it, mving fm thei cne psitins. The system wu nt have a tenency t etun t the symmetic shape, but athe wu have a tenency t mve away fm it if istube. 005 Peasn ucatin, Inc., Uppe Sae Rive, NJ. A ights eseve. This mateia is ptecte une a cpyight aws as they cuenty exist. N ptin f this mateia may be epuce, in any fm by any means, withut pemissin in witing fm the 5