ph132s04_hw4

# ph132s04_hw4 - PH 132 SPRING 2003 HOMEWORK 4 Assigned 50...

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Unformatted text preview: PH 132 SPRING 2003 HOMEWORK # 4 Assigned: 02/03/03 50 SHEETS 22-142 100 SHSETS 22-144 200 SHEETS 22-14] BP. The electric ﬁeld inside a nonconducting sphere o with charge spread uniformly throughont its volume, directed and has magnitude qr . W o):- o tineoRl' 50') ‘-= Here q (positive or negative] is the total charge within and r is the distance from the sphere’s center. (a) Takin the center of the sphere, ﬁnd the electric potential V(r sphere. (b) What is the difference in electric potential point on the surface and the sphere’s center? (c) If q which of those two points is at the highet potential? EM: 6!) V (r4 R) b)av= wen—VCR) - one >0, is We wan, or 1‘5 V(R)> We)? Elea‘n‘c Pa'mﬁhf due 1‘0 a. méhuous dt'ah'émﬁm Cafe/143.: 0) 714a MSW-lo Pm b) e Posi‘ﬂvepo v(a)—- vac) >0 5 O S HEETS 22-142 100 SHEETS 22-144 200 SHEETS 22-14] a ﬂMﬂAD a... [ a ________J. M: l‘nr'ﬁh' Paaf’h‘m 016% : 5:0 ﬁnd P095”: anti, I Z Hid: 63-)er W 0""2 b)6how Hie deem; polmb‘al. an(1 a chaotic! shad- 3.5 V: V0 " (fa); lﬂP. Figure 25-30 shows. edgem, an inﬁnite nonconductin' with positive surface charge density a on one side. (a) 25— l 8 and Eq. 24-! 3 to show that the electric potential of an sheet of charge can be written V = V0 — (tr/259); where electric pmentia] a1 Ihc surface of die sheet and z is the - ' Work M £25 an Eleofn'c Field, Eka‘n’c warm! I») V“ 3655 "Lg-J Comba'm'wj 1%{2 {we «1414‘;th gI'eIds: W=jff°d? i' Applginj Hat‘s 1?: +4": pmbIem= Wig—.345” W ,izgdi‘ (E‘Era sheaf of" chaﬁeozé‘g cg. ZV-LS p.ﬂo)(§:£d;m3 = giilz = ANS. I I E ‘7'.) W{0*”?3= “Z[V(z)-V(o)] _ . ' 5on ms 45; we): I I ":14! .. wan—we) L % V(z)= Vm- 67‘? Use 441: ram {m a) V( = W — 1 £53: 5 a) 0) 23(26.» 22 I4] 50 SHEETS 22442 H30 SHEETS 22-]44 200 SHEETS @ i . _._____..~_i____.__ @ﬂ’ﬂ‘V(o°)=o ' a”? jar-'36 2’ We. V(x)=o _ and let the paniclcs have " 1;. =1+q and 42 = -34A I Eleddc. Pam! Jae 'Q‘v pow charges deﬁne: XI :Céﬁﬂﬂcc 9C g! Er; job/a Poi/1f 654,38 Xiaﬂdﬂw bdwn 7r andcgz 69!. 25-26 P403) There are 3 case; 7‘» examine-‘1'. x>d J 12'. mo, ZIT.()<x<d P . I xﬁx W y E if 1?: tha)=o,+§¢ G}de _ i X 0’ x,=x—d g;;(fj:;f‘;j;’"w~’°% - E’ + g! 3’ k 5 .‘~. I x-d - x x—d rk[ (K~d)--3¢x]: k “Zex 1d = 556%) \ i ' 1W xéc-d) X X-d [ x>d",sa (x-00>O. Also "-sz ~d ,so (ﬂex-#0. 712:5 mam V5040: 2 Unﬁt): [i3 L‘X‘3Z]; 133 w]_o d—t/X:O => i X 6"” X d‘X : 22 I41 50 SHEETS 22-142 100 SHEETS 22444 200 SHEETS @ In Fig. 25-33, point P is a: the center or Lhc rectangle. with wm‘ b: 0 at inﬁnity. what is the as: electric potential at P due to the “W charged particles? P vp 4% 1 Eledﬁ'p Poknhhl due pa‘nf charges 6 V 2 2 _._ d k I" - q. a. an 2 .4 a :5 g '— e., I; ) G‘G‘QJL‘W *4) 2 '3 '3 Z .. _2.0Q __ 3-Oz + 5. _2_0 +3 . R Vd'+l§)‘ ’ g (id’ﬂ‘y' {3% ,y" +2 ﬁ%1 (5.0 3, 0 +5.0 r3. 0) + 0—3-2620?! 0-)] = _10_'-.3:kq,'—1-Q—-g,é£.—l—O—— kcz dt+(_)1v d. "a- l‘I-q’ 0’ V? 64.45%] = §£(2.94—9)= ANS- 3’ 22 141 50 SHEETS n 22-!42 100 SHSE'I'S 22-144 200 SHEETS % In Fig. 25-”, what is the net potential at point P due to the ' fou: point charges, if V = 0 at inﬁnity? 22.141 so SHEETS 22-142 IOO SHEETS 22.144 zoo SHEETS alan ’0) 5 155. A plastic rod has been formed into a cirble of radius R. 11 has .- ‘ = 1r .- I a positive charge +Q uniformly distributed along owe—quarter of I . ﬂow] 6 o A, A! 6 haer - +Q . . its cirwmfcrenoe and a negative 3.); wh—at 13 that “7 dmgcof—GQuaﬁfounlydiSlrib' mm: (a) at the we! C #31“ . from 9 " Y "‘3' 2” charge :- - 9Q med along the rest of the circum- circle and (b) 31 [301!“ a WP"; '5‘ ' fermcc (Fig. 25—37]. With V = 0 an the central axts of the are c a v (00) : O ' - - - ' _ dim“: z from mmnwr? \$5411 Eledn‘c. Pdmﬁal due. 1‘0 a cmh‘nm dzlsirxbuﬁ'm 04 charge 33 is (new 1’.) do pal:t b) ﬁnsi' in 3% «azasz exprwz'm 19>" We) and 441M (152. H 6r #1! Spark! Case; at”- " [0) look “1‘ 0'? f'nﬁm'ksr'm" dmwm‘ 01‘ charjerﬂﬁ 6% a dz‘Jche r from 2P af an 1: 9.11m infeng 1h: 3e! MW pokm‘zw. we show . do #195 #1 auto pfecas ,sa'noe Mare. me ﬁve dlmwd afﬁrm aFcﬁarJz- .— 99:31 W] = EGG-m} £93 {99%) [email protected]ﬂL-z r— : - kQ 22 I41 50 SHEETS 22-142 100 SHEETS 22-144 200 SHEETS a ma dfx: 28?. Figure. 25-40 shows a plastic rod of length L and unimel pos- the axis, at distance d from (med iLive charge Q lying on an x axis; and of the rod. : With V = 0 an iTIﬁlliiy, ﬁnd the elccu'ic potential at point P. on: Efedn'c PMELI due 1‘0 :2 Wm gamma deluge.- chaged rod [00k 42‘ ﬂ)? lh'ﬂhﬁéSIMd/JIJM afﬁx?! 4% , of/Mjfé d7, ﬁch Tﬁe 1:5 mﬁﬁrm guy-ilk ("061,50 we ('0? we m. x. 4/3: 2/2: 4/50, 2- *f? =3§= £945. 507:: My, 12; We; d+x L(d+x) a pm»?! my? 22 ‘41 50 SHEETS 22-142 100 SHEETS 12-144 200 SHEETS - ﬁctive mcxmiod {attire I 41. assumin the charges Ere-Imi— ‘ work required to set up the four- ' Lialiy inﬁmlely far 2pm. £1 chmgc conﬁguration of ﬁg. 25- whaf Eﬂgﬁ Work regalrz’d in 5d Up * - +58 cauﬁﬁumﬁbd 8 0 9' FIGURE 25-50 Exercise 56. yeah-c W21! Mark 6/ paw 61:49:: We pod HM {15.2.4643 c/Mrgc (9} deargc, '19'00615 Me work. (3" 4:153 )‘o bn'nj ad 0976 I51. ' I++nbsnam¥obr.'rjzhz. f l i W a = ,5!“ (e3. 25—43 , P. (015) -' M2" griﬁf‘ikir tie" ‘12.? 1g _ _.Ja = - RML I: 3 k, : W24' m 'v‘zﬂﬁm) 50 SHEETS 22442 100 SHEETS 22444 200 SHEETS 12-14! 6 AMMD 59?. In the rectangle of Fig. 25- 42. the sides have lengths 5.0 cm I and 15 cm. q] = -5.0 ,uC. and qu= +2.0.uc.wmv=0ar I I r (,wEZM. '- £=C7JSM wzaosbw _9 it 12—30201?) C : Z..Ox /O—6C 2;. _ inﬁnity, what are the electric po- tentials (a) at corner A and (b) at corner 8? (c) How much work is required to move a third : ' 45 = +3.0 Jc.r.C from B to A along a diagonal of the rectang (d) Does this work increase or decrease the electric energy the three-charge system? Is more, Iess, or the same work required if 43 is moved along paths that are (e) inside the rectangle but not on a diagonal and (1’) outside the - reclangle?,§ﬂf E 3' . Q———-£————_,A NOTE: warez—56m I 07", AT'A . r ‘0.) rs; r‘AuMLR = 3304’ a): “ﬁg”: 5154:7222: gram ?eaTEr-‘T7AL enact; WBJk “3:9 P69. 7H£Y£WQW C): / m swmsam IE) and; 772’; 355295?ch WIS A Lough/A7212; FOP—42.", THE Wm \$054.»: :59 \$35.57*. 0"“ THE 3mm. 5%” A105. A9 .21.: lie so sustrs 22-142 100 SHE£TS 22-144 200 SHEETS 2244] CH53525 52f. Consider two wider separated conducting spheres, I and 2. ' - R g 2 R + the second having twice the diameter oflhe ﬁrst. The smaller sphere I V ° 1 ‘ initially has a positive charge 4!. and the larger one is initially un- ‘ r .. _ charged. You now connect the spheres with a long thin wire. In'ﬁal Charje of 5we I — q, (a) How are the ﬁnal potentials V, and V2 of Ihe spheres relaxed? ' t r _ (b) What are the ﬁnal charges :1, and g: on the spheres, in terms {MW chdﬁe 0(5PMC 2 - 0 of q? (o) What is the ratio of the ﬁnal surface charge density of sphereIwmalofsoheI'eZ? I . V1,“; . b) q, dz r9676. ’ I l i uz ANS Once canceled, ﬁne? ﬁrm a ’ dwmmdmmmwwmwwﬂ' } We” dish-{bank rise/F an fﬁeSarﬁce a!“ W fmdaerérso male/{paws 014m cmdﬂd'r' 66m: 76 Mammy“ P, 4/6, b) We. wzll 055m #w‘ q; and f: are cfmempaw c4176: :11 Me (mica: 01c spheres IIHdZ. We can do Hui: bemdmw'c‘tlsﬁmnfhy _ %_k. a . - W "” or“ 73': "“ ‘4‘ \$14: §,=éso.z=z‘ezct> 57m chach is catsuvaﬂ diffz =f (a) Combahdg 0) (India): 9‘ =2 _W a, Q ' c) 6" area. " WK" 2. 4 z e a \$5.:- _ W \$111— .2. ngz :- ERz ;- J- Rzal R2. z-J 2' 6: qt 3; (we: 43R: 2 f z :5.) 2(2') HMS PH 132 _ Suggested Problems 2E. The electric potential difference between [he ground-and a cloud in a particular thunderstorm is 1.2 x 109 V. What is the magnitude of the change in the electric potential energy (in mul- tiples of Lhe electron-volt} of an electron that moves between the ground and the cloud? «we .... ..........._... -. - .. .... . . 45. When an electron moves from A to 3 along an electric ﬁeld line in Fig. 25-29. the electric field does 3.94 X 10‘” J of work on it. What are the electric po- ' tential differences (a) V8 — VA, 131 m (b) Vc — VA, and (c) Vc — v8? 5:]; line \ \ N —- ” \'\ B \ H. __ __ C, Equipozenljzls th. 25-29 Exercise 4. i l l l I l l l ! 6E Two large, parallel, conduct- ing plates are 12 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electrostatic force of 3.9 X IO‘ '5 N acts on an electron placed anywhere between the two plates. {Neglect fringing.) (a) Find the electric ﬁeld at the position of the electron. (b) What is the potential difference between the plates? on aa— aqxtoﬂst’u M: #17:: héx-lo “H...— O 50 SH£ET5 22-142 100 SHEETS 22-144 200 SHEETS 22-141 ® H 559. {a} Use the result of Problem 28 to ﬁnd the 21mg ﬁ ' ' ponent E, a1 point P, in ﬁg. 25-40. (Him: First substitute ' able .1: for the distance d in the result.) (b) Use symmetry: mine. the elcctric ﬁeld component IEJ 31 P. . ssm POIM) WIT/7’ cwmpcwm. x19 qugm 3% Q g x-L. X : ——_.—--- —— ‘* i | i ! 3% = 2': Ki? éﬂﬁg‘iﬁéiu ; l i . ~ C? .2[ 5.1—] — -9772”; 9x QM *3 —Q A? AH: N11NIT£\$IML b '97—. IE Cowm 2. %I~=T\$Vor~ﬁ Ezrﬂgﬂ— 9:136‘9F 3/ A:qu A HUG W15 __L 1‘0 TWE- K—Ax15' . :30 7742/1 ELEC/‘ﬁ-IC. P07. mums?) Eff THE WARIG‘TOM bl? "~ “23¢ FIE-Kc) WERE :LEZ ﬂHE WQ Folk“; AM Sig-UAW}; gymmlcjw 61M I _ _., ‘ZE' WES ,— ._ 72... “~HEJR W73f‘"”"5 N *- .. I WW'RJQEIJCEE I?DT'- BIFF: 4-5 ZERO. M 5‘? "'0 THE— 50 SHEETS 22—142 IOO SHEETS 22-144 200 SHEETS 22-14] 6 mm I 55?. (a)learthhadanctsutface charge density of1.0 electron 6,1ng '- ' per square mctcr (a very artiﬁcial assumption). what would its po- ' D _ ’ mm be? (Set V = 0 at inﬁnity.) (1:) What would be the electric <52: _— __,¢‘3—‘ 3; “M H ﬁeld due to E31111 just outside its surface? I ¢\$w3>w¢7fh6 TREAT 77795: EARTH A5. A snag j.“ W" 7H5: ?07. L911 6‘ Q5 5 : .____é-'.._ ivy:— BETHE g 9%: 2_ 5AM: A: THAT I Z“: I PE or k ?I- c.sz I 2. 36? AT [-112 ' 4’?ng 6;. 3‘1 n F E? K“ moi I i MEG, swam ' ail—‘- __ 4—: +9 I i )E THIS? I H—EMS b: Zea—£1; PAIN ALI—‘1’ .TAquAftb, Au- Ilu 200 SHEETS - d? 2.06M.“ 0.020;”, ' Vtw>=0 End: a) We) . WV}. 1‘!) brlrl'y a =f29uc fa. Pofnf C. b) w= «gay-v...) (ef. 25.7,Max:731“ewr-waww is 0). EE ave dommd‘ﬁcﬁ'ad,” .4 W z(v(c)—- we») = 2,00,) -o)= got/(c) W up #18 Wkr‘J-‘hka'lb Jaw/deed! 1-? ﬁfe no work. 75 mag ﬂag, (,4): = (3.442709%; ﬁ‘ﬁft i} 50‘]- 0| w: A”; r (9.3: ...
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## This note was uploaded on 04/23/2008 for the course PH 132 taught by Professor Ramsdell/wick during the Fall '08 term at Clarkson University .

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ph132s04_hw4 - PH 132 SPRING 2003 HOMEWORK 4 Assigned 50...

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