241_hw-answers - Homework Answers Elect rostatics 1 yes...

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Unformatted text preview: Homework Answers Elect rostatics 1: yes, attractive, yes, repulsive 2: no 3: 230. 4N, 1. 86 x 10 34N 4: A distance D to the left of Q1 5: 0. 005164N, 84. 00 below the +x axis ' Qqa: 8w3d360m _ Q ~ QGQ 6. F = m, T = T 7. 0-201fiN. 0.0250493—N, Jillii-trjolerV — 47,10,113 8:0: Qq l—l 9::E,no 27reom a: d 10: p in :13, 6* in —5:, 0.00719m, 13.19771, 14371m/s, 2.637 x 107m/5 12: 2N/C', 16.?0 above the +x axis, direction as in part a, 4 x 1019m/s2 13: stable, unstable 1 —Q : A —Q . a A0132“: 1 1 I 14: = —— E,, = , ,,, = —— — i— x 47reo(D2—v L2/4)x’ 47T€0D2$ E 87mg (D + L/2)2 (D — L/f/J)2 ,5. ~ Qy ~ Q1} ' 3‘: 2—W60Dx/4D2 + L2 24ml)? -' —A0y 1 _ —' AoRZbgboé' 16: E = — — 2 z _ y 47TEOR ($0 2 Sln( 9‘50 3(3)) E: 27TEO(2‘3 + R2)3/{2 —' 00.30 1 1 A " ("l-0'2 17:E=— ———— E,=— z 260 (Zn «1122 + 33)?) 2E0 _. —00'Q _. "3003} _. 00y“ 260ml) 18! E = E = E = —, t = y 260 7 y 260 ’ y 260 3q00 Gauss’ Law 1: 0,0,E0a2 eosa, —E0a2 cos a, Ego:2 sin a, —E0a2 sin or, 0 2: no, yes 4: 6%, no _ 5 _, 5 A 5 H 5 5:15. = E = :0on 2R1)?” ! E _ P01R2—1211T, 0 = 90(R22 fl) 5EOR1T2 560R2T 5R1R2 « Q7“ - 3Q?c —22Q 3Q 2wcor2’ ’ 47mm“21 0 471'R2’ U 47TR2 2 . 2 A pop .0 a poRlp ~ poRlp —poR PoRl 7:0.28N 8: E: ,E= ,,0 E: — , 360R1 360,0 360,0 3R2 3R3 9 = —260m9tan9 10: E = 119029" E = 01.001314?) q 60 260 11: E = pgaa 13: no, yes, yes, (maybe, yes) E0 Electric Potential and Potential Energy 1' U: Qq (— — l 1; = ‘Qq_m— l _ l ' 277607711 3: d ’ 2weoml(m1 + mg) m d 2: 4.84 X 109V, —12.6J, +, 5.58.] 3: 450m/3 Q ) 24/3. (rid/3,0), 7:V=— 1 4..., (W '” W W §=QI(L_— ngyi—3_ I 47,60 (5,52 +yz)3/2 ((3: _ d.)2 +92)3/2 ’ 14 47,60 ($2 + y2)3/2 ((2: _ 03):; + y2)3,12 A0 D + 13/2 4 AOLD 8: V: 1 _ E = —— 44:50 E D —- L/2' D 4350(1)? — L2/4) R3 9: V0,, = i, 14,, = 3363122 — r 2) 10: 2780006— 11: 8992N/c, 5995N/C‘ 3607‘ 660 Conductors, Insulators and Capacitors 1: 1.15 x 10218_ 2: 4": 277j0R2/3 3: B, 4.35 x 10‘5m/s, 22983 4: all increase 6: 4.17 x 10—70 7: (200V, 0.00120, 0.00040), (0.00030, 150V, 50V), (0.00060, 0.00020, 100V) 8: yes 9: underestimate 10: 2MP, (16. 6V, 0 0001330), (16. 6V 0 0000660), (50V, 0.00020), (33. 3V, 0.00020), 2.41113 11: no 12: 411R 0.000133J, 0.,000066J 0.00128J, 0.00032J, 0.0048J, 60V {12536014 Uf: L + ne(d—— L) 13: F = 14: 0 — —— — h 2604 “0’ L + ne(d— L) U, med 3' and C C ange _ _ 60A _ _ Lori? at? 15. 0 _ 72.4 (3,, +332) 16. 0— d (1 23) Direct Current Circuits 1: (501/, 5/1, 1.66/1, 250W, 83.3W), (1.25/1, 12.5V, 37.5V, 15.625W, 46.375W) 2: 13.75W 3: (14.1w, 23.4w, 100W, 60W), (0, 60W, 100W, 60W) 4: A, (B,D), (0,13) 5: RB, RA 6: 551, 0.334, 0.6614, 1A, 0.4/1, 0.44, 12V 7: 19/87A up, 2/29A down, 13/87A down 8211 + I4 = 12 + 13, 61 — Ile —" 11123 + 62 "- 12R4 —' 11R] = 0, 12124 — 62 + 63 — 13R5 = 0, I3R5 ~63 —64+I4R7+I4R5=0, I4 —I3 OI‘ 11—12 9: 43.2V, 19.4V, 17.43V 10: TlIl2 11: 36.6V, 37.4V, RA 3 0.29, 5/1, 50V 12: 5%, 16%, underestimate 13: low, high, 5250, 6159 Magnetism and Magnetic Fields 2: down, ug and to the left, zero, right, outwards 3: outwards, right, inwards, perpen— dicular to F 4: 3 x 106:7:N/0 6: q > 0, m = 45—4,: 7: 1397 orbits, 0.76 orbits, yes 3: t t 34—; 9: 0.0895V, left wingtip 10: left, 2.6m/s 11: 24Nm so it rotates inwards, 9.8rad/s 12: E0, = 1133,21}, F10...“ = —IDylg}, F}... = —0.5I(y% — was, 13.19... = 0.516% — 119:3 13: stable, unstable Biot-Savart and Ampere’s Law 2: [email protected]fi1 yes: yes: _:f:3 _§:: bi: gm 01 [email protected] 3: 110, 110, YES, 2m from I2 @3101 770; 6: 6.67 X 10—7T(—:f:), 1.65 X 10—5T, 6 = 50.20 below —X axis 4: 0 5: B = outwards ~ #01 (4 + 7r) . . 1 new : = —— : 1 : B = 7 B 87rR 1I1wards 8 opposrte, 136A 0 27rR outwards 11: no, yes 12: B: [wgb [email protected], 1. 78 X 10 4T, 4.0 X 10‘5T WDR2 1rp ZWjORz -* MOIPn+1¢ : = B = —-— = _1 13 I n+2’ 27ar+2 ,n —a . —a . . —‘ ‘ (1A 14: |B‘ = ,uojgy, |B| 2 #0300/2, A = 300, no 15: B = #030 y} yes 16: 0.06824, 110 Faraday’s Law and Magnetism in Matter 1: CCW, CCVV, CW, none, CCW 2: 13.80, I10, Q = (@(0) — @(tD/R N2 2 2 6 3- P— — #fit—a 4; 0.0628V 5: right, 4m/s 6: v— — B, 7: yes 8: CW, CW, CCW, CCW 9: 10 turns _. —I —t/'r _. —I R2 —t/T 10: no, yes 11; IE] = w, t = 0, IE] = w 2?“ 2p?" 12: a.) = 203(1— cos 6)/I 13: 'u = 1.09 x lofim/s, 1.85 x 10‘23Am2, ~ 2,13, 0.388T, 29.4T, —2 Inductors and AC Circuits R 1: 1.0053, 0. 433Tm2, —57.9V 2. R1 < R2, L1 < L2 R—1 2 3: LCQ:ZL“1LEQ zzfl. 4313212: E 13:0 11:13 —' 12:0,t=I1() 1— R2 {mt/L), R1 + R2, 1 R1 R1 R1 + R2 6 ’ E _ f RIR‘Z L It: _tR/L,It=-— 1_ tR/L)1Rl: , 3..— 2() Rl+R2tr3 3() R1 8 R1+R2 T R’ 5: 998819, 0.009553 6: 1.89 X 10‘11F < 02 < 8.22 X 10—101U1 7': 1;; = 0.04814, IL = 0.096A, IO = 0.30A, 1;; = 0.055A, IL = —0.080A, Io = 0.25A, Ibaflery = 0.22514 8: 16479, 0.0364A, 0.426md, I(t) = 0.0515 sin(750t — 0.426)(A), VB = 84.9V, VR = 77.3V, VI, = 57.9V, V0 = 22.9V, VB = 6321/, VR 2 73.7V, VL = —17.4V, V0 2 6.9V, PB = 3.11W, PR = 3.62W, PL = ——0.85W, PC = 0.34W 9: (decrease, increase, decrease, decrease), (increase, decrease, increase, increase), (decrease, decrease, decrease, increase) R 1 L 1 : ' : = —-- : — —- 12: 1 0 0153H 11 Aw L,Q R C 0 Electromagnetic Waves 1: CCW, CW (viewed from a point on the +x axis) . _ 2 _ atz _ I 3. q -- 0.5m , E -— 21T60R2’ both B — £ng 5: E(z,t) = 300 sin(105z — 3 x 1013t);9(N/C), 00000628711, S = 238.7 sin2(105z — 3 x 1013t)2(W/m2), —0.0754£(T/m), 9 x 1015fl(N/C/s), 4.33 x 10*17N, 6 = 4.240 below y axis in ya plane 7; |E| 0c; 8: 15.5V/m, 5.16 x 10-32”, 2.12 x 10-11N 9: 7.48 x 103N, 3.53 x 1022N 10: 473m/s 11: 5.26m/s 12: Solenoid axis horizontal and perpendicular to a line drawn from the solenoid to the dipole ...
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