hw2 - 7 f 6 Your name 0-1 l J‘ v i{Unlike/m PHYS 1304...

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Unformatted text preview: 7 f' 6 Your name: 0-1 l J‘ v i» {Unlike/m; PHYS 1304, Homework assignment 2 Due September 15, 2009 Problem 1 A circular ring made of an insulating material is cut in half. One half is given a charge -q uniformly distributed along its arc. The other half is given a charge +q also uniformly distributed along its arc. The two halves are then rejoined with insulation at the junctions J, as shown. Ly If there is no change in the charge distributions, what is the direction of the net electrostatic force on an electron located at the center of the circle? 1. Toward the top of the page @ Toward the bottom of the page 3. To the right 4. To the left 5. Into the page Briefly explain your reasoning. {Igffij I w if {lib l: {p p: Way ,yxflury '1'; I; M (33541,; if? [115/0 ! ‘1! “44:5! éill/ a c m 9 0:43: #7 of [41:70: 0wsz 9 4.1: h». rtozl ("3% (571,? Q. [WW K 811’." 1"“. p?:,fi{.l‘fl{\: ' (J SOW‘ETM‘V‘ ; 7 Cam Skim/9}“?! Sf/W W‘Q'JJ‘I’y DUST/w: ,awirw FT WQQr/AV‘) {05"th 1 ‘ F s' . 4% all“ a; as?" m; +2», comm/V 9%“ HM mm 1:: 5Lw'M-«lpl I” .1 g 1» y A ‘ . ‘ A, My \ ,_ PM,“ 5'; w}; a lick lGrJ rm p CMV:“€£ Mfiflfidy‘h 4' 5' “79 0 inc. VIM/0H,» CW. v o 'i'l’Vfi Hopi-4"", “TEE/‘0‘ Owl Q (i- 9f>chrm5 vii: locrl'i'cm {51"7'2’270 “("767 . r, J ' l w Problem 2 Two uncharged metal balls, X and Y, stand on insulating glass rods. A third ball, carrying a negative charge, is brought near the ball Y as shown in the figure. A conducting wire is then run between X and Y and then removed. Finally the third ball is removed. if i: Air in {it in}; ‘i‘fil‘i'if When all this is finished © ball x is negative and ball Y is positive. 2. ball X is positive and ball Y is negative. 3. balls X and Y are both positive, but ball X carries more charge than ball Y. 4. balls X and Y are both negative. 5. balls X and Y are still uncharged. 6. ball X is neutral and ball Y is positive. 7. ball X is neutral and ball Y is negative. 8. ball X is positive and ball Y is neutral. 9. ball X is negative and ball Y is neutral. 10. balls X and Y are both positive, but ball Y carries more charge than ball X. Briefly explain your reasoning. if ! x . , ‘ . . l‘ . ‘ \ l ,v - ’ a '_ «’50 ,icq-n-i x gr? " 3" “i '. r . "I; law’le Dal ‘ M42 “L ‘\ lap-M 6" ‘~ (“ V’Jlig i X elim- V in X, Y Po; iii: / my! if H a mi» N , _ ‘ \ _/_. :if c u, , v _, > Mr] L . g 3“ Problem 3 Two identical conducting spheres, A and B, carry equal charge. They are stationary and separated by a distance much larger than their diameters. A third identical conducting sphere, C, is uncharged. Sphere C is first touched to A, then to B, and finally removed (to a far away distance). As a result the electrostatic force Ff between A and 13, which was originally Fi, becomes Ff=(1/2)Fi Ff=(1/4)F-. . @Ff=(3/8)Fi 7. Fi 8. Ff=Fi 9. Ff=OFi wewve Explain how. you arrived to your conclusion. I > The! “(:19 “ET: {*«flafl'iii‘: VF. i * ‘h’kl o QAL/QAA{L{ ("6"! ( C“ "~,~ 7* ,g“; . k ‘1 ’ > ,,- I ‘ . t5 OL‘S‘Kflbijb‘k/éff” “a?” “a u . .: “H.ch 3515.62! rM" c r; ! / / ,r s ’7 £ ,‘ x , f I v i ‘ L\ * L, it: H {m f .3 ~; I ,7; ra; f A; :4.- ‘ f to _ I u , 9‘3 “5" “fl; “w ("OJ {‘3‘ ‘ A if * fix 1' ‘(M x L»! N f #1! n ,I i. s», t \ (1. I.“ I! .1 l . « u t x ~ ~.l i ‘ . I .i :24? .4] *5... r )k i l L g v . I, C n ’w‘ . a». , If” i w I ~ " ' 'i ' 5; Ct mm 4 a Problem 4 r ‘ A ’L¥”'\\“‘<) {Mimi (,t'iiaiige-‘s of 3 ('3 2m" lut‘ékflffli in the .1:y~»p§2uu:n one at ll {11. 33:3 111‘} and the oti‘ic’w 311‘. {Si} m. {,l m). Fémi the Liiaguéiinclo of the <i>i<=u“l‘;fi<' livid at: tile might (£110 to thaw» two Villli‘fgfltri. Alls'\\7<*’l‘ in {Hilts of f0. Finrl the single l")("‘1"W{;"("'I1 HM" \W‘lzcn“ for The clmttric livid at the origin “mi a \“t‘tf‘fui‘ in tile .T'J minus .1thlifriiction. ..~"\.111;~sw<\r in units of 1. Sketch and clearly label the coordinate system, positions of charges, point where the electric field is measured, the vector of the electric field, the vector V in the minus X-direction and the angle in the last part of the problem. If it makes sense to assume .__/ that V is a unit vector, do so. 3‘ “a V (I. ’ e r 2. What are the components of the electric field? What is its magnitude? Answer in terms of equations before plugging in the numbers ' : \ i, ' C? .‘ r 7:2! 1 l; i‘ {A “’8: . 4' in; L",l~ amn/ u, 3. What are ’the components of the vector in the minus x direction? Given the components of the electric field and vector V, what is the angle between them? Write down an equation and solve for the angle numerically Problem 5 Given :: sqimi‘t‘ with side a. Citzuigos 21.1? A B _ piavoci Hi" E1511}? («jititot‘s oi" at. Miniuw oi <".§.12u'1;:<:> Q I - (9:1 —ql (:28 :'.:::::‘. .::'.'.::': “R'hi QB :.::.:: —q. ~, ; i \L Eros;)vvl'é‘vvév {:st {ignite}. : - ‘ T' h i' ' i rote: "the Enin-=*i§1:1:;; is ('inc'riuvistzn " ' ‘ ‘ : I) ( ‘ Determine the direction and magnitude of the electric field 59 at center 0. Determine the magnitude of the electric field EC at C due to the charges AB and D. Determine tang, where 9 as the angle between the horizontal line and the electric field at C due to the three charges at AB and D. 1. Which principle is used to compute the total force of several forces? 1 )M set»! M r =? a r l ,r :‘ 2. Sketch the coordinate system in the figure and start with the electric field at 0. Write down x and y components of electric fields created at O by A, B, C, and D. From this, find the x and y components of the total electric field at 0; then the magnitude of O; sketch the direction of the electric field at O in the figure 3. Repeat the'sameproce/dure/for C: write down x. and y components. of electric fields created by A, B, and D; find the x and y components of the“ total electric field at C; then the magnitude of C;_then tanfe’. n \/ ~= - . ,\ l 7: ,‘\ A 7, v v > 5’ c A L V NProblemG Eight Paint. Charges 3331,13. t”;1l<'11111.‘-‘~. luuuvriz , 2» 1 lililb ill?) 3., it” Hf “jg-111x 1’}i'vilil 471:12113ggfie. mph ml" 111:1;411i— Hlulu 22 fl Ill—3' (:1. is luwe‘itrid I51] lllv M IJ‘.11I'I“~s Hal «‘1 Mllw with sides: ml leauglir :3 in :15: slim-.311 in ill" 11211112 Final tho? 1*—<%u,.>1111‘1u111mm: ml iiw 1‘; drink: gm! T- Wu- t’fxr-l‘lmpl H11 the“ tx‘he'trga‘= liléi‘fil’i‘i'l nit painlfi A luv?" l'lli" Milli-.1" c’lml’m‘ls, AIIIBR‘LFT 111 11111th i if N: 1. Before proceeding to the calculation, enumerate charges in the figure, with 8 corresponding to the charge at point A. For each of charges with i=1...7, visualize (or sketch) the vector of the force Figs exerted by this charge on charge 8. Which of these forces have non-zero x components? Flag 3 Flag 9 flag} flag 2. Add all non-zero x-components of the electric force analytically [33 . F gi:%0:l<fz:.; F :K :13— r lagx 1 tax ‘ ((5 f2 2 ; Hg): W562 5 E: k}: “0+2. 3. Evaluate the resulting x—component numerically P5115»? Jli',!*2z:.:i"1f$ We Hi 7 ir—Qflxios N Problem 7 Hanging {:Tl'lrirgcs 33MB. ralzrlllllr‘». 11111111."!in(7. L22» ‘1. mini, (I34 Given: 9 : ELIE lllflf‘égi 'UEV‘BCIJ' iélt‘llii-ull 8111122111 i”ij£l,]."v_~‘,l“¢i1 filrhwl'ifira 11.31134, in equilibrium with eqlial masses an“ alumni. in l 11*» ilgflll‘u Til“ lung 11 ("if 131“ Mil l‘iIl‘Uth 31]?” ilii‘llgll and the single ifaiwmi in {he [immuij with 1114* W?“ 1! :11 1%.»; iilmrl lull. fiiWifif‘fiifififififi {a )_ ’4’" fi w; ,0 Q“ {3; (i «p {Z} l mu 1mg!" Find the 11142.1;1111‘11ilw Hf the r‘llairgv iféll mwli spha-re-i Aim“ ‘11:“ 111 units of," (1‘, 4. Draw a sketch showing the forces exerted on each sphere. Describe the type of each force in words ;T’ T; {mac Morris's? F“- ;F,‘ ‘ - >> \‘- 761 = gram“; Iv: we, ~ )3 I ’ fl +9 8 Fee x eUC‘t’A/(‘C ’{WQ (fermty *; i6 5. Which physics laws will be needed to solve this problem? What does "equilibrium" mean as far as the sum of forces on each sphere is concerned? Write down equations describing equilibrium, separately considering the sum of forces in the vertical and horizontal directions Néuffoh’fi was] low Coulomb: E “Equal/Ciph‘um” WXQMS 'H/LQ gum: fry/“(.125 cm ecu/l4 Sfmei‘fl 204/0 :5 :“ T9100 *— Fe 740 1..., “1-— Zzi‘y {£55.le :- 6. Solve the equilibrium equations for the magnitude of the charge in an analytical form 2 x Tm i ‘ $lZI=1aS§n9 Ti??? YE: 3. a SIMS 7. What can you say about the sign of the charge? I . . , . (Ne (Cw. not {ml (Wrif «the. 338 Y1 of HA2 (MM 99.. “UMLM {'0 M I, , J J _ My.” waiim PM: 4-11" cl» omLté we Cam Vhakg 3M6 "3 this lime, We Saw», a3 7 9M} V'WFQL each 8. Find the value of the charge numerically. Does it make sense? Problem 8 A rod 14 (“111 30115;; is uniformly <~11z‘11‘5:;m1 and has e-i i‘nl’ztl charge of —2‘3 ,u-CT. Dmit‘l‘lliilw flit". Liietgiiiéiiulv ul’ tin." electric field 211031;: the axis uf the rmi an“. a point :jij cm from the, {‘(‘iiful‘ of fhtf‘ rm}. AEJH’WVI‘ ill units 0f N/(Lfl. 1. Sketch the coordinate system, the rod, and the point where the electric field is measured. Also show any distances that may be necessary. How many spatial dimensions does the problem effectively have? ,A _ V ‘ _ _,,_,.,/\m.,W O ‘ ' > X" I «3.256% 2. According to the problem, charge is distributed continuously on the rod. Write down an equation to compute the electric field E(r) for a continuous charge distribution. Simplify this equation by writing it only for the relevant coordinate component(s). How do we compute dq in this equation? 3” .. “A,Qi ‘ 7/152, {gig/iém/ grow"? 6/ i m 1'3 ’1 j, J ~~ A f v tiri}: Iii 11-41;?) r r whérfi {)(Tl‘) i€ pila’7c L... {17.5 A, JimchICIEM§ ,i xvii“; 222' , «we: we . {2-0 [/‘il’lear‘ O/Léifyif Wit”??? / . AdX 3. Evaluate the resulting integral(s) for E(r) analytically. Write the final equations, and evaluate them using the explicit numerical values given in the problem. 9‘ i ‘L‘fLL a K “s W10 g in rrrrr ‘9’ fix-£0.23?) ...
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This note was uploaded on 04/05/2010 for the course PHYS 1304 taught by Professor Staff during the Fall '08 term at Southern Methodist.

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hw2 - 7 f 6 Your name 0-1 l J‘ v i{Unlike/m PHYS 1304...

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