106-20082-MT1 - PROBLEM (1) (25 points) A cube with side...

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Unformatted text preview: PROBLEM (1) (25 points) A cube with side length L is placed with one corner at the Szaop) 56 (back) origin as shown. The electric field is not uniform, but is given by 2': Ax?+b§'+2€zi, where A ,B and C are positive 53 (rightface) constants. (a) (15 pts) Find the electric flux through each of the six cube y faces, i.e. €251, £152, (153, CD4, 475, and C06. 3 : «63+ lei} Ma} 'r 0* AL *0 : (QC-teal} : Que/en (c) (5 pts) Find the electric potential difference Vat, = Va — Vb between point a with coordinates (0, 0, O) and point b with coordinates (L, L, 0). 1; -5 EM? : [gtxax + [(9 e137 1: ‘0”.41 L L :+£E :fAXAx+fBAj 0 O ‘73 a fig} QL Phys 106 First Midterm Examination Page 3 Saturday, April 04, 2009 PROBLEM (2) (25 points) An insulating sphere of radius R has nonuniform volume charge density p = Ar2, where A is a positive constant and r is measured from the center. The sphere has total charge Q. Take V = 0 at infinity. (a) (5 pts) Find A in terms of Q and R. (b) (10 pts) An electron with mass m and charge —e is released from rest at r = 2R. Find its speed at the instant it reaches the surface of the sphere. Ignore gravitational forces. 5. Mi Nisan at, What (mime, r we“ M Wm 932mm ., u: («Wm #515ng river L a ’J L Q _ EA’W/ : Q/eo “a t I Lfll’é’o-F; Kfi‘ ‘ \l ‘9 \ v7 + (-€)\l(£) - '7' "M r .a ) H ‘ . V(r)- \ltm) : - f Er.” = +f E’Aqy ; 9%(Vlm" vain) ' «wow °° co / fl {Q .. B, Jr ._ 23 \,i '5 If: , M60 7: 3 _ V“. 21%) (z a?) Arreofim ( (c)(10pts)Findtheelectricpotentialatr=R/2. E, Mi. (“sac ai’ «awe 443%“ \/(r)’ vew i “(3’ fi> gr s 343)., 62:; ’ ( EV“ (‘5 ’0 r. q 1‘ gm» _,_\é ff Am‘ur’ ;L 9; _r ELL .31— o o r ' area a we» r5 it A Phys 106 First Midterm Examination Page 4 Saturday, April 04, 2009 PROBLEM (3) (25 points) Positive electric charge Q is distributed uniformly (l = constant) along a thin rod of length 2L. Take the X Q . l<—'L +14 _>| P |<——x—-——>l 7? : 4H, I ‘L“ AAXV VA 34v, i xvi potential to be zero at infinity. (a) (10 pts) Find the electric potential at point P. 9r: 9,. F:X—7/( 1L (c) (10 pts) Find the electric field at P from Coulomb’s law. A kl JQ \ 33% a“ 60 (L ._,x) J, 4' L an’ A ‘ A'L/ Lia-ea LXbX vL/ :3. (L. A.) AVG/o X*L_ X-tu Phys 106 First Midterm Examination Page 5 Saturday, April 04, 2009 PROBLEM (4) (25 points) Two identical parallel—plate capacitors (with the same plate area and separation) having capacitances C = 2 nF are connected as shown. A Q1 Q2 material with dielectric constant K = 3 is inserted between the plates of the capacitor on the right. The capacitors are charged until the charge of the capacitor on the left reaches Q1 = i6 nC. The charging battery is then disconnected from the capacitors. (a) (5 pts) Find the charge Q2 on the capacitor with the dielectric. ................................................................... .. Cat?oxc(‘liars \nqve SQW‘Z Folefih‘m‘ .5 QL5KQ‘ cliquemé . x euc V— 9; —, 9L, " 2’ ' C‘ C7, @1:4KWC _ @i ’ (97, C ' Kc (b) (5 pts) tEl and E2 be the electric-field magnitudes in the capacitors, respectively. Find the ratio E2/E1. ................ .. Le i? oi : Sequ H‘M bei'wem Via-‘63 (c) (10 pts) Find t e work required to pull the dielectric halfway out of the capacitor. ........................................................... .. (We, chat/SC C : cf 0/; + KC/Z QMzQJcCQz :2 (HS! :Z’M '-‘\ 6 I: does moi Cl/QMSC (iwfi‘na We : Q. -+ 4 + 3 :1 ‘4 [bfoccss ‘ Thi‘eQ Q/“efgj 7. aim: 1A-, (19+; : Q‘ix‘fic') [2,6th C31 3 Q42: CJYKC ‘ L" 2x 3nc5'0' 21+Z'218nF :géido—fi’j 3376“: Afler ac (a KL/Z ¥inai pow 0:“ We, («faci‘i’bfs Q: 91 QM 2n n C .} [1 V _, ___.__.-:, C cf; 6 M: 7) «2";gmmiavl (Q: : ng Phys 106 First Midterm Examination Page 6 Saturday, April 04, 2009 ...
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This note was uploaded on 04/09/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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106-20082-MT1 - PROBLEM (1) (25 points) A cube with side...

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