Q3 - 3804 Fun A 1 Two infinite conducting planes are...

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Unformatted text preview: 3804 Fun A 1. Two infinite, conducting planes are parallel, at a separation distance d and carry the respective uniform surface charge density +0 and - 0.. Suppose the _ positively charged plate is "grounded" (V = 0.). 3 (a) Draw in the equipotentials and the electric field. 3' (b) Calculate the potential of the negatively charged plate. (2(c) What is the potential Vo of the equipotential surface at a distance x (<d) away from the positive plate? \1=O t/Vw l t l a) Wk; WW _0_ retreat: mm E l ' v I L')I\'\¢ljwflg E: 0, To 7MB 5J wcogvttct 03c "Lt/JO MAC/MLAVLLB P, ‘LL; “£1,ch ‘, 7- 'Q:_Q:fi __ D E‘aeax+%:\i(() WU (M50, “Mugabe; otm7 N07. -r A t) Av=V;—V;: flan mlwwvfi (OVA—5 'F'o’“ +14, (“vfliww'fll J‘C ‘l‘i‘le Aéjn'iw‘t Pick; ‘\n 5\ EL‘w pwwrlie 'Lo VLLL X— owns go (>me 692:: OQXX ,E:E)2 ;—:-.;£ @(Q5OOUWQQ'LOVK> ‘ t'SAi' +0\)F,1o.i*"0‘J So \I,‘=0 MWWW+V;. I 0? J 90 AVA/WV"; Vf‘0;\/7° : if Eélxa'g A» 0 - ,‘d \lp: fijMwB , €00) C3 V0 Ai’ on? oa‘l'i‘wte X<J l5 "EN“J L7 SULg'ith‘iflD X lgfiol M Ho. VW” [Mlle ,j— Ho, «fiscal. -m <9 -6. Seem B 1. A small sphere of radius r is placed at the center of a larger sphere of radius R. The spheres carry charges q and Q respectively, spread uniformly on their surfaces. ' 3 (a) Draw in the equipotentials and the electric field. § (b) Calculate their potential difference. a (c) Suppose you connect the two spheres with a thin wire. What will happen? a * ; (RH/(r) :j: _ 01/ :44 in (AV V Lfri‘éofi Lin—69" ems (R r) qu7 la 14nd, i +l‘5 ““5 WV) g‘L‘Ce, V’CW’J’JsLQ wlvfe/ V:O fowl Q @ . Av: ~figM 09;: = (LU-Q GD K , _ _~K -i -4) : eff—fig»: afiWW/mii r ADQ‘M) i '1 01(07- C) Him/‘HVJ‘ of 40+ +L6 31%,”; W WJVc-L‘MJ w MSJH—qJ-NS) J'Lo/ ahargg/ Ni“ rec’bli‘n‘mfifl [VJ—59L}: OV‘V J‘LL M Splints) IMAM.) @ 0\ .a,’ M )9an CFA-Vuf So rflp'qw (p 1/7 7/; {A P'“+ L) 0M7 you w W/ MULLLQZ j 2. Given two points P, = (0, 0) and 132 = (2, 2), calculate the line integral of the electric field given by E = K (yi + x3) S- (a) along the paths joining the two points along the y axis from P, to (O, 2) and then from (0, 2) to P2 parallel to the x axis. S (b) along the straight line joining the two points. 7 .Pa Q E>K(v7+Xf> “(03* almjlwa)X\/wmfivm 04°; 0-17.19 E. M.=k<fl+03>°dv3 , 300’ Eana:K(Q/”+Xj>'oix7 : RX (9 a 2 fgoiz: o rfawx: aha—o): O Seam/l «its 3. A circular plastic rod of radius R has a positive charge +Q uniformly distributed along nne-qunner of its circumference and a negative charge of ~6Q uniformly distributed l 0 along the rest of the circumference (see figure below). With V: 0 at infinity; what is the electric potential at the center Cof the circle? 3 gulp, A “l. (owl C _________ P'( 566““ B, ai‘ foM+P . - I (See (/0me 39-37> -6Q ”Wu/e Ltave M Oe'S'}rtL/itufuj we, WM 49H claw”; + Q) J’LLOVHQ/ ml‘la “kill LLLML ——6Q S0 V; ._._L. 6Q +(—6Q>§ ; qweofl ‘irraofl, ...
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