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prac exam 4 - is ’1" ‘ An infinitely long line...

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Unformatted text preview: is ’1", ‘ An infinitely long line charge of uniform linear charge density. +1.. is placed along the axis of an infinitely long solid conducting cylindrical shell with an inside radius of R, and an outside radius of R,_ The cylindrical shell has a charge per unit length of -51. Find the magnitude of the electric field and its direction. for each of the following regions (where r is the perpendicular distance from the line charge): a) 0<r<R. b) Rl<r<Rb c) Rb<r d) What is the charge per unit length on the inside surface of the cylindrical shell? e) What is the charge per unit length on the outside surface of the, cylindrical shell? 45 Fit? = gill"? S W57 W- C)’)~ S'vr'faeg @ 9+ was Av. E f(2rrrl.)— 32:31,)" Lia/g?” A? Y‘: )9 Y‘ai‘tafiy UTHIGVJ @lo\ Twyla cauclvo‘iar ac?//' 5:0 \ C.» éE-JA = i q%a L.-_ ____'__M/‘_,.. 5 501% ‘ 12:325— /" a, __ 76°C} ,1 arr. is mltally ihwré I (b; I! O ’ / E 2151-9 7‘ .- 7. , - a.._.——----- 69- §thce £=0 Aw R44?“ R» ,he‘i' Gift}? . )k side C7) 0+ yacht/9 Y‘ =0 ', \ @ - go a“ {made SVY'Ptfié. LUNG. ”A I, a) Cay—mama a. 3/th c @ 56 MOST hmVé if pqx 014, 00*Stéfl. S’Vl‘ycac‘q O ------ ..... GENERAL PHYSICS 11 ~ PRACTICE EXAM I SPRING QUARTER 2000 ' SOLUTIONS J (/5 m3 ;s _ z A mass of 120 g moves up and down on a spring with force constant of 3.0 N/m. At time t= 0 its displacement IS 3!: —+ l 0 cm above equilibrium (y: 0) and it is moving upwards at a speed of 5.0 cm/s. a) What is the angular frequency of the motion? i . b) Find the maximum speed of the motion. ! ._ - c) What is the amplitude of the motion? Write an expression for the displacement y at time _t_. _‘ _ _ . d) > ABW:W=W{%V {/59 rM/s f1,” . (ta ‘- 7. . 2. “m“ “ 91‘ Ar X “‘33.; D L) EziM/V; " ”5"“ ELY; ’ ‘pf‘éf'is ( a- [91+ 6m“: ”31+ we / _ .LJMELW “57%) +— (6/5) (Mn) .. ?o7an/, 1': :tHfl, (@55 “A ,.~ -Arm 1.2.1 )3]; ’5‘th 'vf’ 5.0/5 ”6;" - A ‘FV‘O'N ”3),. A charge of Q = +104 C is unifomtly distributed around a circular ring of radius R = 30 cm. The ring is in the yz plane with its center at the origin. The axis of the ring is the x-axis. a) What is the linear charge density, 1, of the circular ring? b) Find the magnitude and direction of the electric field vector. E, along the axis of the ring at the point x: 40 cm. c) What point charge 9 could be placed at the center of the ring, it: 0, to make the electric field zero at x: 40 cm?. _,_ ,. at) %=Q/= ’06 =53x20c ZKK jar/ask} 5> Ex i g): amen) ;, ding"- 6K ME 36 439/ 2 or 4, /\ d3: 65- 0594:— dE (Y) ‘ W5 dE: “'3’ ' 0’1” )tha Where 9 is aye Moon} my mor‘) 1"“ ARX a5: AU 39: AKx A9:- 231'...— S as“ Xi”,- wear’ Wear 9mm" 4 f7 , A )sfi __ oQi—'—— 4, r. ' E1!" 5% fizws areal” ”7-. .gL—efl- mfg; l°c)(0~‘lh\’~:_ (0.11.“ +0 3h) C> waif—E Egflw’q ‘13 La :u -? (’Rr,)'$9 a l} “941.,‘Ve _ “’9‘” ij~ 4—, :1 E1593}; arm " a) A charge of Q is fixed at each of two opposite comers of a square. across a body diagonal. A charge q is placed at each of the other two comers. If thénet electrostatic force on each Q is zero, what is Q in terms of q? (97 to, E1: be m i”? (9 C6; haule Ofraije $2” a, 62 . '77.“) ‘3’ Es] 4“an .30 @ ”BB/{sway =.:_él£L—-——: ' L/flfo(2a) Mac); r :4- » . 2% 7; 55/?- W433 b) A cenain charge Q is divided into two parts, q and ( Q — q ), which are held at a fixed distance D apart. What must q be in terms of Q so the electrostatic force of repulsion betweenqand(Q—q) ismaximized? D Q73 _ E = 3(Q‘i2 @ %, , (Q’Q ...
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