2212_Test2_Key - Problem 1(30 Points A solid'circular glass...

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Unformatted text preview: Problem 1 (30 Points) A solid'circular glass cylinder has a radius R and length L. The axis of the cylinder lies along the :1: axis, with the left end at the origin (see figure). A net positive charge +Q is distributed uniformly throughout the cylinder’s volume. Calculate the net electric field E at observation location 11) by answering the following sequence of questions: (a 5pts) Consider a disk-shaped slice of the cylinder of thickness dx that is a distance :10 from the left end of the cylinder. Find the position vector F that points from center of this slice to the observation location w. a —>; a r: r055 " rswrc-e. .—. (wjoltb -— 090,0) .3 r: (wagop) (15te [alert it: 0,0,0» (b 5pts) Determine the expression for the charge, dQ, in terms of the disk thickness dx and relevant known variables. Raul-w» a; char“, = (Rx-la 0C [$414k oi I ' &: ’5 :5 A62: ’CE‘JX (c 10pts) Derive an expression for (ii, the electric field of the disk at the observation location w. Note that dE depends on If], the distance from the observation location 111 to the disk; however, you may assume that l?! is small compared to the disk’s radius R. (Hint: the following expression copied directly from the formula sheet may prove to be useful: [Ediskl w %é0é[1 — 7%) accuse 44M cqlc’ndtr can be «001616;! 45 a 511‘ ml 74619 Shekel olf'fk /W¢ will (4;: /£;(,~,k/ 14 d5, ME/ r: flé—AD' g/zj 2 % NAIVNAS We a“:~/nnc-¢, ' h «Hm abservwh‘ovx (“”745“) A 45 = zaLmez Problem 2 (20 Points) In a recent lab, you wrote a VPython code to compute the electric field of a uniformly charged rod by using a set of identical point charges distributed on a line. The VPython script shown here is very similar to the one you wrote; however, the script given here is incomplete. Answer the series of questions given beknv. from _future__ import division from visual import * # constants (in SI units) oofpez = 9e9 L = 8 Q = —5e-10 N = 7 scalefactor = 0.2 dz = L/N (N = Q/N R = .5 # list of charges list_of_charges = [J z = -L/2 + dz/2 while 2 < L/2: list_of_charges.append(sphere(pos=(0,0,2), radius=.1, color=color.green)) z = z+dz print len(list_of_charges) ## print number of items in list # list of arrows; tail of each arrow is at an observation location dzz = ((10/8)*L)/1O list_of_arrows = [l for z in arange(-5*L/8, 5*L/8+.001, dzz): for theta in arange(0,2*pi, pi/4): list_of_arrows.append(arrow(pos=(R*cos(theta), R*sin(theta),z),axis=(0,1,0))) dzz = ((10/8)*L)/10 ## calculation of field: for thisarrow in (list_of_arrows): ## take arrows one at a time rate(10) Enet = vector(0,0,0) for charge in (list_of_charges): ## (a 8pts) Add the statements needed to calculate dB, the field due to the piece of rod (located at charge.pos), at the observation location (located at thisarrow.pos) r: 4h€54rmw.gos —-clmg$e;gos wku’r : V‘Zmugor) 4E = 00ng *461 Z wrath) ‘HQ * rlm’r ## (b 6pts) Add the statements needed to calculate the net field at the same observation location. fut = Eye-gt +olE. thisarrow.axis = Enet*scalefactor thisarrow.color = color.magenta (c 3pts) In the code given above, what is the sign and magnitude of charge on each piece of rod? (Your answer should be a number with appropriate units.) a 0 C AQ ., 310’”) 0 : 4.! (d 3pts) What is the position vector for the end piece of the rod that lies on the negative 2 axis? (Your answer should be a vector whose components have numerical values in the appropriate units.) (0,0,‘9- +—— 52%).“ =<o,o, 34>”. 3. Problem 3 (25 Points) A very long, thin glass rod of length 2R carries a uniformly distributed charge +q. A very large plastic disk of radius R, carrying a uniformly distributed charge ——Q, is located a distance d from the rod, Where d << R. (a 5pts) Without a calculation, deter— mine the sign of the potential difference V0 —— VA. Justify your answer. Emir Poin‘i’s +° ‘HM .3; MM and so 4m 0” (b 20pts) Calculate the potential difference VC — VA. Location A is located a distance 111 from the center of the rod. Location C is located at the disk’s center a distance d from the rod. If you make any approximations, state What they are. 62/4 2 Q/L J... A<<K 50 Ml Edt'skg: E: 4 gm!“ r 47?» 0 VIVA/ff 3 " (glazed? ’ %[ d! If» Ecli'dsk Problem 4 (25 Points) At a particular instant, a proton at location (—2 X 10—9, —3 x 10—9,0) m moves with ve— locity 17,, = (0,—5 >< 106,0) m/s , and an alpha particle (a helium nucleus, containing two protons and two neutrons) at location (2 x 10—9, 3 X 10 9 0) m moves with velocity =(0, 5 x 1060 0) m/sq #3110sz x Y‘ 14o 3v xr B: "HT 1:: "If (MS (a llpts) Calculate the magnetic field Bp due to the proton at the origin -9 > M 7;” (/10’7 TM) 0 a Io "a; (a, .5 lo“, ow: x<2 w m ,o I C ‘ v. ;—.________—____L————————;———"—/"_——L——_~ " ' A ((mm + (m LP) L -3 : (a 0 0.003471“ = 3.4.10 “IO/'57” ’ I (b 11pts) Calculate the magnetic field [3; due to the alpha particle at the origin. -4 - E 307047314) {31-W0 QC) (olfwo’flo) m/5x(~2.lo ,440 ,a)‘ at (I 2 (O at) 2* (3'10- ”01)”: ’3 * (0,0, v0.006%>7:t6‘3'(0 <0, 0,4)! (c 3pts) Calculate the net magnetic field End at the origin. a '3 ... ‘31? t '3; +3“ :— 3.ch <0,0,">' ...
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