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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 diskshaped 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 " rswrce. .—. (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. Raulw» a; char“, = (Rxla 0C [$414k oi I '
&: ’5 :5 A62: ’CE‘JX (c 10pts) Derive an expression for (ii, the electric ﬁeld of the disk at the observation location w. Note that
dE depends on If], the distance from the observation location 111 to the disk; however, you may assume
that l?! is small compared to the disk’s radius R. (Hint: the following expression copied directly from the formula sheet may prove to be useful: [Ediskl w %é0é[1 — 7%) accuse 44M cqlc’ndtr can be «001616;! 45 a 511‘ ml 74619
Shekel olf'fk /W¢ will (4;: /£;(,~,k/ 14 d5, ME/ r: ﬂé—AD' g/zj 2 % NAIVNAS We a“:~/nnc¢, ' h «Hm abservwh‘ovx (“”745“) A
45 = zaLmez Problem 2 (20 Points) In a recent lab, you wrote a VPython code to compute the electric ﬁeld of a uniformly charged rod by
using a set of identical point charges distributed on a line. The VPython script shown here is very similar
to the one you wrote; however, the script given here is incomplete. Answer the series of questions given
beknv. from _future__ import division from visual import * # constants (in SI units)
oofpez = 9e9 L = 8 Q = —5e10 N = 7 scalefactor = 0.2
dz = L/N (N = Q/N R = .5 # list of charges
list_of_charges = [J
z = L/2 + dz/2 while 2 < L/2:
list_of_charges.append(sphere(pos=(0,0,2), radius=.1, color=color.green))
z = z+dz
print len(list_of_charges) ## print number of items in list # list of arrows; tail of each arrow is at an observation location
dzz = ((10/8)*L)/1O list_of_arrows = [l for z in arange(5*L/8, 5*L/8+.001, dzz): for theta in arange(0,2*pi, pi/4):
list_of_arrows.append(arrow(pos=(R*cos(theta), R*sin(theta),z),axis=(0,1,0)))
dzz = ((10/8)*L)/10 ## calculation of field: for thisarrow in (list_of_arrows): ## take arrows one at a time
rate(10)
Enet = vector(0,0,0) for charge in (list_of_charges): ## (a 8pts) Add the statements needed to calculate dB, the field due to
the piece of rod (located at charge.pos), at the observation location
(located at thisarrow.pos) r: 4h€54rmw.gos —clmg$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 = Eyegt +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) {31W0 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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 Spring '10
 SHATZ

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