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Unformatted text preview: Name:
StudentID: Section Number: PhysicsifiB Spring 2008 Lecture 2
Midterm 2 Version B I Please write your name on every sheet of the exam. 4 Closed boolr, one 335 index card in your own writing is allowed. Non pro~
grammable calculators are allowed. c If a problem is ambiguous, notify the instructor. Clarifications will be written
on the blackboard. Clieck the board occasionally. a Time for exam: 50 minutes
c There are three questions, check that your exam has all 6 sheets. a When applicable draw diagrams and show your work. Partial credit will be
given for signiﬁcant progress towards the solution. Partial credit will not be
given for random1 unitless numbers left for the TA to decipher and interpret.  The permittivity ofii‘ree space is given by £0 = 8.854 X 10—]2 Cg/(N 4112).
You might also ﬁnd it = 1/(élrr50) = 8.988 X 109 N  rug/C2 l'ielpful.  The problems as well as their a)—d)/e) parts are ordered in increasing difficulty.
You might ﬁnd it advantageous to work your way into each problem and attack
the {ll—e) parts at a lai‘ier stage. Remember that partial credit will be given for
the right idea or reasoning.  If you cannot ﬁgure out part or b) the result of which you need in a later
part. you are provided Ean alternate value (’if you cannot ﬁgure out, assume State clearly if you decide to take the alternate value to be able to receive full
credit for that later part. 0 Stop your work when the time is up  an announcement will be made. If yOu
continue your workafter the announcement is made 5 points will be
taken off the exam immediately. Good Luck !! Please do not write in this box [—Problem Points 1'. Problem 1: Multiple Choice 3) (lpt) Check that you have written your name, student ID number and section
number on the ﬁrst page of the exam. Please write your name on every sheet
of the exam. b) Consider a region of uniform ﬁeld as shown below Points 13, C, D, and E
are all a distance d away from from point A. Between point A and which point
is the largest potential difference? (a) (VB — VA) largest
(VD — m largest
(c) [V5 — VA) largest
(d) they are all the same
(e) {VC — VA) largest
c} A battery of voltage V is attached across a cylindrical wire resistor of length
L and cross~sectional area A, a current I ﬂows. If I double the area of the resistor (but attach it to the same battery), what happens to the drift velocity
of electrons (vd ) in the new resistor? (a) W decreases. (T)? Jd stays the same. (e) not enough information to answer. (cl) the magnitude of ed is unchanged but the direction is reversed. (e) ed increases. M Va A V: ll 3
,3. <
3—
3? cl) (ilpts) Three capacitors of the same capacitance are arranged in the following
configurations, If the same voltage is applied to all of them, rank the stored
charge of the conﬁgurations. %AHW iii} a m (ﬂlQ1>Q2>Qa>Qa
“3) Q3 > Q2 > Q1 i> Q4
(‘3) Q2 > Q3 = (94 > (21
(‘1) Q] = Q2 = Q3 = Q1
(‘3‘) Q2 > Q‘I > (23 > Q1 @Q2>Q3>Q:I>QI 0:.9 CF C+ 42: %c 3
CL: u
‘l
O Q=CAV Somaﬁ C e) (dpts) The following graph gives the charge density of a spherically symmetric
charge distribution as the function of the radius a". P R1 R2 1' Which of the following plots best represents the electric ﬁeld of the shell as
a function of radius? E“) (1) Eu) (2) EU) (4] I Em (5) (a) case 5 t (b) We 4 Wis! ELK 00 c lmarwk
(c) case 3 I (d) case 2 . (e case 1 — additional space for Calculation (Please clearly mark which problem you are
working on)  :2 LO Problem 2: A charge Q; = +5.00 X 10"'3 C is located at $1 = 0, y: = 50.0 cm
a charge Q2 : +5.00 X 10—” C is located at :52 = 0,192 = —50.0 an. Neglect
any gravitatimial force in this problem. a) (Supt) Calculate the m agnitudc and direction of the force the ﬁxed two charges
excert on a test charge Q0 : —3.00 x 10—6 0 and mass mo 2 3.00 x 10—3339
which is located at ya = (J and :30 = 1' (Le. ﬁnd the expression for arbitrary 3;). @1620
r41 __ A
"4‘: F' ID Frat Wig H1 X Cla‘la'liom l {(0 Q0 (afl (XZ—r qul 2
hm; : {please tum. over) cox b) (5pt) Calculate the work required to move the test charge Q0 from inﬁnity
to yu = 0,550 = 200 cm PomiikU—Q
V" Mi 6114'621 "r c) (6pt) The test charge is released from rest at ya = 0,529 : 200 cm. Find
an argument that the test charge will cross the yum(is at y = 0. What is the
velocity of the test charge when it creSses the yaxis ? iHaQaciT/b, Vuf y mmc_litu i3 Mo :‘AWL 'qu I
’1’“ 1, 9;.) m ﬂtuﬂucukm 1147' @‘ﬁmz is 22m rtr“ Y yer:— 0
ALL ~+ AK 1' 0 Problem 3: Electrostatic cylinders A long cylindrical shell of negligible distance is a radius a" = 5.00cm away
from the x—axis (see Figure (a) It carries a uniform surface charge density
J = —10.0 pie/1112. The permittivity of free space is given by so = 8.854 x
10‘12 CQ/(N ‘ m2). You might also ﬁnd It =1/(47r60}= 8.988 X 109 N  1112/02
helpful. Note: You can treat the cylinder as effectively inﬁnitely long L >> T" and
L >> R. To receive full credit you have to derive the electric ﬁeld using Gauss
law, integration over a charge distribution or any other method you think works.
Simply quoting the results is not enou h. _
' g ' lLl—cim .— for (a) forﬂaj snd(c) L {please tum a ver‘) a) (tint) Find the magnitude and direction electric ﬁeld due to the cylindrical shell at a radius 12}: 14 cm away from the xaxis. b) (513E) Suppose the first cylindrical shell is new surrounded by an second
metal cylindrical Sllcll. The second shell is initialyl isolated and has a radius
R = 8.00 cm, see Figure 4 b). Find the electric ﬁeld at the radius i" = 1&1 cm.
Neglect the thickness of Lhe cylinder. Explain your reasoning. “i: Scwe M a)
he £0 c) (6131;) The larger cylindrical shell is now grounded, i.e. its outer surface is
connected to earth. What is the electric potential due to this setup at the radius
9" = 14 cm ? Explain your reasoning. E: O Crmti'éiA—IL 5P, (Viz/mi» by G'wmss; .
Av ._= 0 0147 FM?’ Ong+SiOLIL  Sit/{Q My gm; K ...
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This note was uploaded on 10/21/2008 for the course PHYS 6B taught by Professor Wu during the Spring '08 term at UCLA.
 Spring '08
 Wu

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