This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: El University of California at Berkeley Physics H7B Professor Boggs Spring 2006
Midterm Examination #2 9:3011:00 am, 21 March 2006, 2 LeConte
Print Name SO i U’i' I on 5 Discussion Section# or Time
Signature Student ID# This exam is closed book, but you are allowed one 8.5" x 11" (doublesided) page of
handwritten notes. You may use a calculator. Remember to circle all of your ﬁnal answers. Read through the entire exam to start. Work to maximize your credit ~~ try to obtain at
least partial credit on every part of every problem. Do your work clearly so we can easily
follow. Show all work, using the front and back sides of this exam paper. If you do not
show relevant work for any part of a problem, you will not be awarded any credit, even if
the answer is correct. If y0u recognize that an answer does not make physical sense and
you do not have time to ﬁnd your error, write that you know that the answer cannot be
correct and explain how you know this to be true. (We will award some credit for
recognizing there is an error.) Do not get bogged down in algebra  if you have enough
equations to solve for your unknowns and are running out of time, box the equations,
state how you would ﬁnish, and move on (you can go back and complete the algebra later
if you have time). And if you have questions about the interpretation of a problem, please ask! [it I. (20 Points) A small bead of mass m and test charge +q is constrained to move along a
thin frictionless rod of length 2L. Two positive charges +0 are placed at each end of the
rod. (a) Calculate the force on +q as a function of x (relative to the center) along the rod.
(b) Set up the differential equation of motion for this bead. (Do not solve.) (c) Show that for x << L. the equation of motion describes simple harmonic motion.
(d) Calculate the period of oscillation for the head in this limit. C4) C01. X LLL/ M J‘QJ‘U‘Q/ a Swat” Fara + I
774m on!» com petunia dim. 61'. 01c M0 Io» g5_ cllx __ #1402 6
jg: '— mr,‘ (Ii:62
E 3 I4
“w T a»; Mclin —' ngchS 6‘26 4' 0(6)
“3/ w j (be? P Dram (ll/M OHM +st m lad”) 0"?) "‘9‘ ‘2“ if; a: ”9.916: #37. x
d+1 mL'l' MKS ‘ ﬁH‘érwdh'tbi 30“ (CUM LE”; NUNCJ 'dia‘f' '“F ["94 CJJICUFQ‘ILCJ #24 Poiadv»? ems/‘33, [1(3) 9.“ Hal: ejsfémy x43 ”My; 4., ﬂ“; mmmm. I ﬁlm/{cm ma, Gan. (7/le UL?) aroma] (:0: [1(1): Uol Kid—g .. 90 / :. ’eE
£51m” 4+5?" *5.“ "a": Mo” K QXLm' fo) 4w,” pn+ (a)J we, km ,Df 5 LII/Owl '1
1 L 0x
,4 ”We £116 1113!
(LI*X1)A:O (L H) «=6 /
= 129.} »0 “” W'i‘ihaew
L, L3 El 2. (20 points) A thin disk is centered with its axis along the yaxis as shown below. The
disk carries a charge Q, uniformly distributed on its surface. (a) Calculate the electric potential along the yaxis (relative to inﬁnity). (b) Calculate the electric ﬁeld along the yaxis (check signs for y>0, y<0). (0) Verify this electric ﬁeld is correct in the limit y>>R. (Do this only for y>0.)
(d) Verify this electric ﬁeld is correct in the limit y<<R. (Do this only for y>0.) [Hintz figdiff = N‘xz + a! ] 0/) “Fa; y '7") R J JQ‘CHJez :: E; (R1 50 ﬂ” 6)!
” _‘ Y
flue/n Z'HO’({ EL) : 220 __ Y _ ’ZG l g
'—  —1 “' and 20‘ n ~
V 6 H W)“ 71[—;:~:g+emj A: \%L ‘ (by Jrolﬂflj a” gut +10 [Ming 40mm 1‘" /
+14, own/#610“). 14 Looks ALL aﬂﬁlxz—vza _ ._....._—/ I
f: ) 2V0 (To (€619,125 010th)  I+ [mics [steam chnﬁe w  n+6)“ " 5M“ 192/
(H5) + T + 1pm, ecci 4“ WM} 7% Wm WW 05 4m ‘ . ’ PHCO) '1‘ Ht
Wt)  «((0) + P (0) e + 33’ e L 5—4;) 6» Jr. 3. (20 points) A very large, thin plane has a uniform surface charge density 0. Touching
it on the right is a slab of thickness d with a uniform charge density p. “PPM—‘7 M
(“an 0' d (a) Calculate the electric ﬁeld to the left of the thin plane.
(b) Calculate the electric ﬁeld to the right of the thick slab.
(0) Calculate the electric ﬁeld everywhere inside the slab. (Take x=0 at the slab center.) .’ Fm» M [9in G Fmat's 0M+Mwéj$
Lc/ ‘i’v'f/LQ/ 270 F01 fLL slab) U‘ﬂ/ Gauss" W" A @6,5Ac%9%¢ :7 25A: meclja
€7 0.de (owwk) [it"r'jlple vL (nods‘y #IS Gifaa‘l'l‘j:
._ 2 j —
fir ._—.q1rO~e,.c:a ZQA‘WPAtzx e= Limo x (mm LE; F...———a Lil 4. (20 points) Three concentric conducting spherical shells have radii a, b, c such that a <
b < c. Initially, the inner shell is uncharged, the middle shell has a positive charge +Q, and the outer shell has a negative charge —Q. (a) Find the electric potential of the three conducting shells, ¢(a), (Mb), ¢(c). (b) The inner and outer shells are now connected by a thin conducting wire that is
insulated as it passes through the middle shell. What is the ﬁnal charge on each shell? Fm. a single, 5W} LPG"): 5%— outsmlﬂ, Mal LPG): % {a “$546,449 1'15 ram
(wkm=lQh "1 #14 1/10er5 01: .Hu, ¢,th_ O r7C.
a\ P0» Tints mcrjum‘i'ronj 6: 9;; C7r7b
O L_,‘7(‘ g0) 411473 (p10 ,l— MGMy) W, Com ,ﬂ'l'eﬁrai'g
‘Pf‘l’a‘ f:b E 'ols +0 7cm”! [PM (me'd (F‘ ‘
9i C/emr f?“ 03mg 646°" “0% +Lb+ M, gig! hut.
LP: ~95. 1, Q; (2} (mm; LPq 1,9 Inward?) {6 JR
7+ '\ Rem, +0 f’°”.‘”'F'“‘+‘/; 1,“; +L4+ n
:ﬂhlw ﬂiuw W 4”” “W5 “WW0 m W";  9(— ac
______________,___._____—a
 " a (113 (—’ ‘ +1, Hun} um, N‘fntd HK
{’DKO‘OT—O‘ZK‘ > /(N0  9 ’— in)
C2 ‘ Q \/ Minus 9b,, ' Ly am PM, FM“; OJ+I< Look 51+ hmﬂ'nﬂ )eraJurl Fm— 090) Clo“ 0 mm} (la: 61, {MAN/In Wit“, W95” H" ”Lug, 90+ 41¢ Fomaéwv Q rcO ewe +0 0) yw m4 Iw my dar‘ﬁ‘g' Mm. Fm, 0.905} Gaza—Q9; 0%.: ’O(l%) WLulvb Adm(.115 )
a eplbxiw’e (Zapacd‘uL ”444‘ LP “6 +11. MIN/v 6W 9/2,?“ 147w? +0 0
may}? ﬂ‘ﬂ.’ €dﬂ+ton *0 pincer” ’13'52, up 1m“ 14d“
a9 ab
0"“ I" /: LP. 9 6. kph 051':4kpa+ GLPb 9'"?— L175 ”é rid{i : ”gt—Q
314+, KP‘GO and 0‘5: 0: go 0,“: ’L' 5/“ I: 60) 741° 50322 by)“, C? 99 (ft! {42, 0M7‘M sm {4 a'f' ,mrqmI'y) i‘? #9 6W ﬁg. 6‘ 2’5W 9de;uf QFZ’LanJ (is /# éAA‘ILllf! w .l S. (20 points) Consider the circuit below. (a) In steady state, what is the voltage across the capacitor? (Hint: what is dQ/dt on the
capacitor in steady state?) (b) At t=0, the battery is disconnected. Give the current ﬂowing from the capacitor as a
function of time. (c) How much energy is dissipated as this capacitor discharges? u "+ I”
0x) in dual? 6+4?) Ibo wrW+ 10/90“ +1.”th +114 W’) n” 50 on “a”; I
I r5 #157. J 1"
is gait—x— KHWL 5v m.LI1 E
‘ '1' 9'7 €013 % 60E 5 3(1/ LN U 302. M Q pawl/E} pas/6+?» Ginao WU" 1/0””? 0U.” 90 1': [Amp LFWQ’J—s W794. 1"” 441‘ 504””, qoil = go I] CL) gI; :11}; ..
’ "" ‘2 A/ "" :3 (Er“00¢ if‘I‘L' IA”IJ) ‘LP 5' F) .Lzﬁ— "é—AWP Vﬂaaovi:%ro: {GELMop: f1? again,
(,0; _‘
C‘loﬂF l'ol 1.0 U Ct: lO/F ) (Zr. 33.3)),2. j m Vaz'LOV (22190” H’v'f' m UaHabg, across "HQ, Wu‘f‘w jn gar/”1 M C/kom’f'
 AL P i.
is My ua "C ,2: Re
a So 17%)— ,Q g ..i?_— 5
IQ): 06 9, 333.3}; Amps ...
View
Full Document
 Spring '01
 StevenBoggs

Click to edit the document details