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Unformatted text preview: 1% PondS TRMTIQE FOR FRU loo‘ me. Wmu__.wm w , —. PHYSICS 6C FINAL EXAM Name Sb 11370“ s
FALL 2001 December 11, 2001 Signature
100 POINTS TOTAL Student ID # __ SECTION A: Multiple Choice
2 points each (no penalg for wrong answers} A B 1) Consider two identical metal spheres. ® @ Sphere A has a charge of +4 microcoul,
Sphere B —12 microcoul. They are touched together, then separated. Then @q 4’
. Sphere B .is grounded, They next are touched together again and ﬁnally @
separated. The ﬁnal charge on each is: El +4 microcoul El 1 microcoul
Cl +2 [a 2 U +1 D 4 El 0 El none of above 2) For a negative source charge qs, the
electric ﬁeld E points:
atoward qs "E“ z
E! away from qs * a;
El concentric around qs [:1 none of above 3) For two points A and B separated by 10 cm in an electric ﬁeld E = 100 Me (as shown), VA —— V3 is: E
+O———r———)
El+1000 volts [:1 + 1 volt E] 100 volts h B
D +100 1:;  1 [31000 e—l‘M—‘a 04,
7 El +10 1::l 10 tjnone ofabove AV AV: ‘0“ ,, E: if Avxrox/ 4) In the previous question, the work done by me (an, external force) to move a charge
of+ 0.01 coul from A to B is: bodes {mulls} 'ou.)
13+ 10 volts uwoﬁoku 1:1 1ng
El +1 [3 0.01 E; ~10
El+0.1 12:1 0.1 [:[.none of above 10) For a magnetic dipole moment (“mdm”): If the current is Edoubled If the area is Eldonbled
doubled,the mdm is: Dhaived doubled, the mhalved
[:1 unchanged mdm is: [:1 unchanged
[3 none of above mnone of above
32
11) Two slabs of Aluminum (which has a nonzero nuclear magnetic A
dipole moment) are being studied with NMR as shown. 3*: m T 316$ A
The primary ﬁeld in the z—direction changes such that 8; ‘ 1.71. 5 5‘ t, B
Slab A has B1 of 1.0 Tesla on it and Slab B has 1.2 Tesla
on it. The ratio of the 13x oscillation frequency to excite _ mm
the nuclei in'SIah B to that for Slab A_ is:
[I 1.44 [I 0.83
El 1.20 [:1 0.69
£11.00 [:1 none of above 12) For the diffusion situation as shown, If the cross~sectional area of the tube is doubled, the current is: Edoubled
ﬂhaived
munchanged
gnone of above If the length of the tube is doubled, the current is: Ddoubled
Eﬂhalved
{Junchanged
[31mm of above 13) Heat transfer by conduction in air applies in cases of : 13 moving air
Emmimoving air Heat trait. 'fer by convection in air applies in cases of: 13 moving air
I] non—moving air [9 Points B2) Consider an inﬁnitely long straight wire of uniform 5
——""" charge per unit length .\ = 10A6 coulfm. We will £_ _  _ 5'"
aim to establish the radial electric ﬁeld a distance of {6 oc }\= O'btl'm
5.8 cm from the wire.
a) State Gauss’s Law precisely (either mathematically
‘ (‘91) or in words). g email = Lurk Qwiml b) To pick Gaussian surfaces which
{I pt) make the integration of Gauss’s law ,
easy (for some particular source
charge conﬁguration), what criterion
or criteria must the surfaces satisfy? c) What shape Gaussian surface would
(I 9") work well to establish the radial electric
ﬁeld near the wire? watt) 5
.3 u (I) Find the algebraic expression for the @E‘ R (l A '' 0+ 0 ‘l' El?) Inn L  q“ k L k (3 pt.) radial electric ﬁeld near an inﬁnitely
long uniformly charged wire.
Find the numerical value of the radial
electric field at a point 5.0 cm from a
wire with charge per unit length of A = 10A6 coal/m. =7 EM= Mot/R r6
_ '1thqu y lo 5’
: , 1 l
‘05, “um t/c i '\‘
(Fit L‘lli‘UO Vb: ‘9. U
SECTION C: “Medium Length” to p.. h’ts 01) A container has 2.0 liters of salt}’ seawater with 60 gm m
of NaCl in it (as shown) and also 20 gm of K" ions. ’—
The atomic weight of NaCl is 58 and of k" is 39. M
A9 for NaCl is 12.8 and for Kl is 7.4.
The seawater has a hollow insulating cylinder of length ”tn“: "‘3‘?“ 10.0 cm and radius 1.0 cm immersed in it (and filled with
seawater). A 12.0 volt battery is connected to metal plates (Area: It r1)
on each end of the cylinder. [Note: (fr' ha‘. (2'. ] l?» ,1.) a) "Talculate the conductivity of the electrolyte.
‘ I i I G‘Tot‘ 0"" u'l' 01+ ': A ll‘lﬂQl) Quelsl 'l” As it." H C mu = 6:31.53— "' snhole/liicr P. k.“ = 3‘7:..—= It“. Male/tier O. 1‘.) b) Write the ormu a ior {lie registiwty 1n "
P terms of the conductivity and calculate ' the resistivity. =) (Egg lmmsn asmtts ‘ESIA—m (a .12) 0) Write the ________fprrnula for the resistance between the ends of the cylinder in terms of the
resistivity, etc, and calculate the resistance. (5. t.) d) W through the cylinder. ’
P I =V/R7 ”/3732.“ 0.31191me 2.
{Q t) e) Calculate the power diSSipated into the E) 51151 '5 0,311 '3! 37.3.. "3 3. 8 l: ”Mlt
'P .. electrolyte within the cylinder. [7:512:10 ‘3 Po‘: n1. (39*) Us 93) H at) misﬁt"N SECTION D: “Long” Del) A mass spectrograph was one of the very arduous
(but viable) ways during WWII in which ﬁssionable
U235 (0.71% abundance) was separated from U238
(99.28% abundance). 'In the process, Uranium atoms (92 protons; 143 neutrons for I U55, 146 for U233) were ionized, typically with 7 electrons V = no.0!) a removed. They were then accelerated across 40,000 volts and entered a 0.3 Tesla B—ﬁeld at right angles and traversed a semicircle . (as shown). The U235 has a slightly smaller orbit and was k, ion source. e? collected in a different slot from the U238._ ‘ t?:§§,::£3§‘:uf _ _ _ 7 7 _ _ _ 'nn‘vud (hmovttn .
a) Derive the algebraic expressron'rfor the speed of the‘Uramurn 10115 when they entered. the Bﬁeld and then the expression for D (the distance of the slot from the entry point) in
terms of the Uranium mass, the net ionized charge of the Uranium ion, the accelerating voltage and the size 01th:: Bfie d. 
V .
m..— s 07’ GbV=€w~v1 ear: m 2mw¢s
12. 1.
1. " b m m
ovguﬁm‘té’: “33:: 9:23
a D
._—— t V
_ _ :1th 1m 1 V _ 3:» EL
'753'1.;75"3bg\imrei 1, [—————'—‘—', 
[16.35th way across
\ hate my "I 3;. b) Find numerically: D235, D233, and their
difference (it’s not very bi gt).
You may use the mass of protons and
neutrons of 1.67 x IDA27 kg. 0) What is the fractional difference between F _ __ )
D235 and D238? freshen“) btuercucﬂ. " (Note: If need be, this can be answered without = 0 .0953 = G  L32:
doing part (b).] [a Poi ntS (int) it (11ft) (iit) SECTION B: “Short” [ r—ir 31) For the circuit as shown: a) Find Im the total current ﬂowing out of the battery. b) Find the potential
difference VB .. V...
c. 5 o g 0' c) Find 150 (the current in "' 32: ' 0J5”?
the 50 ohm resistor) and
Im (the current in the 200 ohm resistor). unI’ U; V ‘VL . E" _
l1“ £5: "an— 6‘0““? ENott ' T$e+11ou= To] (1) Find Fm (the power
dissipated in the 200
ohm resistor). Rm? has“: noo= 0.32. We ll
loam. 5) A parallel plate capacitor has an area of 0.001 mg, a separation of 2.0 mm, and a dielectric constant of 5.0. Its capacitance is: A‘iOahn‘ J
i=1 M
[213.5 x IDA—9 farad [max 10A—11 farad “‘F—Fs ‘r "‘
Elaax ion—11 C14.4x10"—11 JR A
[34.4 x10A11 1:] 8.8 x 10"13 C : Ha
[I 3.3 x IOAll [:1 none of above q “ K 6) For a sphere of uniform charge qs, the electrical equipotential lines are: ,. 1r
E] toward qs concentric around qs D away from L}, a , 53 none of above
7) For the circuit shown, the time constant to charge the capacitor is: .
[110“+8 sec [:1 10A+2 see a 10m sec vb: 10 v = W”
1310A+6 [:1 10A+0 u IDA6 I , _
EllO"+4 [:110A 2 a long L— to
' 1:] none of above
8) For an electron moving it? a magnetic ﬁeld as shown, the force
iii [:1 down E Into the board
Elleft C] out of the board 9) For an elaqtron moving in the opposite direction from a proton,
the mforces between them are: _, e on the electron is:
[1 up n U right gnome of above ;
it
———9 E attractive a zero
grepulsive 1:] none of above A:
f t
l? PetrolS 82) At t=O, the switch is closed in the circuit as shown. (a: 0.1;»; V3: 10V [I pt) a) Calculate the current tltmnghtheresismLanQ—\ _ V}. to
\l. “WOWﬂ 42 F0: 0. i can)? (591) b) Shm; til—atlas t1 approaches inﬁnity: My: 0:, all ultimate“ in“). ctllgg‘l‘giéé‘iﬁew;
‘ I * V0 ‘3 {lavought R. :2 = 3 32:: f. V 5 it“! “t“ Qt: VI CI: 16‘1”“; ‘ 10MB I
3 = f . . ‘ .J, __ l, _.3— = J’ ‘ ..
Ql =20 m1crocoul cz‘lts “‘“ﬂ‘é' " Cat—“why" :1" C3 Elsi: 5:4 " «31;;th Q2 = 4 microcoul S‘ V A! a to .  ,
Q; = 4microcoul name 3 c i Q‘r‘v“: Q1‘ Q3 2 VCva: lm‘t‘l' Lime (3,91) 0) After all capacitors are charged up ® . 91mm ® _
(in part (b) above), at t’ = 0, capacitor $_ —— "H
C2 is shorted out (as shown). [80, all \I U Q
C p? of +Q2 on the top of C2 flows and V51 10v "—3.  ' { neutralizes all of —Q2 on the bottom of C2.) .  Q3 '1“ At t’=0,whatare: V V andV —V ‘2
Vk'v c: l G V (1W (3 P10 e) For t’ > 0, write Kirchhoff” s Second
Law for the sum of the voltage changes
around thencircuitcohkotwemg 'lzlu. Inﬂu + (.3.
outﬁ'h ’ﬁ ghoul: (at A 3 (.30 °l°El<w\5u
3: it'll R  ﬁctive. +Vh=0 ,0 ’3‘) 1') What is the numerical value of the ti
 constant as C, charges up ? l T = RC3: 1063114,.“ 1 g 1695““ l (3 t) g) At t’ = infinity, what are the numerical
? values of the current through the resistor
and the charge on each capacitor? itt'm) =0 g
Q :LV551MFﬁlOI=3XlQ L
\ Q3 =c3vb= 1»? m) =1x 155;, (Q3 [0 Pet“ts CZ) In the “classical” Bohr model of the atom, in a Hydrogen
atom the electron orbits the proton in circles of radius é‘i‘ﬁ'm pain“ A
0.529 x 10A10 m and at a speed of 2.19 x 106 rnfs. IE :uJJu s
+——. B (1 Pt) a) Show that the period is 1.5 x IDA16 sec and the current is
1.05 x IDA—3 amp. ”.mm “to
an; r : e.smxlo , _
T n; W: x [641; I: inbixig ”’SCC 1.; 1/1,, Lexis” l.§'>.xo"‘ = Le s’xto‘3 (.1 pt) b) Calculate the magnetic dipole moment M =IA. W
A: n w‘:[o,§1qxlo"°:l ﬁ= ‘E‘J‘ix loll»: M: I A ' Logxto'z x seq 7: [014 2 61,13 k 30"“ WW"? (3 Pt) 0) If it is in a magnetic ﬁeld of B: 0.1 Tesla,
calculate the potential energy difference
between the maximum potential energy
state and the minimum. Compare this with thermal energy of ~ 6 x IDA21 joule. Will this B ﬁeld be
able to keep the atoms polarized with
the magnetic dipole moment along the B field? APE. E PEmkx'PE'Q‘“ whim(i FE:P££.E
= nam<>°mawl°°
e lusts 1:1“..13): libH xOrl
= 1353‘ [0'12“ 30min.
m Em,“ ~LMH$WK ”33—2di w‘,“ 53: Keep «items
olcétimd ii («at “‘03" zﬁ‘km‘
l—m ' 0
1mm: =M3Wq‘3 5»
—1
= 9.33M?" m =11; no nm d) Show the direction of the magnetic
dipole moment (relative to the direction
of the B ﬁeld) for the maximum torque
on the magnetic dipole moment.
Calculate this maximum torque. l3 9'1) 7200 !2 Po‘mts 33) Consider the expression for the potential V from a
electric dipole oriented along the +x—hat axis, as shown. a) Rewrite the expression for V in terms of x and y
(ht) (rather than 1' and theta). b) Show that this yields the correct expression for Ex,
U! pt) the x—component of the electric ﬁeld. “ﬁlthy A
T
a A
——"—"—‘>+x
34 me
T? ...
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