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: PHYS 2212, Test 4, November 19, 2008 Name (print) _______ __lÂ§_Â§_._ ______________________________________ .. Instructions 0 Read all problems carefully before attempting to solve them. 0 Your work must be legible, and the organization must be clear. 0 You must show all work, including correct vector notation. 0 Correct answers without adequate explanation will be counted wrong. 0 Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything
you donâ€™t want us to read! 0 Make explanations correct but brief. You do not need to write a lot of prose. 0 Include diagrams! . . . a4, 8x103 5x106 _
a Show what goes into a calculation, not Just the ï¬nal number, e.g.: m = W â€”
5 X 104 0 Give standard SI units with your results. Unless speciï¬cally asked to derive a result, you may start from the formulas given on the
formula sheet, including equations corresponding to the fundamental concepts. If a formula
you need is not given, you must derive it. If you cannot do some portion of a problem, invent a symbol for the quantity you canâ€™t
calculate (explain that you are doing this), and use it to do the rest of the problem. \ Honor Pledge â€œIn accordance with the Georgia Tech Honor Code, I have neither given
nor received unauthorized aid on this test.â€ Sign your name on the line above The PHYS 2212 FINAL EXAM will be:
Dec 9th from 11:30am  2:20pm
Please read the announcement on WebAssign. PHYS 2212
Do not write on this page! Problem
Problem 1 (30 pts) Problem 2 (25 pts) Problem 3 (20 pts)
Problem 4 (25 pts) Problem 1 (30 Points) A bar (length L = 18 cm, height h = 5.2 cm, and thickness d = 2.1 mm) made of a new conducting
material is connected in series (as shown in the diagram), to a power supply with emf = +115 volts. The
bar is oriented along the xaxis. A voltmeter is attached vertically across the bar, with the leads directly
opposite each other, as shown and reads +2.8 X 10â€˜5 V. Large coils not shown in the diagram create a
magnetic ï¬eld of 0.7 tesla in the +2 direction, as shown. Voltmeter Remember, that a voltmeter gives a positive reading if the negative lead (COM) is connected to the lower
potential location, and the positive lead is connected to the higher potential location. (a 3pts) What is the direction of Eâ€, the electric ï¬eld inside the bar due to charges on the surface of the
wire, and in and/or on the power supply? in is Eda eSâ€˜VCxLUslmcl g W badOm â€™
ï¬‚xmgsli 'â€œUâ€˜O
(b 3pts) What is the sign of the mobile chargesâ€™iMW ' A â€˜
h â€˜ I â€œmove. 1A
,VC Lek . (Tm mem 6&3) >
â€œ"6â€ ashram cm â€œX @330 
(c 3pts) What is the direction of the drift velocity of the mobile charges?
â€œFur â€”Ve Â£935 wobble. Mao Q cw â€œ Mod #15 'm
+â€” x sanctum . Comâ€œ? En D (d 3pts) What is the direction of the magnetic force on the mobile charges? Ema â€”â€”_ (e 3pts) What is the direction of El, the transverse (or perpendicular) electric ï¬eld due to the magnetic â€œmowe 90104360 as Swabâ€)
in . Tm; AJSâ€™MBTRâ€˜lah \W '\ 1A a $3424. â€˜1â€™" , (problem continued on next page) pblarization of the bar? E
M (f 6pts) What is the drift speed of the mobile charges? Show all steps in your work. fling?" 3â€™ 0 53> ï¬t limzj
in aâ€”slvedim ï¬‚ELzï¬CV XE) Â«K E)? VB â€”' > V2,â€œ:  V?) Va )
Elâ€ Mia ï¬‚ ' . Veiec'xfaï¬‚/ 3 mil/â€˜9) â€™6
:; 1: 7&3
54700â€”2 )k'OT? . (g 9pts) There are 4 x 1024 mobile charges per cubic meter of this material. The absolute value of the
charge of one mobile charge is +e. What is the value of the conventional current in the circuit? Show all steps in your work. : \n
3:; neAv : caulk)! A â€™A d  Ls
: Woolâ€œ x Lexmâ€™â€œ X 2.\X\Dâ€3 xsambz x 7.1 x10 â€” â€”2 2: 00538 Amps ; ï¬fekmo ANS.
W
W. Problem 2 (25 Points) At a certain instant a horizontal metal bar is 14 cm above a table and is being pulled upward with speed 7
m/s. There is good electrical contact along the two vertical metal rods that are 24 cm apart. Throughout
this region there is a uniform horizontal magnetic ï¬eld out of the plane of the page, with magnitude 0.8
T, made by large coils that are not shown. it voltmeter Boo? \â€˜ï¬mk '
Analyze this situation to determine the sign of the reading on the voltmeter. The mobile carriers are
(positive! holes.
(a 5pts) On the diagram, draw an arrow representing the magnetic force acting on a mobile charge in the d) ï¬‚ 6f.
horizontal bar, and label 't F . Â» V r â€™ v Q a 7 MO Vâ€œ 1â€™
1 mag {30: 4mg Mac, 591an 7? , x E 6 gave. (b 5pts) On t diagram, indicate the charge buildup that occurs due to the magnetic force.
WWO 'l'VL X VÂ£ Chair â€˜50 gLouows in "* .
(c 5pts) On thgâ€˜ï¬agam, draw an arrow representin the electric ï¬eld in the horizo tal bar produced by the charge buildup, and label it E. TM b034,} U60 W183 mam an 80%: M (Â£1 5pts) On the diagram, draw an arrow representing the electric force on a mobile charge, and label it Felec â€œPM We clam/Bea 47k {jam 'wfb \w W W: p
â€E:orâ€â€. 4:, on, WCâ€ Qae/lel. (e 5pts) On the voltmeter in the diagram, indicate the meter reading as thou rtw, 0% W is (kw 3â€˜, Problem 3 (20 Points) The electric ï¬eld is measured on a cylindri
cal surface of length 20 cm and radius 3 cm
(See Figure). On the curved part of the sur
face, the electric ï¬eld is perpendicular to the
surface, and is found to have a constant magâ€”
nitude of 3 X 103 V/m. On the ï¬‚at end caps,
the electric ï¬eld is everywhere parallel to the
surface, but varies in magnitude. On the end
caps, the magnitude of the electric ï¬eld is
4.5 X 103 V/m at the radius shown (1.5 cm).
What is the magnitude and sign of the charge
inside the cylindrical surface? Carefully and
explicitly show all steps in your reasoning. Wm: 31.: 0 mt 6Â»
1 râ€œ x 3M6?)
" C} '7â€˜ 6Â° *1": A] : 6~7< 3X\Q3 x(2W
.4 "at
â€™ â€˜vâ€”mâ€” XBXZOXZTTXKD , m a
â€œW a
WXâ€˜WMD : \â€œC.
[7/41 Because if \5 \â€˜n [:6 â€˜ [ta Wee
0â€˜1 â€˜3 \ï¬ (2 gï¬‚ï¬aâ€˜rm 30 W 03% SD
A? f 6 3{ E 3A demahï¬u
E a :21â€œ â€˜5 cm 0 Problem 4 (25 Points)
You measure magnetic field all around a triangular path and ï¬nd the pattern shown here. â€”â€”> â€”>
Going around the path counterclockwise, ï¬nd f B  dl for:
(a 6pts) The bottom side. Show your work. â€™
me, We, a \e Mmeâ€”E)" E
V
2. 8:5. g; a; Mm sdr Â» me'sxjtmiï¬lx (p.959 â€ (b 6pts) The sloping side. Show your work. â€™ â€˜ 09
Fe: stools?) sac Mat: \Demmzn E 2. on s r
â€˜ â€”5 h ,â€” .._ â€˜ nâ€”" I u
8 .Cu .1. muosx Â§ilÃ©xmso â€” 2 2 â€˜0 Tm
oo (o 6pts) The left side. Show your work. 3;â€œâ€” Ls?r slate. await Mmem E2& :36
3 02,390â€œ :â€” Q .' , $3 .43 :2 Q
(d 7pts) What is the magnitude of conventional current passing through the triangle? Show your work. Tm Mixamï¬ie Dre W cm lac,
omneA mus Â«be Amfe/rÃ©o lowIQ , Le, fuel: 6M
5? +62 LBW loof~
31> : loq +0 + 224))Â«xoâ€™5 : 1.17xmâ€5
3 z. â€˜47?â€œ55: H7ND'"5 m W :. .glA 3
Pâ€œ orâ€œ x167 3â€˜ $2) This page is for extra work, if needed. Things you must know Relationship between electric ï¬eld and electric force Conservation of charge Electric ï¬eld of a point charge The Superposition Principle
Relationship between magnetic ï¬eld and magnetic force
Magnetic ï¬eld of a moving point charge Other Fundamental Concepts 4_ d1? d5 _ a d1? a.
aâ€”dt 273â€” net dandeâ€”Jtâ€”~ma1fv<<c
AUel=qAV AV=â€” .ondlzâ€” EmAx+EAy+EzAz)
cel=onadA (Dmag=fBoï¬dA
onï¬dA=M3 fï¬oï¬dA=0
60
â€”o 4 d<I> â€”. a
iemfl : fENC . = (17:09 f B . = â€œ'0 z Iinside path
s a do s s d a A
lemï¬‚ = fENC 0 dl = (gag f B 0 dl = [1,0 Iinside path + 60E); f E O ndA]
Speciï¬c Results
_. 1 2 s , ~ 1 3 .
iEdipolemis â€œ 4WD "rig (0n 3X15, T >> S) â€˜Edipole,J_â€˜ z 4ND Zâ€”3 (on J. ax1s, 7' >> s)
_. 1 d 4
Emd = (r _L from center) electric dipole moment 1) = qs, p = a Eapphed
0 73/?"
E â€” 1 â€”â€”â€”â€”Qâ€” (1" _L from center)
"â€™d 4m m/r2 + (L/2â€”)2
_. 1 2Q/L . ~ 1 (Iz .
End ~ 47m) T (1f 7' < L) Emmy = mm (2 along ax1s)
~ Q/A Z . ~ Q/A Z Q/A .
. = _  z â€” â€” m f
Edzsk 260 1 (Z2 + R2)1/2 (2 along ems) â€˜Edzsk 260 [1 R] 260 (1 2 < R)
â€”Â» A . ~ A s . . .
IE0â€,th % 62:0 (+62 and â€”Q disks) IEfrmge z 9% Just out31de capac1tor
a IA? â€œ a a #
AB = 5â€”0 r: r (short wire) AF = IAl x B
" #0 LI [to 2] â€”+ _.
â€˜ere = am 3 E7 (7â€œ < L) {Bwire = â€˜Bearth tang
a _ M0 2I7rR2 N no 2I7rR2 , _ _ 2
Bloop â€”EW~E 23 (on ax15,z>>R) Mâ€”IAâ€”IWR
4 2 . * 0 ,u .
'Bdipole,awis z (011 axxs, 1" >> 3) leipole,_L z (on J_ mus7 1 >> 3)
_. E d
â€”. 1 ~ (1 A A A â€”Â» â€œ1
Erad 2 4W6!) :2; v = rad X Brad Brad 2 c
z'znA'U I=qlnA17 17=uE
I L E .
Edielectric = applied AV = q i â€” Eâ€” due to a point charge
K 47r60 rf n
IAVI . . .
I = R for an ohmlc resrstor (R 1ndependent of AV); power = I AV
Q = C IAVI
IAVI . .
Q = C AV Power = I AV I = R (ohrmc resrstor)
a a 2
K % %mv2 if 1) << 0 circular motion: 3â€”:i â€” ERI z %
Math Help
Eix 6: (am,ay,az) >< (bz,by,bz)
= (ay ()2 â€” az by):% ~ (any bz â€” az bay) + (am by â€” ay bx)2
/ dx â€”ln(a+x)+c/ dm â€”â€” 1 +0] dx â€”â€”â€”1â€”â€”â€”~+c
w+a_ (m+a)2_ a+x (a+m)3â€” 2(0L+:v)2
â€˜1 2 2 a 3
/adac=ax+c /amdx=Â§x +c fax dx=Â§a3 +c
Constant Symbol Approximate Value
Speed of light 0 3 x 108 m/s
Gravitational constant G 6.7 X 10â€˜:[1 N  m2/kg2
Approx. grav ï¬eld near Earthâ€™s surface 9 9.8 N/kg
Electron mass me 9 x 10â€”31 kg
Proton mass mp 1.7 x 10â€˜27 kg
Neutron mass mâ€ 1.7 x 10â€”27 kg
Electric constant 4 1 9 X 109 N â€˜ mZ/C2
7Tâ‚¬0
Epsilonzero 60 8.85 x 10â€˜12 (N  m2/C2)_1
Magnetic constant 5â€”0 1 x 10â€˜7 T  m/A
7r
Muâ€”zero no 477 x 10â€˜7 T ~ m/A
Proton charge 6 1.6 x 10â€˜19 C
Electron volt 1 eV 1.6 x 10â€˜19 J
Avogadroâ€™s number N A 6.02 x 1023 molecules/mole
Atomic radius Ra z 1 X 10â€˜10 m
Proton radius R1, z 1 x 10'15 m
E to ionize air Eiomze z 3 x 106 V/m BEarth (horizontal component) BEarth m 2 x 10â€˜5 T ...
View
Full
Document
This note was uploaded on 09/12/2011 for the course PHYS 2212 taught by Professor Kindermann during the Spring '09 term at Georgia Tech.
 Spring '09
 Kindermann
 Physics

Click to edit the document details