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Unformatted text preview: a: —aL[—J:+L —L
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are 1nd1cated. Also shown ar o‘loo s to be used 1n an Ampere's Law calculat1on. Rank 1. (8 points) The ﬁgure above s waitphree currents of equal magnitude, whose directions the loops in order of decreasing magnitude of § B ds along each loop. That is, rank them from largest (first) to smallest (last) magnitude. Be sure to note carefully whether
the loop passes over or under the currents. 0(7C :CL7b 2. (8 points) Light with a wavelength of 420 nm passes from air into glass that has a
refractive index of 1.5. Indicate whether the follow quantities increase, decrease, or
remain the same in the glass as compared to the air by circling the correct choice. (a) frequency
(b) wavelength
(c) speed (d) angular frequency INCREASE INCREASE INCREASE INCREASE w: 1% DECREASE ,f— @ SAME DECREASE ’? dye/WIS 07’: soukce only 50 ﬂemat‘ns SaW'e \/ demeoses In Jr‘he akssl ,c ) 60 X d 9514267585 _C
n _/.,_ glass ' ' Vélqss / Wall/15 5W Polarizing
direction 3. (8 points) In the ﬁgure shown above, initially unpolarized light passes through two
polarizing ﬁlters. The first (P1) is oriented to only pass vertically polarized light (as shown) and the second (P2) is aligned with a polarizing direction 30 degrees from the
vertical (as shown). The initial intensity is 1., . Circle the correct choice for each of the statements below. The intensity after passing through P1 is approximately: (b) 0.2510 (c) L, (d) zero ® The intensity after passing through P2 is approximately: 4. (8 points) For each of the following statements (all are true), circle the ones which are
true because of Gauss' Law for magnetism. (b) a timevarying electric ﬁeld produces a magnetic field (b)0.866Io (0) 0.7510 (d) 0.43310 (a) magnetic ﬁeld lines form closed loops (c) magnetic monopoles do not exist (d) a magnetic ﬁeld cannot decrease in one coordinate direction while remaining constan
in the other two coordinate directiOns 5. (17 points) A long, conducting hollow cylinder
has an ' I‘lbel‘ radius of . cm and an outer radius
of m. A current of 100 amperes, uniformly
distributed across the cross section of the cylinder,
ﬂows along its length in a direction out of the page
as shown here. Let r be the distance measured from
the center of the cylinder. Annswer the following
questions. SHOW YOUR WORK FOR FULL CREDIT (a) What is the magnitude of the magnetic ﬁeld at r=l.O cm [6,” 90,03 2‘ OW _ ,_‘ __z) «9 ‘ [VI/cm J 5‘7 B “O :ﬂo/[WJ
(b) what is the magnitude of the magnetic ﬁeld at 7:3. 0 cm I
. )4 [do (0014) Ban/Q) fﬂo 4am?
; , J j [00 j . ‘ y
0%. V36»! 4040/ I 377(103’") 17"
(c) what is the magnitude of the magnetic field at 716.0 cm /Ua[/pa/l) . ‘ : r _ “7'
a)! IYGH.‘ ,(‘Qmop MOI?) B Q77(_)06M)b5i3)(10 (d) make a graph of B versus r from r=O to the end of the axis using the results from (a),
(b), and (c). ‘ 6. (17 points) In the ﬁgure below, a spherical concave mirror has a focal length of 15 cm.
An object is placed a distance 7 cm in front of the mirror, as shown. (a) On the ﬁgure above, draw rays to locate the image. Show the image in the proper
height, orientation, and distance. (b) Calculate the distance of the image from the mirror
35” l/ _L fr/s’cm 40: 7047
.. JO A
‘ «4 ‘3 — l 3 . / c M (c) calculate the magniﬁcation of the image (including sign). 2 )3»/cvv ._
Why—5:4 +/.9 76”! (d) is the image Virtual or Real? Circle your choice. $Lux iﬁ+° Paper Int/leases WrH’i +z'me. f,— ihducleFIUX Mae‘i' 5C 092‘? i)qu 1.5 60 CHAAanll/ [DJ PHE/ hat/3+ ie .——_ 7. (17 points) In the ﬁgure above a bar with resistance 0.2 Q is sliding on frictionless
perfectly conducting rails 1.5 meters apart, as shown. A constant external force of 2 N is
applied in the direction shown. There is a constant magnetic ﬁeld B=0.1 T into the page. (a) What is the direction of the induced current around the circuit formed by the bar and 9
U1} rails? (circle one)
/ CLOCKWISE COUNTERCLOCKWISE AW (b) When the bar reaches a constant velocity, what is the magnitude of the current? g/Y/ V; cohs‘fam‘i’ / arce/‘QQILI'W: OI I 30 géf’uﬂes : O
50 Femé = 7E :: 1’0 3W0 — “oi
5g 7
5% (c) calculate the terminal velocity of the bar. A
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JR 
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r velvety
3‘7 v~ E ' (in? X16143 ' mam mom I) 8. (17 points) Your cell phone has a power output of about 0.5 watts. A typical cell phone
tower receiver requires a signal of 0.2 iLW/m2 to receive your phone. (a) what is the maximum range of your cell phone? e Po ,S‘M/
: . 10 ‘77» : 3 If.“
Silva ‘2 x m 77" 7'?? WT 'A’Z (b) at the maximum range, what is the magnitude of the electric ﬁeld generated by your
phone? Snvq : (c) at the maximum range, what is the magnitude of the magnetic ﬁeld generated by your phone?
/ F
6 +5 __ ~MnX ,H F.
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3 137W C 4. 1X10 / // Question 1 [11} points]
{i} [5 points]
In the ﬁgure, the current element idi, the point P, and the three vectors (I, 2? 3} are all in the plane of the page. The direction of (EB, due to this current element, at the point P is: _.~‘ lN
in Jr V
WT L,
e r' r , r
i; Tact/ II ‘5 I e" ’ r
A. the magnetic ﬁeld is zero. .lm Fwd {j
E. in the direction marked “2” h "“ "“I _ . : l}; . n r
rare. x v fr?" “egg;
1‘: _ C. in the direction marked “3”
D. out of the page E. into the page {ii} [5 points]
If the current in the length element at! is zero, then the direction of the magnetic ﬁeld will be; ne'err  —H__HHH"‘_'—*—"—'Iu__._
. . “ETI ' 'fWlﬂ'l r . :I J”) 1H." I" 'Iili‘l' 1 '
A.thelr1agnet1efteld1s zero. rel“ 6‘" ' ' ' 13. in the direction marked “2”
C. in the direction marked “3”
D. out of the page E. into the page Problem 1 (a)
A selencicl 1.35 m 10:: g and 2.9L“) cm in diameter carries a current of Ill] A. The magnetic ﬁeld inside
the snlennicl is Ill] m'l‘. (i) [T paints] Calculate the number of turns per unit length For this seicneid.
E;
l ﬁt. 1 ree In“ T
r. ljfg’dg . HTF'IJCJF'J H/W EXt'nwl (“NI ml: {ii} [T pﬂints] Calculate the [en tit cf the wire fermin the sawmid‘
g g ml ‘ 'a
' r. F“ : 'A
II {I .I IILII_.I IL PHI1’1. E 5 If “Till
J HI: IL :
H 5 WQ { “VAFl ' LIE”:qu ’a— til).er
: Ears: « 71May? w ., .IIr"l'_2‘rm L It} “'f F thlem 1 [h] [6 points]
Twn long straight wires are parallel and carry current in the same direction. The currents are 31} and IZA and the wires are separated by H.413 cm. Find the magnitude of the magnetic field at a paint Inirit'razrr between the wires. i I I 1 1" I
r e '. E13 33mm mist. ' ‘3' 
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cm lgmr i at l [tsEl k girl all; [J51 J
‘r'ilrlllﬁr H/w I, last E n Fl h LI mew ,_
" —''—____  __ .a { '.. ,
Fr t w Int: {Ith ﬁx " M] ' " __.' ._ Quest‘ien 2 [ll] points]
The figure shows two circuits in which a conducting hat is slid at the same speed v through the same
uniform external magnetic field and along a U—shaped wire. The parallel lengths of the wire are separated by 2L in circuit 1 and by L in circuit 2. The current. induced in circuit 1 is clockwise. [a] (4 [its] Is the direction of the external magnetic ﬁeld into or out of the page? . , “ 'I 5 :Jr .
("JOHNCute “NF “"‘5' Ethel L'5 w h: FAF t.
l
rim: we. tthﬁ . . .~ ' ELtt‘ Wreath 'l/SIC" m in" END” {1’
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..——'—"j I {h} (3 pts) Is the direction of the current induced in circuit 2 clockwise or counterclockwise? {1i ti'i (A it? letCH’rﬂ 13' & HA .' C: MKS "t f :3” t‘U—tl: lg w a _,_. Em gt s new s Harrie CC; 2 Eel— 1 U : rixPL") V ‘2 rs
Se gt > E52 Problem 2 [20 points} The ﬁgure shows a rectangular loop of height h = 2i} cm and width w : 40' cm, which is perpendicular
to a uniform magnetic ﬁeld H directed out of the page. The resistance of the loop is R = it) 5.1. At time
t = l], the magnitude of the magnetic ﬁeld starts to change according to Bit} = illI t1 + [15, where B is measured in tesla, and I is measured in seconds. T [ﬁﬁtﬁ I‘fl‘l'! IT."L 31' {a} {ti pts} Calculate the magnitude of the ernl" induced in the circuit at time t: Ll] s. ;'  I If '1 Eli—HA Erhre {'5 etcti'lﬁn m. , III' — _
r  —_._”Lﬁtw , — teeit “ma tgt a cattlew
'3 ' at ' h J
' '* ~ . t  lamb V
IngllflbjIL : D,;? {in U..:.L1I Dlma r O (b) {T pts} Find the magnitude (3 pts) and the direction (4 pts) of the mom i induced in the loop at time t = 1.41] s. Indicate the direction en die ﬁgure. “3 . l V
' — .i ' r: U ﬂ A.
t — “I” F in 3" .___________———""'_" PE
"*1 J
:., _ 41 I 3n, ){acf
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Do‘rclwma ' at; H” C MAE L J if' F J?
El [ fiﬂCthJiJ f
le. (c) [7' {its} Will the direction of the induced current sta}.r the same for all times aftert = ﬂ"? (Answer yes or no, and explain}. Elli T " ' we now? Sui'ch i=0
13H} turner; th moi n 1": GIT I .I. '   ’+' t o . I _
Iii“3 G r .I' kid? TI ' ;. :51" IE. .5. i 3. IL
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Ia M It .ﬁ’.l...::_,2J If: : Inft C .1“ (IL. (:1 Err ( ,_ ﬁt I_.r ‘ r y I.‘ I ad
"If Question 3 [10 points] In an LC circuit the switch is clcscd at r = ﬂ and the current oscillates as shown. We ncw dcahlc [ha inductance L cfthc inductor and alsc dcuhlc the capacitancc C for thc capacitor. Circlc the ccrrcct answcrs to thc statcmcnts bclow. (a) (4 pts] Thc frcqucncy ﬁfe" ............ _._ x
Dcuhlcs {K Dccrcascs by Half Stays the Same 1
x __ __._, _. s. —— : ‘_* m
L‘Jc ’ ﬂ}: ﬁmﬁMﬂc 1Nisalc '7 “*3
Ii
“F " .: 1'.
[c] (2.913;)..Ithriud T: Dcublcs Dccrcascs by Half Stays thc Samc
k“ ~Hq____.....~aF"
i
'i c r
{d} {4 I}sz The amplitude I a Hmsc‘iilatians:
Dcuhlas Dccrcascs by Half Stays the Same
Eggus“ rcuscrruaii'dm jhjit': _
” «J . if =
‘x 7? ' ILL — '1 r. T '1' E”
_@__F ,_ LEI _ [.— “ _L '3 m JET) . qEI' Li:
2 C b
.. r 1 MINIMI. L. “H3 P L. C. r c “7' ' ': I ' «
,I'
" Jwrh] “L " Problem 3 [20 points] An alternating EMF generator Eff) : 5m Sinﬁndt} drives the series RLC circuit shew in the figure. Elm
The EMF has an amplitude cf 5m = I ltillv'r with a frequencyr of}; = ﬁﬂI—lz. The values fer the resi stance,
the capacitance, and the inductance are R : 3.0 52, C = 3:0 InF, and L = SJ] rnll. {a} [6 paints] Ccmpute the capacitive and inductive reactauce, KC and XL.
I I f
XL : at : let"F'C : avast“ Email: : ﬂail51*
xi : apt. e mi L = FTr~vvtm'—i’H~
L, . 2iT{303"~‘7{~l1'ibh'5i'l ‘ Igii": IL—
(h) [4 points] Compute the impedance Z. ———___. .._... ._h L 2_ ,..
_ _ a z '2 + lEE‘I— U‘Siuﬁ ‘‘ :,I'{
{4me < a. » .=:__a?~ [e] [S pctntsl Ccmpute the EMF 5(3) at time i = Lt} a. 51(th = rimstamina”
: rlev  3m ( 2n 'éﬂa“  1.3) : 3 9*» (L Sim CW3” ) F" {3‘ {cl} [5 [mints] Compute the overall circuit phase ccnetant qt.
’5: ‘E”. K: _. ye ' x5
.U é r 133'; dri _. IiiER” .Ji. “1 : 0.39"?" 1 at “we  [an .5 IL *— Vac». [3 2
Sr. rurrrrk‘l inn“ " "1
t. ._. Question 4 [10 points]
The ﬁgure shows the inside of three capacitor plates, with electric ﬁelds perpendicular through them as
shown. The rate of change of the electric field is also indicated. In each case, which way does the induced magnetic field — if an},r — point around the platesr.l Circle one each for clockwise (CW), counterclockwise (CCW), or no magnetic field {NONE}: 4) rm CE 91cm d’ Hiram 
a c {ii/War r E. J I; {an
,13‘3. SD E") [M oi g 'f mm
w w NONE 1"“ r1 "‘= ..._t.. E.) if: ‘ £9 'K ("i i"
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{'3} CW @ NONE G) ti/(‘Ir’n 5 I . Saul“ fillTE!” ." .11.] lID ﬁg {film i .4 _
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Etj ta *3} Question I [10 points] The ﬁgure below represents a snapshot of the velocity vectors of four protons near a wire
carrying current i. The four velocities have the same magnitude; velocity V2 is directed
out of the page. Protons l and 2 ate at the same distance from the wire, as are protons 3
and 4. Rank the protons according to the magnitudes of the magnetic forces on them due to current i, greatest ﬁrst. ‘_l__
alt is;
O G B 0%{' Of» V2 V1 E OLA
I lgl " V4 % dQCl‘EO.§’€,.§ wig; all ’3 :3 if}
2: K j,
PE 5}
ha a U3 K
“’3 i “w 7»,
® Pg mﬁ ‘ Hat ﬂog: “.33
it ‘...r ammo...“s.m.u._...u,...wt.=.t Problem 1 [20 points]
The ﬁgure below shows a cross section across a diameter of a copper pipe of inner radius
a and outer radius b. The pipe carries a uniformly distributed current 1'9 into the page as indicated by the x’s in the ﬁgure. a) Using Ampere’s law ﬁnd the magnetic ﬁeld for r < a. “t “*1 P s
(g anis ﬁ/L‘o""we£ ‘” Q
as 't .s
tam/{mam Mal/)5 giﬁuoﬂj :2 Bylaw so
, t; b) Find an expressmn for the current density, J, within the copper pipe. \ t: {a CO
0 = ,4 "" TbL'Tn} ‘ ﬂexes?) c) Using Ampere’s law find that the magnetic ﬁeld, B, for a < r < b. Make sure that
#011302 ‘02)] your logic is clearly documented. [Hint the answer is B = 2 2
2m (b — a ) “’1 i p§.§{s 'r Egga41th
dammedﬁ v 6136:» 9 8" i
E
E
E
l
I
I Question 2 [10 points] A square conducting loop is moved to the right 31 a constant speed Ivl relative to the
shaded region which contains a uniform magnetic field pointed out of the page. The loop
and region with magicﬁc ﬁeld are shown at four different times in the drawings below where :4 > 13 > I; > n. For each time, indicate whether the induced current ﬂows clockwise, counter
clockwise, or is zero in the loop. I} I: D i L i :2 O
I ‘ f3 ' r m 5w
‘2' {341C f~§QE§Li§§ \ ﬁsgwbg g 1 LL CiC, a v
t3 @ {405 we: ah , é J ME A were 5 r
2 WWW Problem 2 [20 points] A rod oflengthL =10 cm is forced to move at a constant speed M to the right of4 m 5'1
along a pair of conducting rails. The rod has a resistance of 0.3 Q while the rails and
connecting strip can be assumed to have no resistance. The apparatus, which forms a
loop, lies in a nonuniform magnetic ﬁeld B that is constant in time and points out of the
page everywhere. The magnitude of the magnetic ﬁeld is given by LB] = 5.0 x 10'3 y2 T
when y is measured in meters (a) What is the magnitude of the induced ENIF in the loop? / 8 l = L
I”? w: = (Hot
d 5 (5’25 iffy/Lt J 3 .‘
L w — L .5‘. ya '1’“
P "_‘ ,F E _/w . _ 4 =7 “a. ' w—I
., 540’ Jet/ZNHALy : 5‘30 mz'ﬂﬂZ 5] 3” m
.y C) m C}
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(b) What are the magnitude and direction (clockwise, counter clockwise or no current
if the magnitude is zero) of the current induced in the loop?
re
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‘ : _.._—v 5; _————.— , 2 2 t ‘ K e 253 “ 2 '
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=‘ 5 (06km {2.5 g? L and Question 3 {10 points] +
0000 +
0.00 {1) (2) (3) Examine the three circuits above. The resistors, labeled or not, all have the same
resistance. The inductors in all three circuits are the same, as are all three batteries. At the instant the switch is closed; (a) [4 pts.] Rank the circuits in order of the amount of current ﬂowing through the 9. battery, using the language 1<2=3, 2>3>1. CL .2. 0
R z 222 , £2 1 3’3
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ﬂ _._ [Q + “F If” :2: X f‘ '2: .:; R [,3 > L
3 ,Q {1 After a time very long compared to the inductive time constant; (1)) [3 pts.) Rank the circuits in order of the current ﬂowing in the resistor marked R. 24% Ctr/feta" 756%}; fatC75,“! 5‘1355’3}? ’a t {73
fig .25 m1? raise I) 53% ﬁe (c) [3 pts.] Rank the circuits in terms of the magnetic energy now stored in the
inductor. (ta rﬂrﬁ’eL 35:7 5 a? I: K13; :' 29,245 a  ’2‘?“
er ﬂu ﬁe .J i5 Question 4 [10 points]
The ﬁgure below shows the oscillating emf and current in two different simple circuits driven by an AC generator with an emf E = Em sin((cdt). In each of the two circuits there
is only one circuit element (other than the generator) — either a resistor, a capacitor, or an inductor. (i) The circuit element in circuit (a) is a (circle the right answer): @ Capacitor Inductor C‘ M f; Lmi—«i (ii) The circuit element in circuit (b) is a (circle the right answer): Resistor / Inductor Probiem 3 [20 points}
In an oscillating LC circuit in which C = 4.00 uF, the maximum potential difference
across the capacitor during the oscillations is 1.50 V, and the maximum cunent through the inductor is 50.0 111A.
(2) (a) Calculate the inductance L. F“ . ( 5’ E
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