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Unformatted text preview: Student Name: Student No: Louisiana State University Physics 2102,
6:00PM Thursday April 15, 2010. Please, circle your section:
1 & 6 (Giamrnanco)
2 (V ekhter)
3 (Rupnik)
4 (Bowling) 5 (Rupnik)  Please be sure to write your name and student number and circle your instructor above.  Some questions are multiple choice. You should work these problems starting with the basic
equation listed on the formula sheet and write down all the steps. Although the work will not be
graded, this will help you make the correct choice and be able to determine if your thinking is COI‘I'BCiI.  On problems that are not multiple choice, be sure to show all of your work since no credit wtil'be
given for an answer without explanation or work. These problems will be graded in full, and you are
expected to Show all relevant steps that lead to your answer. Note that you can often do parts (b) or (c) even if you get stuck on part (a).  You may use scientiﬁc or graphing calculators but you must derive and explain your answer
fully on paper so we can grade your work.  Please be sure that all numerical quantities include appropriate units. Points will be deducted if the
units are absent. In addition to magnitude, vector quantities must contain sufﬁcient information to tell
us which way the vector points.  Feel free to detach, use, and keep the formula sheet pages. No other reference material is
allowed during the exam. 0 The only electronic devices to be used during the exam are standard or graphing calculators. All
cell phones should be turned off and put away. Cell phones are not to be used as calculators. Any cell
phone heard or seen during the exam will be conﬁscated. ' May the Force be With You! Question 1 [8 points] Ta k 4371 L (9w? 6, PA Cg all") C 6 am The figure below depicts four identical wire loops lying in the plane of this paper, each carrying identical
clockwise currents, I, as shown. Each loop is located in a region of uniform external magnetic ﬁeld, B, in the
directions indiCated. The magnitude of B is the same in each case, only the directions differ. 9MB I we CW/ tic/<6 1'59 ﬁeﬂmwg 7L0 Hme [cap as i3? I'D/cg” E + . o + 7 Do —>
59 ® @ [email protected] 60 9 Cl B 0
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(a) (b) (c) (d)
"'2) I
I + s
(9 IS nag/e [Win/eel“ 3 m0/ [751me (“GD/:3; ‘ i) Which loop(s) experience the greatest magnitude of torque due to the external magnetic field, B? e g g {ti/fXB :[ﬂgwcgjw 50 WW7!
fwéce tar/L944 (9: ?0° is (d W961!)  ii) Which loop(s) experience zero torque due to the external magnetic field, B? 7,3; M)
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M iii) Which loop(s) have the least potential energy due to their orientation in the external magnetic ﬁeld, B? Note that a negative potential energy would be considered ﬁe smaller than either a positive energy or zero
energy. 34% Qﬂuf ll fun/1 mdlfl‘m .6 Cb) (c) (d) *9
m I‘Yl {W W“ be" WW 7) :' Pct/m [/ej 7L0 B :9 [710% [1 [~me [UL ,‘5 cm7ll~Pﬁw<t/C/ 7L0 Problem1[17 points] acpqp+€d ‘90”?! HW 7/ #12 The figure shows a cross section across a long solid cylindrical conductor of radius
a. The current density in the conductor is directed parallel to the axis of the cylinder,
and is dependent upon the radial distance, r, from the center according to the
relation J 2 ﬁr where J is in amperes per square meter, and ,6 is in amperes per cubic &, meter, and 0 S r 5 a.
f"
b 4 Obtain an expression, in terms of 5 and r, for the current ﬂowing through a cylindrical portion of the conductor whose radius, r, is smaller than a. lineage amt MA; I“ h. ’79 ,‘ m1/91+00ﬂﬁ
r r What .101?“ Aqu 2mm;
jg X3,” ’ Weft I J 7% oétf‘ii :
o ' '0 "’ 3 ’1'“
9% Use Ampere‘s Law and your expression for the current from part (a) to obtain an expression: for the
magnitude of the magnetic ﬁeld, B, at that distance, r, from the center. mm l0“ 5 @343 W122 Us? Tam outage
@8044 : HM alga?" :2; Brﬂﬁ F2. f
5% Use Ampere's Law to obtain an expression , now in terms of 13, a, and r, for the magnitude of the
magnetic field at distances, r, from the center that are larger than a. 3 ,_—. 7001— 1‘70») ,L: ﬁ’TTﬂ riot?“ 1“ ﬁa 1v) Make a sketch of the magnitude of the magnetic
field, as a function of radial distance from the center, on
the axes drawn at right. ﬂgpc/ Dlrechbn‘s,’ RH]?
Question 2 [8 points] ﬂaw; E’C/q Pa'vni‘ i 1 Ch 2 ﬁ 8 i
The ﬁgure here shows three long, straight, parallel, equally spaced 9);? wires running perpendicular to this page, with identical currents either into or out of the paper as indicated by the dots or crosses. 8C 'a b c ank the wires according to the magnitude of the force on each due to the currents in the other two wires. Rank fro: greatest force to least force. 4.53 E %
a=b>c use :1 “F : X B
b>a=c deg—HA? cﬂweuiwﬁ 0M0?!
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flaw #544ng Piggy”. “ WEQk.“ ijCe
0% exPQwQMces CL: weak" an ix 6%”T5” terse] aur 1h oppasri‘c citree'i‘ricms ii) Which wire(s) experience a net force directed towards the right? Ky onlya (a) 7497i 990% ,‘3 T on] b 
b 8:: Quad [6,) V1 9+ 38f QﬂG/ 1 5 
_ ﬂ“ "‘23 ~——a Q 056’ jC : IQIB mud ﬁght}? (a) may” (a) pxpmrehcé?
Aghiwwd J%c€ Problem 2 {17 points} 7am” (g In the figure at right a 20 turn coil of radius 4.0 cm and resistance 10 Q is
coaxial with a solenoid with 50 turns/cm and radius 2.0 cm. The current
in the solenoid increases linearly from 0 A to 50 A in a time interval At of 15 ms. i) What is the magnitude of the magnetic ﬁeld in the interior of the solenoid at the end of the 15 ms interval? 5"? BSOQ 7; Pol/1i : {Fojégtﬁh %“){5‘op)
ifﬂ/l
/ ii) How much magnetic ﬂux (magnitude) does the current in the solenoid produce within the interior of the coil? 63?} a : ﬁll? a Wes m H iii) How much current (magnitude) is induced in the coil during the 15 ms interval?
K“ ﬂ 4) ¢ ‘ ﬂ
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9/07/57 *N/ 4+ "NZ? : [If:f” 075“
' u 5 3 V iv) Annotate the ﬁgure at right by adding "x" or " as appropriate to indicate
the direction of the current which is induced in the windings of the coil. Be
sure to show direction both on top and bottom. Explain the reason for your choice. 6 . ,
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5/14 C? so!“ I S I J {3) 7/“? M0! +0 ﬁx? Atgk'é'j euﬂﬂw+ 50A
in cc)in havle [Mach/cf 9/12): “[0 leg—F (in; ole/">052 Chat/‘61? Question 3 [8 points] An ideal inductor consisting of a solenoid coil of length (3, cross section A, and turns per unit length n, has been drawing a steady constant current, I, for a long time. If we then doubled the number of turns per unit length in the solenoid but kept the current, I, cross sectional
area, A, and length, 8, the same, then waited again for a long time, what has happened to (i) the magnetic energy stored by the inductor
3‘0.
099% 3) 1t remains the same
b) it is twice as great as before
c) it is half as great as before d) it is four times as great as before e) it is one—fourth as great as before M? (ii) the voltage drop across the inductor
b) it is twice as great as before
c) it is half as great as before
d) it is four times as great as before e) it is one—fourth as great as before 15m. : ﬁanlﬂj' l"? KL jg gawk/ed)
L 6960m€$ GS JMUCLL Problem3 [1713mm] 163W HW Cr # 7 A coil with an inductance of 35 H and a resistance of 1000 Q is suddenly connected to an ideal battery of 180 volts.
At the moment exactly 35 ms after the connection was made... i) At what rate is energy being delivered by the battery? ii) At what rate is energy being converted into heat by the resistor? “2 a; if»? :(tueYC/owﬁ) : IQJ W F //—\ W iii) How much mtg} energy h: the battﬁry delivered during those firstggsgljs? ﬂ 0 35.5
: \S‘PBﬁTTCﬂ :j(\/snrr\ J’(ﬂ : jég’ov)['/8pr(l d e ‘9 o . 035‘ 5 2 (337 M) 50w“me : sad/<52 J
O octaqpie‘i/ HW’O ' #3 In the ﬁgure at right, the switch has been in position a for a very long time, and is R v
[I +
a Question 4 [8 points] thrown to position b at time I = 0 s. i) Just the tiniest moment after the switch is moved to position b, the current Pt
“3 3338 m Capone. had hem
e)2V/L Chwépo/ +0 V [Jule Hie
Lut‘i'k SW’LCK Swi‘i‘ci’t W08 51L “CLIr
Ct'tL “13 [MIN/M +A€ SW,‘I‘CL\ mot/63 iv “A
L we! C 714w choci‘le 4416‘s 7L0 kqvﬂ d,5cl]wé:ll:5 [4 EU; Zr
say/1‘8 + Lw/i malL (ct/low Gm 1h57LQM+q”QWS
(mm C M comm»an L’s (wane/ML WQS 0 {997039 +A€ StuﬁLcA
I: ' H H
30' ref/i A9?“th 0 «M5le Q707£€a ii) After the switch is moved to position b the current in the circuit will oscillate at some frequency, 3%.
That frequency, 1?}, wiil be determined by the values of W a)VandRonly
b)R andC only
/ u. . dLonly 12 V ewe}, Q N OWL a'
_ , ,only ft‘F CinCUWL how f)R,L,C,andV ﬂotqmlee/ 70mm #WIO air/OWN
{aka City‘é‘ct‘lbws v.1; A Problem 4 {17 points] 0 g SW 100 (6‘ V96 ; d'ﬂ r
a 5 00+ LuCt Kc] A Gaussian surface is in the shape of a truncated cone. The bottom of the cone has
radius 20 cm and the top has radius 10 cm. The height of the cone is 30 cm. A magnetic field of 250 mT is constant with time, uniform throughout space, and is
directed upwards, passing perpendicuiar to the top and bottom faces of the cone. To specify flux directions, assume ﬂux pointing out of the Gaussian surface is positive. i) What magnetic ﬂux passes through the bottom of the cone? 2— x0) j?) 0? F} __ 6 H [80” — (2 ,.._— 7 _ o H to; I , 6 J H . 2 M 4‘9 av; €01“: QET 607T ) 6 J ( ) :‘SML/XIO'L T“. m1 a; Wot direct/m ii) What magnetic ﬂux passes through the top of the cone? “2” do : {€473 .—. MW, :éwdérrwmﬁw" To! f" ___3 B It If M
:1—7, 85x10 [.ML 1/ means w?
//—\ iii) What magnetic ﬂux passes through the sloping sides of the cone? 3:6
U}? 31h”) ¢7~op+ BH‘T + 3:DE5 f O ' ~— "3 "L ‘2; smes : aﬂopﬂégm :: — 7,85 >U0 Tun  S./V>UO pm _ t ‘ ’1” L \\ l; r“ “I” QHX/O /'m [earl/wad) ‘1“ iv) Would your answers for (i) through (iii) above change is the cone were made twice as tall?
Explain. 6?} HO "' $70? @3077— ”ﬂz CLAW ,__..—— __'""" 50 «316/6; fiat/“3’36 5W ¢7DP+ 307777.: SIDES : O ...
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 Fall '08
 GIMMNACO
 Physics

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