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Unformatted text preview: Physics 2102, Final Exam, Spring 2011 May 11, 2011 Name: Section: Instructor:  Please be sure to write (print) your name and section above.
0 Please turn OFF your cell phone and MP3 player! 0 Feel free to detach, use, and keep the formula sheet. No other reference material is
allowed during the exam. 0 You may use either scientiﬁc or graphing calculator, but not the calculator in your
phone. a GOOD LUCK! Notice that the points in the exam add up to 150 points  since the ﬁnal exam is worth
150 points of the 375 points available SHOW WORK on all problems that are NOT multiple choice. Question 1 (14 pts) The ﬁgure shows two electric charges of equal magnitude q and opposite Sign, on the x—aXis at coordinates
tea. The point P is on the y—axis, at a distance d from the origin. (a) (5 pts) What is the magnitude of the electric ﬁeld at the point P? (k = 1/47r60) e 2kq/(a2 + a?) 2kqd/(a2 + d2)3/2 ﬂ/(ag + CW/2
Ex: _ 2ku View : r2 £2 a. r “23% (b) (3 pts) What is the direction of the electric ﬁeld at point P? m..‘ w‘ws—nwﬂw 0 #4 j T i W (C) (3 pts) What is the electric potential at point P? [/02 qu/x/ a2 + d2 2kqd/(a2 { d2) 2kqa/(a2 + 052)
f I; ,.
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if f (d) (3 pts) What is the Sign of the work done by the electric ﬁeld if a third, positive, charge Q is moved
from point P to the origin? /‘\
0 Positive Negative It depends on the numerical values.
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I; H Question 2 (12 pts) Initially, a single resistor R1 is wired to an ideal battery with emf E. Then resistor R2 is added in parallel.
Circle the correct answers below. ﬂ" (a) (3 pts} Is the potential diﬂerence across R1 now more than, less than, or he same as previously? More Less {2 1 f2 .
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1 R} Q} to... (d) (3 pts) 15 the total current through the battery more than, less than1 or equal to the current through
the battery before R2 was added? Less Equal
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\J Question 3 (14 pts) Two long straight wires pierce the plane of the paper at vertices of
an equilateral triangle as shown below. They each carry 2A, out of the paper. (a) (3 pte) What’s the direction of the magnetic ﬁeld at point P? l,” ,
B I O +— —> Out of the page Into the page kw (b) {5 pts) What’s the magnitude of the magnetic ﬁeld at point P? B : 0 2 x 1052“ 1.7 x 107517 Q 0.87 x 105T wﬂwwx'ﬂﬂ 1 \ :3 Mia,“ :1 m5
’8: 2;: ref Law to ix tan/10’ eff/4M (4,7331 1,17an (e) [3 pts) What is the direction of the force of the ieft wire on the right wire? F:O 4> i T w; {.2 g ﬁClLlL fig—Lil 0.0—1. l1 .' (d) (3 pts) What is the magnitude of the force per unit length of the left wire on the right wire?
F = 0 10"5 N/m x 10%;th 4 x 10’5 N/m
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7?. §‘\~. Question 4 (9 pts) The figure shows two circuits in which a conducting bar is slid at the same speed 1: through the same
uniform magnetic ﬁeld and along a U—shaped wire. The parallei lengths of the Wire are separated by 2L in
circuit 1 and by L in circuit 2. The current induced in circuit 1 is counterclockwise. gig) I B 22." ’U" 30 inmﬂijL'Lé—Q’ Wt“ &J_
P l P :5) V‘ L‘ MC D (I’llﬁjg—(‘prm Illa
mil/l Frog'wa 52 'HZ; ‘ “Mr.” Ufggﬁwg Mi” 2” y I {it arm 9‘ r; g] z A: a at) ﬁﬂjfﬁaufm 73.1, {airbag} i2. #1 Ou‘i' 9:0; Hog So Ubu‘jcorm 1/ (b) (3 pts) What’s the direction of the current induced in circuit 2? //r, llll “ﬂﬂm‘NN
Clockwise Counterclockwise If; Rightward Leftward
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C \ 5 5W 3,] Q ELM; a“ t
our/«Art 4.5m air/Ii; m wig, v r v a; (c) (3 pts) Is the emf induced in circuit 1 larger than, smaller than7 or the same as that in circuit 2? (2;?) Smaller The same W9 Z, £l>§2 Question 5 (9 pts) The ﬁgure shows a paraHCI—platc capacitor and the current in the connecting wires that is discharging
the capacitor. : 3““ 67
 w, i e = wJFQkJ¢Q Emmi,
£12 he it“: ﬁne 3* i“ j. a
(a) (3 pts) What is the direction of the electric ﬁeld 11:," between the plates?
M.
E 2 0 1/ —> ) 4— into the page Out of the page (b) (3 pts) Is the magnitude of the electric ﬁeld E‘ increasing, decreasing, or constant? B = 0 Increasing (/Decreasm Constant ;
\w I‘M/“y” ‘ “ Mme < ‘ <1 Om ﬁg/bgtsiLQF IS 0 and?) d5) Jiéié’itﬂf, 4:590, (c) (3 pts) What is the direction of the magnetic ﬁeld E? at point P? B : 0 —> <— into the page Out of the page
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£4 Question 6 (6 pts) In the ﬁgure, a beam of unpola’m'zed light with intensity IQ is sent into a system of two polarizing sheets
whose polarizing directions make angles of 61 2 62 2 30° with the éirection of the y axis, as shown in the
ﬁgure. (a) (3 pts) What is the intensity transmitted through the ﬁrst sheet? ./ }
IO 10/2 / 100052800) Igcos2(60°) ‘
.\ // x__._r— Mtge mm is eatsgwr‘ﬁeef’ (b) (3 pts) What is the intensity transmitted through the ﬁrst two sheets? 0 Io C034 30“ 100034 60° 106082 300 2 100032 600 2 ]
:\ f]
kﬂ/ 9 s g 9
z” r’ i / , i /// E {I " l ,i, f _ 14? ﬁ¢9;§.;;mj ,_/,./"I’ i [x (I; mt?!“ if“ 1; " r  (é
//'/ r 51/ E w}? ﬂ f? I , r Hwy; Essw'ﬂfe; w Problem 1 (22 pts) As shown in the ﬁgure, a solid insulating sphere
of radius a is concentric with a spherical conducting
shell of inner radius 5 = 2a and outer radius c =
2.50.1. The sphere has a net charge (1 uniformly dis—
tributed in its volume; the shell has a net charge —q.
Answer the following questions in terms of q,a,b,r
and constants such as 1T, 69 or k : 1/47reo. (a) (4 pts) Sketch in the axes shown the magni—
tude of the electric ﬁeld E(r) as a function of radial
distance r. (Hint: answer this part after you have
done the other parts of this problem) (b) (6 pts) What is the magnitude of the electric field within the insulating sphere7 at a distance r < a? f—v‘p “b 5mg? Zea.) 3 3D éEéjii E we?" origin? A9940} U342”)? (gaging? ', / a: : "m‘v
ﬁrm
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c, itﬁrrﬂa w p (d) (6 pts) What is the charge on the inner surface of the shell, at r = b? eeaesndaneﬂihﬁﬂﬁ (gar; 6/51;
s 23 :2
T mi 7g 0 5 “Wm—w! if E’ng is}: (c) (6 pts) What is the magnitude of the electric ﬁeld at a point at a distance r, with a < r < b from the “ii/5Q w . __ F ram{\ k, m m C? «. éric é? W/ £2 \ {WWI gm"; _‘_“ a
m" m
fi‘ innax gm W. {2* 7L, .1‘ 2 I
{to ﬂag a ctargg’ Problem 2 (21 pts) The ﬁgure shows an inductor connected to a battery and two resistors through a switch that is initiaily
open. The battery has an emf of 5V, and the resistors have a resistance R = 29 each. The inductor has L 2 3.0 mH, and is an ideal solenoid with 100 turns/cm. Initially, there is no current through the inductor.
2 32,. (a) (7 pts) At t I 0, the switch is closed. What is the current through the battery immediately after the
switch is closed? \ >
56 hi 5: so, rr cut through , ﬁst 75:0} [member does a W ‘5 1?" i 4: Wm"
39 l :33?» is?) i 2: “13:5” 2" ‘5: ” a» Mrs“ E rm
immi (b) (9 pts) After a iong time has elapsed, the current through the inductor is constant. What is the
magnetic ﬁeld in the inductor at this time? ,. , . r .
Ash; if 3.: so) Loxff‘téufif 5:352: 5:21 i” Q0131 ate / y m ‘ f it
earass if; daisies a Iii: si‘s‘im % ‘5’; b "7 Egg” 3”” e; ' “9 ’1"
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a 3 i9 R 5} r: iih) } 9 WE >45. 455: 2 ~13 """'i :3, F [D ,3
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—.2 (c) (5 pts) After a long time has elapsed, the switch is opened again. How much total energy is dissipated
by each resistor from the time the switch is opened again, until the current through the inductor is
again equal to zero? (Hint: do not attempt to solve this problem using a power calculation  we ask for total energy). ‘ I g If 4‘ ‘ a as? g €142,ng stored to tnﬂvlatdi'ﬂ 1‘“ ma saw ﬁeryWW6?! éi 2
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i _ ,1 i P“ a $5; 2 2 gm??? dissipajiﬂi $7,? resistor“ 1‘5; 4.; 3‘.” Problem 3 (22 pts) In the ﬁgure, R : 14.09, C’ = 6.00pF, and L = 54.0mH, and the ideal battery has an emf of 35V. The
switch is kept at a for a long time and then thrown to position b. (a) (6 pts) What is the charge on the capacitor immediately before the switch is ﬂipped to b?
4 W’s ~,é:
F is .
a Q . I f0 C (b) (4 pts) What is the angular frequency of the electromagnetic oscillations? l i "WM—MW WWW,“me :1 (l: g {3293 (9541’; E:
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an" 3 E
“5 2M9 “9 2i): 'iugﬁ K53 = 9,35 A (d) (6 pts) If the switch is thrown to b at t = 0, what is the earliest time when all the energy is stored as
magnetic energy in the inductor? 10 Problem 4 (21 pts) A green beam of coherent light with wavelength of 54011111 is incident on a plane with two slits a distance
0.2mm apart1 producing an interference pattern on a screen at a distance of 900m, with its center aligned with the middle point between the slits.
Hint: you can use the “small angle approximation“: sin (9 a tan :9 a: B. (a) (9 pts) At what vertical distance from the center will the pattern have the second dark fringe? Draw
a diagram explaining your answer. nun“ I E ' “5 NHL:ﬁ‘h
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A > 2:”! M W d S Q ﬂit} if \ I) T ’<" “if”: i in t“ .37; r: \ 4‘ f2}
elm 0:2; is it} ~ east? is w. e r L ‘ »’
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F3 ‘ : 3 5.0, f Wtsem M" 3W 4H“ (b) [5 pts) What is the path length dilference of the waves traveling from each Slit to the point you found in (a)? A1, 2 @43ng = 3/2 h
0 A/2 /\ \w/ (c) (7 pts) If the incident beam is an infrared beam with wavelength of 1064 nm, wiil the distance you
calculated in (a) b arger, mallet or the same? Explain your answer. .7". x J} m i _ ‘ bl : i“ i“ $0 9’?! 3x lI/i ems ﬂail", "50 5W ” “f w
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