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Unformatted text preview: Department cfPhysica. Lehigh University
Pliyaica El  Introductory Physics II Spring Zﬂiiﬁ F ina] Exam May 3, Eiiﬂﬁ
Closed Note 3:00 AM~1 ] :ﬂﬂ AM
Snident’a Name Recitation Section Nmnber Recitation Leader’s Name =¢gl=—W
The teat is a muitjpieachoioc examination. First, check to he sure that you have twelve— page examination, including the cover sheet and the equation sheet. Please answer each
question by circling one answer from the panel ofchcicea available within each question Space.
Points summary
Part I Part I] Part In Total
1.___{2o} 4.__{15} i._ [15}
1—90} 5._m_ [25} a._ [25}
3._ [25) a. _ [25} 9._ (15}
1t}.__ [15)
SubTotal
{55) _{55) _{?c} _{2ﬂﬂ} Part] («65 points} P l. (213 paints} Two charges are placed a distance T 312] em apart. One ef them has aehaIge of "IS m cm Itiiereeeuiembs, and the other has negative 1'5 +T5 at 15 “c miereeeuleml} charge. as shown in the ﬁgure. .__i_—.
15 em 1:: em A. What is the magnitude of the electric ﬁeld at
paint P shewn above? i.) s; ii.]4.1? x mime; iii.) 3.5 x mime;
arias x mime; v.) T w mime 13. Which efthe arrows shami helew give the direction fer the eleetrie ﬁeld at paint P? i.) ii.) iii.) iv.) v.) No ﬁeld
(3. 1What is the magnitude of the force exerted on the positive charge by the negative
charge? 1} 2250 N ii} 158.3 N iii] ii N; is} 552.5 N; v} 337.5 Poi. D. What is the magnitude of the electric dips1e menith of the charges as an electric
dipﬁle‘? i} 2.25x1ll‘5‘ Cm; iiia1.512I><1EI'5 Cm; iii} 2.25:: 113'3 Gm; w) 1.13x1tr5 em; v) Ii. 2. [213 points} An isolated capacitor is
composed of two parallel horizontal plates. n. The capacitor is fully charged. If a thin
dielectric is inserted a short distance
hehaeen the plates, how will it more when it
is released? i] up; ii} down; iii} left; iv] right; 1r] stationary. B. When the potential difference across 1he gap is 95f} V, the parallel—plate capacitor holds 2.3ilx l 3'3 C of charge, with the gap in a 1raeunrn. If this gap is ﬁlled with a
material of dielectric constant K = 2, what is the total capacitance of the system? i) c: ass nF; a) o: ass as; iii] C=2.95xlﬂ'm s;
is} C= 1.1sx1tr‘“ F; we=s_ssxrc'“ F. C. A parallel plate capacitor is connected to a T5 1’ battery,F and allowed to charge fully.
The capacitance of the two plates in ﬁnespace is 2.6 at". If the capacitor is then ﬁlled with a dielectric material arpamaaasr s = 5.31 a or” clr (N ml), with the baaer am
connected? what is the change in the charge on the capacitor?
i} Charge increases by a factor of 15; ii} Charge decreases by a factor of 6;
iii) Charge increases by a factor of 2; is} No change; 1;} Charge increases by a factor of 12. If the hatter}r is now disconnected from the capacitor, what is the change in the energy
dentsit},r within the capacitor? i} Charge decreases by a factor of ti; ii} Charge increases by a factor of 2;
iii} No change; in) Charge decreases by a factor of 3; r) Charge increases by a factor of ti. 3. {15 points} The ﬁgure shows three separate pairs of' parallel plates with the same
separation; the value of the electric potential is also shown for each plate. The electric
ﬁeld between the plates is uniform and perpendieuiar to each plate. {1} I till l (3} l dd V +15t] V at: V +200 V see V 40h V
A. Rank the pairs according to the magnitude of the electric field between the plates;
greatest ﬁrst. i) i=2=3; ii) l=2,3; iii) 3,2,1; iv} 11:3; v) none of the above
B. For which pair is the electric ﬁeld pointing to the right?
i) 1; ii] 2; iii] 3; iv) 1&2; v] none of the above.
C. IF an electron is released at the center of the plates (case 3); what will happen?
i} remain there; ii) rnove rightward with a constant velocity;
iii) move leftward with a. constant velocity; iv) accelerate rightward; v] accelerate leftward. D. The ﬁgure below shows; in cross section; three cylinders; each with charge Q per unit
length. Concentric with each cylinder is a cylindrical Gaussian surface, all three With the
same radius r. Rank the Gaussian srn'faccs according to the magnitude of the electric
ﬁeld at an}.r point on the surface. listing the greatest ﬁrst. {a}  . . (bl. """""""" r r
I' i‘
+++++++ " i} a=h=c; ii) a,h;e; iii] c,b,a; iv} a=h;c; iv} none of the above. Winch of the three cases has the highest electric ﬁeld strength at the surface of the charge
column? i] a=b=c; ii] a; iii] h; iv}c; iv] none of the aheve. Part II [65 points)
4. {15 points} The ﬁgure shows {our wire loops {a= h, c and d], with edge lengths of either L or 212. All four loops will move through a region of uniform magnetic ﬁeld
(directed out of the page) at the same constant velocity a same A. Rank the four loops according to the maximum magnitude of" the emf induced as the},r
move though the field, listing in the order of the greatest first. ilalbﬂLc; ii]a=h,c=d; iii}e=d,a=h; iv} e, d, h, a; v] none of the above.
B. The graph gives the magnitude Bt’r} of a uniform magnetic field that exists throughout
a conducting loop, perpendicular to the plane of the loop. Rank the ﬁve equal time regions ofﬁtc graph according to the magnitude of the emf induced in the loop, listing in
the order of the greatest ﬁrst. Bill i} a, h, e, d, e; ii) c, h=d=e, a iii) h=d=e, a, e;
iv} h, d=e, a=c; v) none of the shove.
C. if the speed of the loops is tripled to 3 i3 , what happens to the maximum magnitude of
the emf'generatcd in each of the loop?
i) hostesses by a factor ofﬂ; ii) Decreases by a factor of 3; iii} No change; iv}1nereases by a factor of ; v} increases by a factor of'l 5. (25 points} An electron is propelled into a uniform magnetic ﬁeld of [LES T, with
velocity 5 x in‘5 me, in a direction perpendicular to the applied ﬁeld. a. What is the magnitude of the force on the electron due to the magnetic ﬁeld?
a r sin” n; ii}4 x Ic'i‘n; an: stir” in; a} a. E. 1What is the radius of cun'atore of the electronic orbit in the ﬁeld?
i) 1115 cm; ii} I192 mm; iii} T.i mm; in} 13.57" mm; 1r) infinity. {2. What is the magnitude of the magnetic dipole moment of the orbiting election?
a inane” emits; in inane” Crmlr‘s; iii)].43x1tl‘” emits;
iuj2.onlﬂ']5Cm2fs; u}?.l$xlil']6Cm2ts; D. Suppose that the magnetic ﬁeld is conﬁned ndthin a circular crosssection ofScrn
diameter, and the electron is orbiting around the center when the magnetic ﬁeld is [HE T. if the magnetic ﬁeld is now decreased at a rate of tl.9><1 [1'3 Tie. how long would it take for
it to be no longer possible to contain the electron within the hon? i} TELS 5; ii] 23.1 3; iii} 54.9 s; in} 35.6 s; u) inﬁnity. E. Suppose nonr that the magnetic ﬁeld is gradually.r increasing at a rate of 5x ill"3 Tia.
How long still it talre to deemsse the radius to zero [i.e., to essentially.r hold the electron in place}? i) 'ltlj 5; ii} 23.1 5; iii} 54.9 s; in) 3513 s; v) inﬁnity. 6. [25 points} The transverse displacement of a string in a standing wave is given by
D = HM sin {0.35 :t') cos (4? t), where .'t and D are in meters and I is in seconds. A. What is the distance between two successive nodes?
i) “15 m; ii) 5.25 in; iii) Eli] m; iv} 91} m; v) 2.9 m. E. Noting litat the standing wave consists of two counterpropagating waves, calculate
the amplitude of the component waves. i} lﬂ.5 In; ii} Ell] m; iii] 5.25 rn; iv} III}.5 cm; v} It} m.
C. Find the speed of the pattieles of the string at I = in to when t= 3.5 s.
i} an ma; ii} an ma; iii} eta mis; iv} 3.3 ms; v) as tnfs. D. Let us now imagine that we have a standing electromagnetic wave in a thin fihn of
magnesium fluoride {index of reﬂection of 1.33} deposited on a slab of glass with
refractive index of 1.54. If the thickness of the thin ﬁlm were Eﬂﬂ ntn1 what would he the
longest possible wavelength {as deﬁned in a vacuum} of the standing wave in the thin ﬁlm?
13551 Inn; ii] Zita nm; iii)425 nni; MESH nm; v}3?5 ntn. E. A. neutron is a patticle of Ltihtlil'” kg in mass but has no electticat charge. To have
a standing wave of neutrons in a onedimensional gap between two parallel plates of
gold, what would be the smallest gap thickness needed for a neutron of 1 eV in kinetic energy? Part III (79 points in total}
T. (15 points}
Consider imaging by spherical mirrors. A. If one wishes to produee a real image in a mirror that is upright and larger than the
object, what kind of mirror would one choose? i} Convex; ii} Coneave; iii) either would work; iv.) neither would not]: B. Suppose an object 2 out teii is placed 13 em in Front of a convex mirror whose radius
ofeurvetme is E em. ‘Wnere is the image ioeatedi' i} ﬂ.3ﬂﬁ cm; 1032? ens; iii) 5.14 em; iv} 6.14 cm
'3. What is the magniﬁcation of the image formed by the minor? mus; ii} eon; iii)[l.29; ivy0.29; v] 4113 3. {15 points} The ﬁgure shews a ﬁsh and a ﬁsh stalker in water. "i A. Which ef the Fellewing statements is eerreet? i) The stalker sees the ﬁsh near peint a and the ﬁsh sees the eyes ef the stalker near point e.
ii} The stalker sees the ﬁsh near paint a and the ﬁsh sees the eyes ef the stalker near peint d.
iii} The stalker sees the ﬁsh near peint h and the ﬁsh sees the eyes of the stalker near neint e.
iv} The stalker sees the ﬁsh near peinl h and the ﬁsh sees the eyes at the stalker near neth {1.
s} hiene ef the above. E. New assume the water level inereases te a level aheve neint e. Whieh statement is
correct? i) The stalker sees the ﬁsh near peint a and the ﬁsh sees the eyes ef the stalker near peint e.
ii] The stalker sees the ﬁsh near paint a and the ﬁsh sees the eyes ef the stalker nearr peint :1.
iii) The stalker sees the ﬁsh near peint h and the ﬁsh sees the eyes ef the stalker near peirtt e.
is} The stalker sees the ﬁsh near paint h and the ﬁsh sees the eyes at the stalker near peint d.
1r} Nene ef' the above. {3. The stalker eententplates using a lens. while the water level is at e, to see the ﬁsh
better. He has a lens whese fecal length in air is it: ern. What weuld he the fecal
length ef the lens when the lens is fully immersed in water? The indiees efreﬁ'aetien
are 1.33 fer water and 1.53 fer the lens material used, respectively. i} 33.? em; ii} 31) em; iii] ll.'.lI en; is} 3.4% em; a} inﬁnity. 9. [25 points} A given star is known to radiate atotal power of about 5 I lﬂgﬁ W. An
observer on the Earth measures the intensity of the star as 6.52 X 10"” Win12. A. What is the alpproxirnate distance ﬂora the Earth to the star in parsecs {pc}? Note that
1 pc = 3.139 K It} ‘5' m. .ﬁisstone that the star radiates light equally in every direction. i} 4 pc; ii) 11 pc; iii} 3 pc; iv) 2 pc; v} 15 pc. B. What is the rms strength of the electric ﬁeld in the radiation observed from the star on
Earth? Magnitude i] [1.5 ii} 4 iii} 0.15 iv} 9 v} 0.? Units
Um]; ii.}nﬂf; iii.}m.iW; iv.)mNtC; v.) Both iii} and iv]; vi.}Nonc of these. C. A second star is thought to he nearby but the feasibility of resolving the two stars with
a telescope has yet to be established. 1With a 3—meter telescope operating at 6th} nrn
wavelength, what is the smallest possible angular separation of the two stars in the sky that can he resolved?
o ateno6 rad; a) scale? rad; an assist rad; iv} 2.4s1o'iraa; v) arena“5 rad. D. You have a Polaroid sheet, whose polarization axis is arranged vettically. A second
Polaroid sheet is placed behind it in such a manner that its polarization axis is at a 30"
angle relative to the polarization axis of the ﬁrst sheet. A third sheet is added behind the
second sheet in such away that its I polarization axis is at a so“ angle relative  1" to that otthe second sheet. 1What is the Light
intensity of the light after eroan all {1. tin ' three sheets when an Linpolarized beam of light of intensity In is incident on the {U ' '
ﬁrst Polaroid sheet? 1} [LSDD Ia; ii}ﬂ.3?5 Is; iii)ﬂ.928fn; iv)ll.21?l'ﬁ; v) 01393 In. ll}. {15 points] A thin dielectric foil is full of eireular holes ofapproaimately 1 nm in
diameter. To make measurement ofthe diameters of the holes, a hoam of electrons is
seleeted as a probe of the ditu‘neter of holes by electron diﬂaetion. A. lrllt'hat should he the lowest value of the eleeIIon speed in the beam for this task?
i)2.25x1ﬂ3 me; a} 2.99mi me; iii]7.25x105 mts;
tosaoxtotnes; v} 1.25xlﬂﬁnﬁs; B. To achieve the distance resolution of 1 nm or better, what should he the smallest
Hnmt‘lﬂlﬂtjt in the magnitude of the eleenon momentum that must he held to? :i} Lester25 kgmfs; a} Lt‘tﬁaiﬂ‘ﬂ kgrmts; iii) Lesxm‘t" legmats;
iv} lﬂﬁxlﬂ'gﬂ kgmr’s; «a matte” tagma; C. Ifa beam of alpha pattieles is to he used instead= what should he the lowest 1value of
their speed? J'ttt alpha particle is composed of two neutrons and two protons; its mass is 6.63x10'ﬂkg.
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