This preview shows pages 1–7. Sign up to view the full content.
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 Document
Unformatted text preview: PROBLEM (1} (25 points) 09  6W Wﬁm®
Two inﬁnitelyr large sheﬂs of charge are placed
parallel to each other. as shown in the ﬁgure. The
surfaeechergedcneitica a1: 4x1HCimz and
a: ="'8"x* 1H Ciml'itr'ci tlinit'cvrmlyr distributed
over the slicets. {Take' £6 =9 >4 "H? (gmmg}. ' I.
(it) Find the directien and magnitude of the electric ﬁeld E. in regions i'. H. and Hi. State the ' 3 cm——>I
direction according to the axes given. " ('1‘! a, celledﬁat Gﬂuﬂldm Wﬁq : : LGaUﬂth«t cg
with End W5 ef‘nm d “‘4. GMSL' In»: M @
jﬁw' Gaelsum wﬁqﬁj gé’g' 63“ = altw: ‘_"" “E15: Ear/‘12:“;
.5 I" ” Erﬁl (13} Find the potential difference between points A and B. t f e a a q
“j; ' "'6. 1 'IEE' 43 ———> vb 11; = aye“. a? #4?de )+{fe3as)
1 C E II 1'! c UUfEZJJE +6... Eds =—§m"(ﬁil+ entire;
5 :1. C '5’:ch EE 7” 314‘; Phjls 1'95 Finalﬁm Page” June hm 10  '
PROBLEM {2] {15 points) ' Two erieal. thin conducting shells. with retlii e and b are placed fer . but ennnected to each
other 1 thin. long ennduettng 1wire 15 shown in the figure. The III are uncharged. A point
charge+qietben planed Entire eenternfthe targetsphere. Find the chargedien'ibtttinne, intlueednn
the inner and outer surface: of bath spheres. in terms of the parameters given. M3 cling: . 5L; 1a Phylﬂbﬁnttiﬁm Pup#9 M5,!“ 1 1
PROBLEM (3} (15 points} ' t“ The circuit shows an ideal battery, two cspuci 
totsC.andCz,sresistotRsndaswit¢hS.With _ ' R
capacitors completely uncharged, switch 5 is
closed on point a. When C1 is completely I  I
charged,3isthrownfromatobsttintet=ﬂ. V Cl ('4
(a) When equilibrium is reached (i.e.. 1—) on) 
what is the potential difference across each 5
capacitor? a b ' "' '  :
0“) WW C1 v.1. mFiM chat/v3th Mel«Mac is ch = CH,
if 5 s mm m as b sawcm m .
Mi‘f‘tbullLJ Lewem ....C', Ml. a3 sum W Mfiutal cWW
be” .n ,. .  qwsjuit =c,v I
can" +c',_UJ = C, V .I .r ii
Up =U'L =i/
I}! V;  u—E—L— V ¢I+¢L {b} How much energyr is dissipated as heat in tesistor it from t = D to tn on? q——l—IC .> t
j 'I i;I___'_c I. L
..Mwa~1uhmtpa§b,d z. ~J——¢+tt V Phys we Final Emu masts June 5. 20m PROBLEM {4) (15 points} A battery of V volts is connected across the
ends of a cylindrical conductor of length L
and resistivity p. as shown in the ﬁgure. The
number of free electrons per unit volume of
this conductor is n. In terms of these parame
ters, ﬁnd the magnitude and direction {accord
ing to the given axes} of: [a] the current density J in the conductor: (h) the drift velocity YD of the free electrons in the conductor; a [c] the magnetic ﬁeld B at C. inside the conductor. at radial distance r from the axis. Usnhj Mpm's (aw, we. Md d5! = 33 [Sec19:19 Phys ME Finat Emu: i‘yo the Bra/{E} an, : fir?) —9 B: h v ﬁe
bi" = 15:“ ‘3
__.___._.......___._J
AJF
.2.
JIM5.2mCI PROBLEM (5) (15 points)
Apointlchsrgeq.withmasamisprcectedintoare~
on of uniform magnetic ﬁeld B, wijth an initial W:
ocity 1'. making an angle of s 1with the magnetic
12:13:. a; shown in the ﬁgure. Sincepglﬂraloci ofthe
particle has a Went to mag
neticgc ﬁeld. the particle 1hull move in a helical path
about the direction of the ﬁeld vector. (a) Does the horizontal velocity component affect the
radius of the helical path? Explain. NG "Mc prmaimm mmﬁm
dﬂwm’m W oi Me Warm.  i a L5, = “m 9 «a some ems... a...me cumin Helical W = you + spiedc541 Tim. mew; of‘hut mm m i. rota/ha 4e MUCMJMdhbAtt U1. M 915': U}: .
(h) Express R, the radius of the helical path, interms of the parameters given. elf ‘_MU"M;1§F
R=iqT§— ﬁg" glib (c) Find the distance x, where the point charge crosses the horizontal line that passes through the
point of projection. PhysIDGFtnniEum Mei’9 JuneJJtﬂl PROBLEM {6) (15 points) A thin wire of resistance R is bent to forth a square
loop with sides of length L. This loop travels at
constant velocity 1' through a re ion of width It in
which a uniform magnetic ﬁe d B is resent, as
shown in the figure. Draw the gra it of t induced
current in the loop as a function e x. which denotes
the position of the right hand side of the Imp. Label
the clockwise direction of the current as positive, and
the counterclockwise direction as negative. in your
graph. Give the magnitudes of the current on the
graph as well. :xxxxxx{
XXXXXXI )4 I X I x:
'l‘ I X X K K X X:
l. :x x x x x x:
Btintethepsae} TL“ JCiLU‘ is zero wines Wimp r}. not sit "I‘m field; H: is BLJ' .WL‘“
W— lonw is» caskets v: M can. as a. 3L1. when 41.1,:us PM'H euj Behring Mﬂﬁﬂ} Ms W H: [5 BL'CL— (x—zcﬂ when
M19011 'gaoriiqﬁﬂq lamina W; 435 V5 xgwit” 4%. i.‘:—d¢‘= 3::— Phys ms Fm: 5mm Fuse $9 ole : 1%0‘ = — (slmof the 1.3%") ir Jm5,2000 PROBLEM (7) {15 points) 1 5 f
The circuit shnws three ideal batteries. three resistms,
an ideal inductor. Initially switch 3 is open. but
closed at time t: D. (It) Find the potential difference across the inductor,
just after the switch 5' is closed. lniiiaﬁﬂu! aw. iciui L41de sarir?
W awn; 4w; WMWH a
rt} itadsmMcpucﬁrmdtst
13:5 Ma WM wwrlwi' fem): wilt MM (MM. FW I'wrl ﬁfeE : +3+tht=°)—?=o —J Mitwﬁiéﬁl 4344. M6 0? Mtgﬁuw “nadirFa S'L‘Ai dot W
Winona WM ‘i‘vu, Euﬁ “gawk M 24 {b} Find the current through the inductor. a "long' time after the switch 5' is classed (ism. t —> on}. A [diam J an I'M ads “th. asW'i ﬁlm. Tim'ch iiibit“) =0: Leftism hm. mwwi v34 loop baft. PhysiﬂﬁanaiEm WW9 Imim ...
View
Full
Document
This note was uploaded on 04/09/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.
 Spring '12
 OnurFen

Click to edit the document details