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exam 4b sol

# exam 4b sol - )~-l ‘05 35 Physics 241 Exam#4\«jl Name*4...

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Unformatted text preview: _)~-l ‘05 35% April 27, 2007 Physics 241 Exam #4 \«jl Name: \ *4 , Section: Electrostatics: Electronics: . ~ I; . Cmﬂomb‘s Law: F : [112qu- Cnpncimnce = C = g T , ﬁcliff'i’2Er If ~ ‘ “ ’ ' ) Resistme = 1?: Z a? f Gmms’s Law: / E‘- Jr? : QM“! I H surf ('0 [= ; ,1 Z L. rlt ‘ (in (‘27- E = L1) “0 Hm = R( ‘0)[1 + an — 711)] I 4 p 2 1} g (I : El! . A 2 ﬂ (I'D (In :1] inﬂ : P : [V N ‘2 , 1? 1.: 2 = as >< 10“ C7,; ; F0 = mum” I) ] m0 " A '" Conductivity = r} z ; J = 5L I Potential: AV : -- j I? - rlf 5 = EMF = AV [or :«m inleal buttery f5 : _ 7 j K TV Energy of elect. chm-go: U : Vq Magnetism: -1 ﬂ 7 7 'nmgm hr ‘— (17- 5‘: 1’ Problem 1 (20 pts) Problem 2 (20 pts) A a I M? X r- Bmt—Snmrl. Law: rlB = [—1— —— Problem 3 (20 pts) ‘lTr r2 Problem 4 (20 pts) {m : 47-: X ll)”:w .42 l :42 ' A Problem 5 (20 pts) d _ z a Aztlpnr'c's Law: %B-dl' = ‘11” [MM +ln)e(|(— E-dr—J. . . mrj .4 A. ' .l TOM! (100 pts) — l“m‘mln}"s Lzm‘: j! I} ~ (16 :: —(TL / B - dFi _ u Nu“; Magnetic Menu-mt: ,v". 2 LT Energy of mag. rrmmenl: U : q? B Problem 1 A solenoid of radius RJr that is wound with N, turns of wire per length d is supplied with current that changes as }'= Gsin(col)i A small coaxial coil ofNC turns and radius R: is located inside the solenoid near its Center. (a) Derive an expression that describes the manner in which the emf in the small coil varies in time. (b) At what average rate is energy delivered to the small coil ifthe windings have a total resistance of 8 Q? ’ Ills: N5 Trial Mock: View” 5 L9» Biol rah—5 D ' M l 1 <r>rtwiwmzmeq :Msgaww s ,, r W ﬂ” 1 , m , o l x :— # klo My 5‘: Wk Cew‘i “J l 'l /I A _ _ L), ..... ~;c__H__V J__.w7 ~ ’ ' M‘L L i l “r r j a. \.2 ..v A ‘ i [10 i r w \r ._., l N C “ ‘* C i we” w 5’ l W. ‘L I 5 ,.,._ ProblemZ r" ix‘l if}? 1'}! ’J Ly x An electron with mass me and charge q=—|e| is moving in a uniform magnetic field and follows a helical trajectory. The magnetic ﬁeld is B=Bx i and at some instant in time the velocity is v = v_,i + vyj. (a) what is the radius of the helix? (b) What is its pitch? (c) Il‘vr, vy, and Bx are all positive, is the helix right handed (like a typical screw) or left handed? (d) What applied electric ﬁeld would make the trajectory linear? l A‘,//’ a ‘1 -' _W_HJ H # t x l 7 “‘11 W> ii We __ £11 1‘4"\ , 3 g I I ‘r " an" V - i». rwﬁwaw‘ My ~ ‘M‘H M "a H u h“ b“— l 1M1 45. i l :9 M H“; M 2m in \l *’ Q M ‘1 \ r \ \J‘ 7\ “w M_M,-,,_- — - f/ N -‘ l 55V.l\) l 1 L ‘ “’2‘ , I v “ E L. l" ":ij 15} Problem 3 The ﬁgure shows 21 top View of a bar that can slide without friction, The resistor is 5.00 Ohms and a 2.0 T magnetic field is directed perpendicularly downward, into the paper. Let d = 1.2 m. (3) Calculate the applied force required to move the bar to the right at a constant speed of 2.0 m/s. (b) Calculate the rate at which energy is delivered to the resistor. l ,r-i m 5:: WM L, -' 9—1 l r "a PM :2» M _ _ e a wwwvw-x H l I ) w. x I, “” ” El 1 1 “as: x T / W M 513:; ix] w; P 3 IV" A l r: ,5 «MMMWW‘ ’ M -) “*"T‘WM l r“ ‘ ~ e 1 "MW v w ~ - .9: F723 N 3 ‘ \‘ﬁj *‘ “ f A .. , 0"” , _ i '” L) ? W “W” ; lad—“4w”: : L1, w i : Foxy. i "\L ' Problem 4 (a) What is the direction of induced current in resistor R when the bar magnet moves to the left? (b) What is the direction of the current induced in resistor R immediately after the switch S is closed? (c) What is the direction of the current induced in resistor R if the current in the wire is 15515 W“ I increasing? (d) What is the direction of the magnetic ﬁeld if the charges are induced as shown in a moving bar? Problem 5 Along cylindrical conductor of radius R carries a current] along its axis. The current density J, however, is not uniform over the cross section of the conductor but is a function of the radius according to J = br, where b is a constant. (a) How is [3 related to 1 and R? (b) Find an expression for the magnetic ﬁeld B at a distance r < R ﬁeld B at a distance r > R. .‘ J "_ (c) Find an expression for the magnetic M” > C, . [9 (x , t: a” b 2T1? lk M ii: Err iﬁ M“ u‘mmA—F»» M WWW“ l _,_V.. vy—W‘w— “Muses.” 3 W “My” . -a 4|n~>>~¥—<‘1 \K‘Mu v- - ’ ‘4’” "m" A _ - .4 ‘ \ 2n r l t \f (I j} 7 > g a N‘ d » dL—‘ —-.~\‘ , ~\ \ New- L J 'k ) # I]! J“ A“ .- ‘ .«t '1 / y”. «K I i? if, I ‘- . wt. V u» *- d.»~ \A “I‘M,” —.ie' N“ W _ \ i" YA 7' ll ...
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exam 4b sol - )~-l ‘05 35 Physics 241 Exam#4\«jl Name*4...

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