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2009finalsolutions

# 2009finalsolutions - Fﬁmaﬁ Exam BMWH n a Name 1 Z...

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Unformatted text preview: Fﬁmaﬁ Exam BMWH n a Name 1 Z Agwwww4.mwsmw; - a - L f g \$9.? 55? 51‘ w kg «2%.. a “2% “3% «3 59\$ Campﬁex Hmpedamm imL Emﬂucmr: 1 iwC ‘9 a u Capadtar Prohiern 31 True or Faiee Quentiong (a) Flux of Magnetic field through any closed surface is zero. (c) A straight current-carrying wire has a finite inductance. ' my?» w. ., m, 23‘“ é: agar/V kw, (d) inductors can store energy“ (e) Electric fieid inside an ohmic resistor Wire is directly proportionai to current through it, Prohiern 2 At t = 0, a charged particle with charge ofq sits at (0,0,0):[X,y,z). At this point” an electric field pointing in X direction is turned on. The magnitude of electric field is E. t E = (E,o,o)] (a) Write force on the particle in the vector form (b) Find acceleration in vector form (c) Find the location of the particle at t=tr ‘“ '"v e f rf'K N5 ‘ N r i '5? it: ‘1 M j i t; \»"\- Y 3“- M,“ j a (‘ a; f /7 t t“, . , ‘éx 1‘ X?) i i v s M 1 ‘ i; a i 33 2 We J a v; x» y X Prohiem 3 A charged particle with charge of q has been accelerated through a potential drop of 1000 V. After this initial potential drop, the particle does not experience any force due to electric field. You may assume that the particle is moving from left to right. (a) Calculate the energy ofthe particle“ 1 eV 2 106x101”. (b) Calculate its velocity if the mass of the particle is given by m. After a While, the charged particle enters a space with magnetic field, which is pointed perpendicular to the direction of its motion“ The magnitude of magnetic field is 1 Tesla and is pointed out of the paper» (c) Calculate the force on the particle due to magnetic field. (d) [Calculate the magnitude of velocity of the particle in this magnetic field. (e) Draw the motion of the particle in magnetic field. (f) Does the magnetic field change the energy of the particle? . \ Mia e a» ’ e “‘ ‘2 '_ w v»... rW f 3 it? w 5‘ é m i; 53% a" i ‘ f a W “Mm. ‘ 3 a2 3}“ma 53 “’2 ”WWW“ ‘V'V*‘\$‘='-.s>”" 556‘» a"? guy 3"! .21? ‘ ”.7” “whim r” ‘In “a Problem 4 Uniformly Charged Solid Sphere (note it is not metallic) has radius R and volume charge density p. Calculate electric field (its dependence on I”) (a) for outside the sphere (b) for inside the sphere Calculate potential (its dependence on r) (C) for outside the sphere (d) for inside the sphere (e) Does potential vary inside the sphere? Problem 5 A parallel plate capacitor has been charged so that one plate has a charge of i. coulomb and the other plate has a charge of —1 coulomb. The distance between the plates is 1m and the area of each plate is 1 m2. (a) Calculate the electric field inside the capacitor assuming that there is no fringe field» (b) Calculate the potential difference between the plates (c) Calculate the capacitance of the parallel plate capacitor (d) What is the energy stored in the capacitor? (e) What happens to the voltage difference if the distance between the plates is reduced to 0.1 m. (f) if the space between the plates are filled (completely) by a material with dielectric constant of 4., t t f a we, we" we ‘ k 41 “I; K? ‘1 t.) N. ii if Elf/W w a u 1i wv‘wﬁx ” 0" w , j v. i ’11 5 r . A»? r; w, " V a x“? X — a *‘ ‘ kw l .‘k W W ‘3 £ t; ”tr ” w i c" «'91 a: any" M W ,‘ ”Ant 3 , x a a l 1 a t a Wu K a w W l w L» ‘25 «3 w“ 1 ml" m; 3w § gm .7 £17” Vet, , he, Prohlern 6 mpgeﬂﬁ. . imertﬁafqug(§mg 9 fxelﬁﬁﬂ'éwiém: we” A,“ Aweigh-c5»: J hwxﬂywazm'“ uw gun—m: ... Given a series RLC circuit as drawn and an oscillating driving voltage answer following questions° l/(r) = Vmax cos(mt) (a) Calculate the total impedance of the circuit (b) What is the expreSsion for the phase of the current through the circuit with respect to the driving voltage? You can assume [(1) = [max cos(mt — o), (c) Draw a graph for power delivered versus driving frequency for the circuit. Be sure to define x axis as frequency, y axis as power delivered and clearly indicate the maximum power delivered. (d) Draw a graph for the phase of the current with respect to the voltage. (e) Calculate the frequency at which power delivered to the circuit is maximized. E 74 « '1 yr ‘~ r um“ M y L 3 vi» ‘3 ‘” 223*» I?“ ” m.a 7;? ‘1’ 20, we ~ ,~ ,1 ‘ 1: r :93: “1”» a? E ‘9’ {a H m, c A W if» i" s a W i 3 Y t; ”it W i 3 , 4 “Ma-m v, ‘ Vi: w t‘ a 6, M » " {kw MM WW hummus”. W. mm, g the," 9:13.: E p 3 1 t 1‘ “v t ,1' at a 1‘ ‘t 3 3 \$1. -. (p ’4», i t z; “a. t i it,» a w W. W Problem ’7 A solenoid has a. length l, N total coils and cross sectional area of A (HRZ) (a) Calculate the inductance of this solenoid (b) lf a current, l, ﬂows through the solenoid, how much energy is stored in the solenoid? (c) What is the voltage drop across the lnductor when there is no change in current? (cl) What happens to the voltage drop across the inductor when the current is changed at a pace of or amperes per second? u ””5” “L l ‘1 hm”? v1» g Q m, r“ :w. 53x i . t ‘ 14cm» “M 3 {a W k 4 l; ’w i 1*": ’ " : ”a x =-'- “c, w =~‘ « 4 ‘ M;,_,.r t _ - A, " cam 1 ‘l ”“ {,3 5: . ’i “‘3 ”a ’“t ”J‘s ; «e g “a“ ' é“? 2w n, W a’ “w- “:4 R «P‘- m g 4% t (we % e, 3 \$1 wt ‘9 ’3" view ¢ K {new ”" 3‘ , he 3 23”” b g a; w“ 5 {A ’33; , Ex Pmbﬁem 8 t Emmi Eaﬁwﬂam Hi and E2 in the a shgwm Baffin mi 7; W View use mm; ...
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