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# Lecture Notes PHYS 102

Drexel

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This page Bundle was uploaded by Satish Boggarapu on Saturday November 14, 2015. The Bundle belongs to PHYS 102 at Drexel University taught by Som Tyagi in Spring 2015. Since its upload, it has received 26 views. For similar materials see Electricity and Magnetism in Physics 2 at Drexel University.

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Date Created: 11/14/15

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z a v y WW W w u 3quot 39rr 5 A Z 5 Fr quoti A 5 6 uXl hf g g 3 i r gt f l x M C w v W 39 s M mmmwwm amammzmwgdm mmmmm 2 X m quot39 g r w A k I j WM 4 wk q vmueuup 27 was u w u xua WWW 4 Aw V W W dam up my 77 39 mumm 7x New WMquot 7w 1 if g I 34 1 g g L3 3 MN mu m m ark quot 7 quot mm 9h 391 43 A ltfqmmmun m r39v w zAuw 2 x539 I f quot1 11 2 39 rawamenity 7 r La W E Ni x M v A 5 LEI w W 3 f 7 7 iquot 1 0 a A 0 a m a 5 PM A if L Av a MAlt m r L a 4 4w 2 Mama a a s mh r 1 mqiucux r Ma a 1 q 5 k4th v i I mhnmm A 1 N Quixan L fk t5 r11 n5 4 5 twf n al if Exam E i lt I l g f n k 5 1315quot Mwaaa w A quotAw I 7 Wu quotWWW nun i J 4 l w HM mah kh Wm mmmmmmwmw w Mmvm M 4 i mwmw VNW a 1 K m e v p a V n a a L s i M 39 V 3 43 r V r r39 g muggy 1 v on iv 5 x w WCJ RWSWMH py V g madmww may f k quot r 2 2amp3 3 4 WWAMAHL t W 8 H 1 I F f g 3 E I lt 39 r l 3quot A J E k 3 quot Y r w 1 i ampw quot J I W I 1 WampGW WWMIW f g A d J 1 m an F 3 i a Jiguvww I v u39wm 1 w W a lt N N W e mxgxuzkaufzv r gt 19 gt 1 7 F P g v v W A MmJaM M1 lwd za lfd Nymwmwji39H a 7 1 by F e vWfr 4r quot1 r a Wb ew MAW mm m m W w 7 I quotWu 5 m 0 r I z m 3 A K J k a r s x s 3 r i it v27 K g i V a u a j bu f M qw J a If 5 I M E w u m rzil mr 2 339 9quot Itquot 17quot W a 2 wgm I W5 L mm wmmmr if 5 F quot 3 3 Maw a E 3 w 5 Bf 4 un quot 339 quot m i w 5 wk nq 1 m mm 4 4anyw l y 1 quotI xyM 4WV x A r39 Mquot M 72241 a r 4 My r 4 M R LI Y a I V P J w WWWmemnuW um mm a U M r quot 1 3 5 J 5 F M Emw r i W I 5 I a y M m 039 I t N i quot N x a A 41 v V gt WWWM FVw mx l m a 4 H mm wwwwh gt A V axem mud 2 MMVZAMW quotM m murq mam n5 M aa mg I wwwmq ma m k H 1 V duema n W w mm wk mPAlk i39 gtltr a www m nummua h m kw Runny m 1 14 3 humm 39 MyraWzk x 1 if k w 1 1 K A Migt gkfwwmw k 39 myquotth mmn39vrmm39wwMW HHquotK w w 3 a 44553 M a m x w OUTLINE OF SOLUTIONS PHYS102 FINAL EXAM SPRING09 Time allowed 2 hrs Name Please PRINT Recitation Sec Notes 1There are five problems in this Exam 2 For Prob1 please circle the answer of your choice for each part For problems 2 5 your solutions must have adequate details and the answers must contain appropriate units to get full credit FBq17gtltB Equ BIQXE 8Blv EdizluoIm szQ IZQZ d ldlzxr 14neok9x109Nm2C 2 8 A At r 47 r k VQ kQ1Q2 1 1 1 r U T C QV ser j jzan C C1C2 AU 2 AW ed AWm V IR P 12R AwAt Ed U QV2 Ex dVdx 0 47r10397TmA Rse es R1 R2 R3 lRT 1R1 1R2 1 R3 1G 10394T me 9x103931kg qe 16x103919c ac v2r 1aThree charges are placed in a line as shown The total 9 9 potential energy of these charges is 0 0 a 05kQ2 b 15kQ2r c zero d 15kQ2r 1b When the charge on the plates of a capacitor is doubled the magnitude of the electric potential difference across the capacitor a is double b is halved c remains the same d quadrupled 1cA at coil of wire consisting of 40 turns each with an area of 500cm2 is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 20 T to 50 T in 20 s What is the magnitude of the induced emf in the coil a 03 b 060V c 300V d 080V 1d If a charge is moving with uniform velocity V under the combined in uence of an electric field E and a magnetic field B then a V is parallel to the Bfield b V must be perpendicular to the Bfield c V must be perpendicular to the Efield d the E and B fields are antiparallel to each other 1e A charged particle is moving perpendicular to a magnetic field in a circle of radius r When the magnitude of the magnetic field is doubled the particle moves in a circular orbit of radius R The ratio of the two radii rR is a 20 b 05 c 10 1 none of the above If Two capacitors are connected in series as shown with C1 2C2 Let U1 and U2 represent respectively the potential energy stored in C1 and C2 Which of the following statements is true C a U1 2U2 2U1 U2 C U1 U2 C 4U1 U2 1 I I C2 I I 825V 1g Two resistors are connected in parallel as shown with R1 5R2 If R P1 and P2 are respectively the power dissipated in R1 and R2 which of the following statements is true I2 a P1 5P2 b 51gt1 P2 c P1 P2 c P1 25132 A I I f 250V 2 20 pts Two long parallel Wires are oriented along the normal to the plane of the page carrying currents I 1 12 150 A Note that I 1 is going into the page while 12 is coming out of the page a Show the direction of B1 and B2 on the diagram Here B1 and B2 are the y magnetic fields produced at P by Wires carrying I 1 and 12 respectively b Using Ampere s law determine the magnitudes of B1 and B2 Express d B1 and B2 and the net Bfield at point P in the usual unit vector notation given d 20 cm The magnitudes of B 1 and B 2 are equal B1 32 hall27w 210715020102 19704 T B I 15104 cos 45quot 139 51124501 T B 2 15104 cos 45quot j 51124501 T BBIBz 30104 513912450j T 212104jT b If an electron passes through P with a velocity 25x103ms parallel to the two Wires and directed into the page determine the magnitude and direction of the force on the electron V 25103kms F q VXB I61019 2970 x 212104j 77 8481020139N 3 20pts A pair of conducting parallel rails are separated by 120 m and are connected at one end by a resistance R 6 00 as shown A conducting bar ab is pulled along the frictionless rails by a force F as shown below with a constant velocity of magnitude 20 ms in the presence of a uniform magnetic field B normal to the plane containing the rails and pointing into the page and of magnitude B 250T Determine a o B F i R gt L120m b a the direction a to b or b to a of the induced current in the conducting bar From Lenz s law or a direct application of F ind q VxB to a charge in the rod the direction of the induced current is from b to a b the magnitude of the applied force F BLv iR ori BLvR The net force on the rod is zero F net F F ind 0 Therefore the magnitude of the applied force equals the induced force F Fmd iLB BZLZVR 25 212 22060 30N c the electrical energy dissipated as heat at R in a 150 sec interval AWPAt iZRAt BZLZVZAtR 251220215060 900 Or P At Fv At FvAt 3020 150 900J 4a 12pts Consider the circuit shown in the diagram i Use Kirchhoff s junction rule at junction b to express I 1 in terms of 12 and I3 I 12I3 ii Write down the Kirchhoff s loop equation for the loop abefa 811 613 241124 0 or 2409 32116I3240 ii Write down the Kirchhoff s loop equation for the loop bcdeb 1212 12 3612 613 0 which can be simplified to 812 2 I3 0 4b 8 pts A proton of mass M and charge Q 16x10 3919C is traveling With uniform velocity V 2x105 k ms under the combined in uence of a uniform magnetic field B 0 6i 05j T and a uniform Efield Determine the direction and magnitude of E F QE VxB 0 or E VXB BxV 06139 05jx2 105k 12j 10i105NC E 122 1012ae10 15610 NC e tan391l2 5020 5 20 pts Two identical cork balls each of mass m are hung from a common point by two insulating threads of negligible mass each of length L 50 cm Each ball has a charge Q 02aC distributed uniformly over its volume The balls repel each other and assume an equilibrium position as shown a Draw a freebody force diagram for one of the two masses T c0s30 mg b Write down ZFx max and ZFy may for the mass m From the freebody diagram above in the xdirection Tsin300 kQZLZ 1 Note that the separation between the charges is 2Lsin300 L In the ya irection Tcos300 mg 10m 2 c Solve the equations in part b to determine the tension T in the threads and the mass m From eq 1 1 T 9 109 4103914105052 2910393N And from eq2 m Tcos30010 2510394 kg SOLUTIONS OUTLINE PHYS102 FINAL EXAM SPRING14 Time allowed TWO HRS NAME Please PRINT Rec Sec Notes 1 For problems 2 5 your solutions must have adequate details and the answers must contain appropriate units to get full credit 2 Enter your recitation section number above Failure to do so WILL result in a twopoints penalty 3 There are six 51 Extra Credit problems in this Exam 4 Please read the problems carefully Relax and good luck leQ2 9 Resistors in series prob Score 1397 r2 RTR1R2 In parallel 1 fidgzh lRTzlR11R2 80 2 k k E g V Q F gt B 3 I r B qV X U EXdVdx 3 X3 4 r Rd 2 I 5 AU AW eld AWexz J uo em I C QV i For a long Wire B uo TOtal In ser39es 1 1 a A 27 1 l gt CT C1 C2 dehller 4727 r2 In parallel C C1 C2 8A At 8BIV 1 e tRC 10394T Q M J me 9x1031kg QZQO etRC qe16X103919C 39 14758 k 9x109Nm2C392 1 dQdt 1 IA nqu M0 43110397 TmA VIR R pZA 2 2 ac VZr PAwAIIRIV szV0QA AzQL 47W3 V SSP 47172 Sp 3 Prob1 Please circle the answer of your choice for each part i Power dissipated in the upper branch R3Q of the circuit shown is twice R 30 the power dissipated in the 20 9 resistor What is the value of the unknown resistor R I2A a 20 o b a 252 79 c 379 d 689 ii Consider an initially uncharged capacitor C in a series RC circuit The switch S is closed at time t 003 The potential difference across R is maximum at R C t0s btRC ct1e037s dtoo 5 I 8 iii A loop of conducting wire is placed with its plane normal to an external time dependent magnetic field Bt If the induced current in the loop is in the direction shown then as a function of time the magnetic field Bt is loop Increasing b Decreasing c Constant but very large Bt G iv Consider a positive charge and two negative charges arranged in two different configurations A and B with corresponding potential energies U A and U 3 Configuration B is obtained from A simply by moving the middle charge to the right Which of the following statements is true o A a UA gt UB UA lt UB c UA UB C9 v 0 3 9 3 B d The distances between the charges must be known to answer this question V Two long parallel wires oriented along the normal to the plane of the page are carrying currents I 1 and 12 The magnetic field B1 produced by I 1 at the site of 12 and the force exerted by I 1 on 12 are as shown Which of the following statements is true B a I 1 and 12 are both directed into the page 1 b I 1 and 12 are both directed out of the page 0 F12 c I 1 is directed into the page and 12 is directed out of the page 391 392 d I 1 is directed out of the page and 12 is directed into the page Vi Which potential V vs distance y graph describes a V V V constant Efield directed along the positive y axis Ans c Prob 2 20 pts The diagram is an end view of three long parallel wires y carrying currents 11 5 0A 12 100A and 13 6 0A The three wires are I I1 normal to the page with 11 and 13 directed into the page and 12 is coming out of the page 3 20m 370 r a12 pts Calculate the magnetic fields produced at the Site of 12 by the 1 2 wires carrying currents 11 and 13 Label the elds produced by 11 and 13 respectively as B1 and B3 and show them on the diagram Express B1 and B3 in the unit vector i j k notation E O 392 X 39 o r12 326mcos 370 4cm and r32 4tan 3706m 3cm 0 81 33 53 quot r The magnitude of the Bfield at a distance of r from a long wire carrying 32 I current I is given by B h Therefore I 38 Hr A uOXSA B1 2 27cgtlt4gtlt10 m 2f1539x10 5T cos 370 sin 370 25 x1039508i 06T B3 L6142cos530z sin53oj39 4 x1039506i 08T 215x 3x 10 m 24f 32x10 5T b 8 pts Calculate the force exerted on a 50 cm section of Wire carrying 12 by the magnetic fields produced by the other two Wires Express this force in the unit vector notation 1 12o512x E where ET 31 B3 04f 4739x10 5T 17 10Ao5m12xo4f 47x10 5T 2351 2x10 5N Prob 3 20pts A rectangular metallic loop terminated by resistance R 509 on one end is pulled in a horizontal plane at a constant velocity 7 by a force F 012iAN through a region of uniform magnetic field perpendicular to the plane of the loop as shown The magnitude of the uniform magnetic field B 16T and the width of the loop w 15cm All gravitational effects can be neglected r a A X X XBX y i V R x x X 5 b X X X X a5 pts What is the direction of the induced current in R circle the answer of your choice below m from a to b ii from b to a b5pts What is the magnitude of the induced emf Since the loop is moving with constant velocity the net force on the loop is zero F FEMO net Therefore the magnitude of the applied force equals the magnitude of the induced force FindFIwB or 11 WE 8IRE 012Nx5g2 25V wB 015mx16T c5 pts What is the magnitude of velocity 7 sBwV or Vi 25V 104ms Bw 16T x015m d5 pts How long will it take to generate 05 of heat at R AW PAt AW AWgtltR05Jgtlt5S2 At P 82 25V2 Prob 420 pts Four capacitors C160MF C220MF C310MF and C440MF are arranged in a network as shown A constant potential difference Vac is maintained between the terminals of the network to fully charge the capacitors C2 The charge on C2 is 500MC C1 a 4pts What is the charge on C I o 3 a b V g C2 C3 C4 C3 Q3 C3 Q2 l500w 250w I I C2 2 b 8 pts Calculate the potential difference Vac C1 C23 Where C23 C2 C3 30MF 500w VbC 250V C2 20g Vab C23 30MF 1 Vb EW7 Vbc 2Vab Therefore Vac Vab Vbc SVbC 375V c 8pts What is the total electric energy stored in the capacitor network C1 C23 71723 4 C C1C23 4 M 40yF 60m Therefore the energy stored in the network 1 U EC V2 30x10 63752J 42mJ ClC ClC Prob 5 20 pts Consider three charges Q1 Q2 and Q3 placed along a vertical line as shown in the diagram disregard Q4 for the moment Q19 200nC 40cm a 9121 s Calculate the electric potential energy of the threecharge con guration The total ener of th th h 39 gy e reec arge51s IOOHC Q4 Q 9x109 gtlt20gtlt20gtlt103918 2 3Ocm 400nc UU12U23U13U13 8X102 J 45gtlt10395J 4 Why iS U12 U23 0 39Ocm Q3 200nC b6 pts A fourth particle of mass m 2 0 03913 kg and charge Q4 40 OnC is placed on the x aXis 30 cm from Q2 i 6121 s What is the potential energy of Q4 in its present position 9x1o9x20x2ox10 18 3x10 2 U4iU14U34U24U24 J12x10394J ii 5121 s If Q4 is now released from its present position nd the speed of Q4 when it has moved very far away from the threecharge Q 1 Q2 and Q3 con guration From conservation of energy UKE139 UKEf l 2 U4 mv l 2 4 v 2U 2X12 35x104ms m 2x10 EXTRA CREDIT Prob 6 10 pts Consider the circuit shown in the diagram In the circuit diagram 12 0 5A Use this information with Kirchhoff s junction and loop rules to determine the battery emf 8 Using Kirchhoff s loop rule for abcdefa 6O5 713 12 513 24O5 18 O 1213 15 0 I3 1512 125 A Applying Kirchhoffs junction rule at 9 gives 1112 13 or 1113 12 125 05A 075A Using Kirchhoff s loop rule for bcdeb 6O75 8 24O5 18 6O5 O s 6O75 2405 18 6O5 75V OUTLINE OF SOLUTIONS PHYS102 SAMPLE FINAL EXAM Time allowed 2 hrs All equations will be provided They have been omitted from this sample Final If you detect any errors in the solutions below please send me an email 1a 3pts Three charges are placed in a line as g r 3 r i51own The total potent1a1 energy of these charges Q Q Q a 25k Q2r b 15k Q2r c zero d 15k Q2r 1b 3pts When the potential difference between the plates of a capacitor is doubled the magnitude of the electric energy stored in the capacitor a is doubled b is halved c remains the same 1 uadru 16 1c 3pts When a conductor is in electrostatic equilibrium the electric field inside the conductor is a Iver Z c q d 47w 0 1d 3pts Two point charges are situated symmetrically about the origin The Efield measured at the origin is zero At point P the Efield points in the y positive x direction From this one can conclude that a both charges are positive and equal in magnitude r O 0 O X b both charges are negative and equal in magnitude c the charges are of opposite polarity but of equal magnitude 1e 3ptsA at coil of Wire consisting of 20 turns each with an area of 50 cm2 is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 20 T to 60 T in 20 s If the coil has a total resistance of 040 Q What is the magnitude of the induced current in A a 020 b 060 d 080 If 3ptsLenz s law says that the direction of an induced current Will a be counterclockwise b produce an increased heating effect c produce a greater voltage d oppose the effect that produced it 1g 3pts If a currentcarrying wire has no magnetic force on it when placed in a constant magnetic field a the wire is parallel to the field b the wire is perpendicular to the field c the wire exerts a force on the field d the torque on the wire is nonzero 2 20ptsThree charges are placed at the three vertices of a rightangle triangle as shown a Determine the force exerted on Q3 by charge Q1 Y Label this force F31 and express it in the usual i j notation and show it on the diagram 02 40 MC F31 9x109x80x625x103912500553 x103922i 500i N 50 cm b Determine the force exerted on Q3 by charge Q2 Label this force F32 show it on the diagram and express it in the usual i j notation F32 9x109x40x625xl039125x103922 cos53 i sin53 j 54i 72j N f Q1 39 c Determine the magnitude and direction of the net force exerted on Q3 FT F32 F32 i Magnitude FT 4462 722 112 4518 N 6 tan172446 920 1 Determine the electrostatic potential energy of the threecharge configuration U 9109 6258030 4062550 80404010391210392 177 J 3a 8 pts A proton of mass M and charge Q 16 x10 19C is traveling with constant velocity 17 2 x 10512 m 3 under the combined in uence of a uniform magnetic field E 06 05 T and a uniform E field Determine the direction and magnitude of E F QE VxB 0 or E VxB va 06139 05jx2 105k 12j 10i105NC E 122 1012ae10 156ae10 NC e tan39112 5020 3b 12pts A particle of mass m 103930kg and charge q 32 x 10 19 C of unknown polarity moving with a A velocity of 106 ms enters a region to the right of line AC B as shown in the accompanying diagram of uniform q gt magnetic field B of magnitude 100 G The Bfield points 0 V gt into the page and is perpendicular to the velocity of the charge After entering the Bfield the charge moves in a circular trajectory as shown a Determine the radius of the circular trajectory var qu r mvqB 1039301063210391910393 3110393 m b What is the polarity or of the charge The polarity is negative c How much work was done on the particle by the magnetic field as the particle traveled the half circle Zero velocitydisplacement is perpendicular to qva 4 20pts A pair of conducting parallel rails are separated by 20 cm and are connected at one end by a resistor R 250 as shown A conducting bar is pulled along the frictionless rails With a constant velocity of 125 ms in the presence of a uniform magnetic field B normal to the plane containing the rails and pointing towards you The rate of energy dissipation in the resistor is 025 Js Determine 93 o3 V l R gt L200m a the magnitude and direction a to b or b to a of the induced current in the conducting bar Direction of induced current is from a to b iZR 025 W solve for i 02525 2 01A b the magnitude of the B field Blv ir or B irlv 103912502125 100T 5 20pts Consider the circuit shown in the diagram a Use Kirchhoff s junction rule at junction b to express II in terms of Z and I 3 11 1213 1 360 1200 b Write down the Kirchhoff s loop equations for the loops abefa and bcdeb For loop abefa 811 613 0 32116I3240 For loop bcdeb 1212 12 36 12 613 0 which can be simplified to 8122I30 c Solve equations obtained in part a and b to determine currents I I2 and I 3 Substitute 12 11 13 from eql in eq3 to get 81129130 4 Multiply eq4 by 4 and subtract the resulting equation from eq2 to get 32 4213 0 or 13 076 A From eq3 12 l813 2 015 A And from eql 11 1213 061A

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