1.. - fisicadcyt.files.wordpress.comouestions 1 for each circuit in fig. 27 -i8, are the resistors...

Ouestions

1 For each circuit in Fig. 27 -I8, are the resistors connected inseries, in parallel, or neither?

(b)

FlG. 27-18 Question 1.

2 In Fig. 27 -19, a circuit con-sists of a battery and two uni-form resistors, and the sectionlying along an x axis is dividedinto five segments of equallengths. (u) Assume that Rr :R2 and rank the segments ac-

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cording to the magnitude of the average electric field in them,greatest first. (b) Now assume that Rr ) Rz and then againrank the segments. (c) What is the direction of the electricfield along the x axis?

3 (a) In Fig. 27 -21a,,with Rr ) R2, is the potential differenceacross R2 more than, less than, or equal to that across Rr?(b) Is the current through resistor R2 more than, less than,or equal to that through resistor R1?

e,FlG. 27-20 Questions 3 and 4.

4 (a) In Fig. 27 -20a,, are resistors R1 and R3 in series? (b) Areresistors Rr and R2 in parallel? (c) Rank the equivalent resis-tances of the four circuits shown in Fig. z7-z\,greatest first.5 You are to connect resistors R1 and Rr, with Rr ) R2, toa battery, first individually, then in series, and then in parallel.Rank those arrangements according to the amount of currentthrough the battery, greatest first.6 Cap-monster maze. In Fig. 27 -2I, all the capacitors havea capacitance of 6.0 pE, and all the batteries have an emf of10 V. What is the charge on capacitor C? (If you can find theproper loop through this maze, you can answer the questionwith a few seconds of mental calculation.)


7 Initially, a single resistor Rl is wired to a battery. Thenresistor R2 is added in parallel. Are (a) the potential differenceacross R1 and (b) the current i1 through Rr now more than,less than, or the same as previously? (.) Is the equivalentresistance Rp of R1 and R2 more than, less than, or equal toRr? (d) Is the total current through R1 and R2 together morethan, less than, or equal to the current through R1 previously?8 Res-monster maze. In Fig. 27 -22, all the resistors have aresistance of 4.0 f) and all the (ideal) batteries have an emf of4.0 V. What is the current through resistor R? (If you canfind the proper loop through this maze, you can answer thequestion with a few seconds of mental calculation.)


9 A resistor R1 is wired to a battery, then resistor R2 is addedin series. Are (a) the potential difference across R1 and (b) thecurrent i1 through Rr now more than, less than, or the same aspreviously? (c) Is the equivalentresistance Rp of R1 and R2 morethan, less than, or equal to Rt?10 After the switch rn Fig. 27 -15 is closed on point a,, there iscurrent i through resistance R.Figure 27-23 gives that current forfour sets of values of R and capaci-tance C: (1) Rs and Co, (2) ZRo andCo, (3) Rs and 2Co,()2Roand ZCo.Which set goes with which curve?

l'lbl 'lal'lFlG. 27-19 Question2.

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Chapter 27 I Circuits

battery t has emfnal resistance rr : Zrlhas emf 8z: I2.0 !/

V and internal resistance 12: 0.012 f). ZrlThe batteries are connected in series with - o

an external resistance R. (u) What Rvalue makes the terminal-to-terminal po-tential difference of one of the batterieszero? (b) Which battery is that? ssMcooll A solar cell generates a potential difference of 0.10 Vwhen a 500 ,f) resistor is connected across it, and a potential dif-ference of 0.15 V when a 1000 ,f) resistor is substituted. What arethe (a) internal resistance and (b) emf of the solar cell? (c) Thearea of the cell is 5.0 cm2, and the rate per unit area at which itreceives energy from light is 2.0 mWcm2. What is the efficiencyof the cell for converting light energy to thermal energy in the1000 C) external resistor?

nRlsec. 27-7 Multiloop Circuits.23 In Fig. 27-38, Rr : Rz:4.00 f) and Rr : 2.50 0. Find theequivalent resistance betweenpoints D and E. (Hint: Imaginethat a battery is connected across those points.).24 When resistors 1 and 2 are connected in series, theequivalent resistance is 16.0 0. When they are connected inparallel, the equivalent resistance is 3.0 O. What are (a) thesmaller resistance and (b) the larger resistance of these tworesistors?.25 Four 18.0 C) resistors are connected in parallel across a25.0 V ideal battery. What is the current through the battery?.26 Figure 27 -39 shows five5.00 C) resistors. Find the equiva-lent resistance between points(u) F and H and (b) F and G.(Hint: For each pair of points,imagine that a battery is con-nected across the pair.).27 In Fig. 27-40, Rr : 100 C),Rz: 50 C), and the ideal batterieshave emfs 8t :6.0 V %z:5.0 Vand ffiz:4.0 V. Find (u) the cur-rent in resistor 1, (b) the current inresistor 2,and (c) the potential dif-ference between points a and b..28 In Fig. 27 -g,what is the po- a

tential difference Va - V,between points d and c if. V, -4.0 V %z: 1.0 V, Rr : Rz:10 f), and R: : 5.0 O, and thebattery is ideal?.29 Nine copper wires of length / and diameter d areconnected in parallel to form a single composite conductor ofresistance R. What must be the diamet er D of a single copperwire of length / if it is to have the same resistance? ssMoo30 The resistances in Figs.27-4Ia and b are all 6.0 C), andthe batteries are ideal IzV batteries. (a) When switch S inFig. 27 -4Ia is closed, what is the change in the electric poten-tralVl across resistor L, or does Vlremain the same? (b) When

switch S in Fig. 27 -47b is closed, what is the change in v l acrossresistor 1, or does Vl remain the same?

(") (b)

FlG. 27-41 Problem 30.

.o31 In Fig. 27-42, the current in resistance 6 is io:1.40 Aand the resistances are Rr : Rz: Rt : 2.00 f,), R+ : 16.0 C),Rs : 8.00 C), and Ro : 4.00 O. What is the emf of the idealbattery? e


FtG. 27-37Problem 21.

Flc. 27-38 ProblemZ3.

FlG. 27-39 Problem26.

FlG. 27-4A Problem2T.

..32 In Fig. 27-43, the idealbatteries have emfs Zt : 10.0V and %z:0.500%1, &nd the re-sistances are each 4.00 0. Whatis the current in (a) resistan ce 2and (b) resistance 3?

oo33 In Fig. 27-44., the idealbatteries have emfs Et :5.0 Vand Ez : 12 V, the resistancesare eachz.O C), and the potentialis defined to be zero at thegrounded point of the circuit.What are potentials (a) V1 and(b) V2 at the indicated points?ssMoo34 Figure 27-45 shows asection of a circuit. The resis-tances are R1 : 2.0 C), Rz : 4.0f), and R: : 6.0 C), and theindicated current is i : 6.0 A.The electric potential differ-ence between points A and Bthat connect the section to therest of the circuit is Va - Va :78 V. (u) Is the device repre-sented by "Box" absorbing orproviding energy to the circuit,and (b) at what rate?..35 In Fig. 27-46, Rr : 2.00f,), R, : 5.00 C), and the batteryis ideal. What value of R3 maxi-mizes the dissipation rate inresistan ce 3?

..36 Both batteries in Fig.27-47a are ideal. Emf Zt ofbattery t has a fixed value, butemf %2 of. battery 2 can be varied

FlG. 27-43 Problems 32.43, and 98.


--+?,

FlG. 27-45 Problem34.

FlG. 27-46 Problems35,99,106, and I07.

between 1.0 V and 10 V. The plots in Fig. 27-47b give thecurrents through the two batteries as a function of '62. Thevertical scale is set by i., - 0.20 A. You must decide whichplot corresponds to which battery,, but for both plots, a nega-tive current occurs when the direction of the currentthrough the battery is opposite the direction of that bat-tery's emf.What are (a) emf %', (b) resistance R1, &hd (c) re-sistanc e Rr?

%z ff)(b)

FlG. 27-4V Problem 36.

v 1..t)

=ioU

(a)

FtG" 27-52Problems 41

and 42.


Rr? What is the power of (d)


..37 In Fig. 27 -48, the resis-tances are Rr : 1.0 O and Rz:2.0 O,,and the ideal batteries haveemfs Er : 2.0V and'62 :'8t :4.0 V. What are the (a) size and(b) direction (up or down) of thecurrent in battery 1, the (.) sizeand (d) direction of the current inbattery 2, and the (e) srze and (f)direction of the current in battery3? (g) What is the potential dif-ference V,, - Vt? ILW

..38 In Fig. 27 -49, Z | : 6.00 VEz : I2.0 V, Rr : 100 O, Rz :200 f), and R: : 300 O. Onepoint of the circuit is grounded(V - 0). What are the (u) sizeand (b) direction (up or down)of the current through resistance1, the (c) stze and (d) direction(left or right) of the currentthrough resistance 2, and the (e)size and (f) direction of the cur-rent through resistance 3? (g)What is the electric potential atpoint,4? So.39 In Fig. 27-50,8 : 12.0Y,Rr : 2000 f), Rz: 3000 O' andR: : 4000 0. What are the poten-tial differences (a) V,q - V a, (b)Vr-Vc, (.) Vc-Vr, and (d)VA - Vc?

'.40 In Fig. 27-51,, Rr : 100 O'Rz: R: : 50.0 f,), R+ : 75.0 O'and the ideal battery has emf (8 -6.00 V. (a) What is the equivalentresistance? What is i in (b) resis-tance 1, (c) resistance 2, (d) resis-tance 3., and (e) resistance 4?

Ff G. 27-48 Problem3T.

Flc. 27-4q Problem 38.

FlG" 27-5A Problem 39.

FrG. 27-51Problems 40 and 48.

(u)

Problems

ternal resistan ce r : 0.300 O are connectedin parallel across a resistance R. (a) Forwhat value of R is the dissipation rate in theresistor a maximum? (b) What is that maxi-mum?..42 Two identical batteries of emf Z -12.0 V and internal resistance r : 0.200 f) areto be connected to an external resistance R'either in parallel (Fig. 27 -52) or in series(Fig. 27-53).If R : 2.00r, what is the current iin the external resistance in the (a) paralleland (b) series arrangements? (c) For whicharrangement is i greater? If R : 112.00, whatis i in the external resistance in the (d) paral-lel and (") series arrangements?(0 For which arrangement is igreater now?rr43 In Fig. 27-43, .€1: 3.00V Ez : 1.00 V Rr : 4.00 O,Rz : 2.00 O,, Rr : 5.00 f,),, andboth batteries are ideal. Whatis the rate at which energy is dis-sipated in (a) R', (b) R2, and (c)battery 1 and (e) batt ery 2?

o.44 In Fig. 27-54a, resistor 3 is a variable resistor and theideal battery has emf 8 : 12 V. Figure 27 -54b gives the current Ithrough the battery as a function of Rj. The horizontal scaleis set by R,., :20 O.The curve has an asymptote of 2.0 mA asR-r - rc.What are (a) resistance R1 and (b) resistance Rz?

Rs (a)(b)

FlG" 27-54 Problem 44.

".45 You are given a number of 10 O resistors,, each capa-ble of dissipating only 1.0 W without being destroyed. Whatis the minimum number of such resistors that you need tocombine in series or in parallel to make a 10 f) resistancethat is capable of dissipating at least 5.0 W?

".46 In Fig. 27-55, an array of n

parallel resistors is connected inseries to a resistor and an idealbattery. All the resistors have thesame resistance. If an identical re-sistor were added in parallel to theparallel array, the current throughthe battery would change by7.25%. What is the value of n?too{J A copper wire of radius a - 0.250 mm has an alu-minum jacket of outer radius b - 0.380 mm. There is a currenti : 2.00 A in the composite wire. Using Thble 26-I, calculatethe current in (a) the copper and (b) the aluminum. (c) If apotential difference V - I2.0 V between the ends maintainsthe current, what is the length of the composite wire? ssM..41 In Fig. 27-52, two batteries of emf V - I2.0 V and in-

between 1.0 V and 10 V. The plots in Fig. 27-47b give thecurrents through the two batteries as a function of '62. Thevertical scale is set by i., - 0.20 A. You must decide whichplot corresponds to which battery,, but for both plots, a nega-tive current occurs when the direction of the currentthrough the battery is opposite the direction of that bat-tery's emf.What are (a) emf %', (b) resistance R1, &hd (c) re-sistanc e Rr?

%z ff)(b)

FlG. 27-4V Problem 36.

v 1..t)

=ioU

(a)

FtG" 27-52Problems 41

and 42.


Rr? What is the power of (d)


..37 In Fig. 27 -48, the resis-tances are Rr : 1.0 O and Rz:2.0 O,,and the ideal batteries haveemfs Er : 2.0V and'62 :'8t :4.0 V. What are the (a) size and(b) direction (up or down) of thecurrent in battery 1, the (.) sizeand (d) direction of the current inbattery 2, and the (e) srze and (f)direction of the current in battery3? (g) What is the potential dif-ference V,, - Vt? ILW

..38 In Fig. 27 -49, Z | : 6.00 VEz : I2.0 V, Rr : 100 O, Rz :200 f), and R: : 300 O. Onepoint of the circuit is grounded(V - 0). What are the (u) sizeand (b) direction (up or down)of the current through resistance1, the (c) stze and (d) direction(left or right) of the currentthrough resistance 2, and the (e)size and (f) direction of the cur-rent through resistance 3? (g)What is the electric potential atpoint,4? So.39 In Fig. 27-50,8 : 12.0Y,Rr : 2000 f), Rz: 3000 O' andR: : 4000 0. What are the poten-tial differences (a) V,q - V a, (b)Vr-Vc, (.) Vc-Vr, and (d)VA - Vc?

'.40 In Fig. 27-51,, Rr : 100 O'Rz: R: : 50.0 f,), R+ : 75.0 O'and the ideal battery has emf (8 -6.00 V. (a) What is the equivalentresistance? What is i in (b) resis-tance 1, (c) resistance 2, (d) resis-tance 3., and (e) resistance 4?

Ff G. 27-48 Problem3T.

Flc. 27-4q Problem 38.

FlG" 27-5A Problem 39.

FrG. 27-51Problems 40 and 48.

(u)

Problems

ternal resistan ce r : 0.300 O are connectedin parallel across a resistance R. (a) Forwhat value of R is the dissipation rate in theresistor a maximum? (b) What is that maxi-mum?..42 Two identical batteries of emf Z -12.0 V and internal resistance r : 0.200 f) areto be connected to an external resistance R'either in parallel (Fig. 27 -52) or in series(Fig. 27-53).If R : 2.00r, what is the current iin the external resistance in the (a) paralleland (b) series arrangements? (c) For whicharrangement is i greater? If R : 112.00, whatis i in the external resistance in the (d) paral-lel and (") series arrangements?(0 For which arrangement is igreater now?rr43 In Fig. 27-43, .€1: 3.00V Ez : 1.00 V Rr : 4.00 O,Rz : 2.00 O,, Rr : 5.00 f,),, andboth batteries are ideal. Whatis the rate at which energy is dis-sipated in (a) R', (b) R2, and (c)battery 1 and (e) batt ery 2?

o.44 In Fig. 27-54a, resistor 3 is a variable resistor and theideal battery has emf 8 : 12 V. Figure 27 -54b gives the current Ithrough the battery as a function of Rj. The horizontal scaleis set by R,., :20 O.The curve has an asymptote of 2.0 mA asR-r - rc.What are (a) resistance R1 and (b) resistance Rz?

Rs (a)(b)

FlG" 27-54 Problem 44.

".45 You are given a number of 10 O resistors,, each capa-ble of dissipating only 1.0 W without being destroyed. Whatis the minimum number of such resistors that you need tocombine in series or in parallel to make a 10 f) resistancethat is capable of dissipating at least 5.0 W?

".46 In Fig. 27-55, an array of n

parallel resistors is connected inseries to a resistor and an idealbattery. All the resistors have thesame resistance. If an identical re-sistor were added in parallel to theparallel array, the current throughthe battery would change by7.25%. What is the value of n?too{J A copper wire of radius a - 0.250 mm has an alu-minum jacket of outer radius b - 0.380 mm. There is a currenti : 2.00 A in the composite wire. Using Thble 26-I, calculatethe current in (a) the copper and (b) the aluminum. (c) If apotential difference V - I2.0 V between the ends maintainsthe current, what is the length of the composite wire? ssM..41 In Fig. 27-52, two batteries of emf V - I2.0 V and in-


ooo{$ In Fig.27-51, R1 :7.00 O,R:: 12.0 O, R.,:4.00 O,and the ideal battery's emf is % : 24.0 V. For what value of Rawill the rate at which the battery transfers energy to theresistors equal (a) 60.0 W (b) the maximum possible rate P,,,u*,and (c) the minimum possible rate Pn,in? What are (d) P',n*and (e) Pn,;n?

sec. 27-8 The Ammeter and the Voltmeter..49 In Fig. 27-14, assume thatE:3.0 V r: 100 0' Rr --250 O' and Rz : 300 f). tf the voltmeter resistance Rv is5.0 kO, what percent error does it introduce into the mea-surement of the potential difference across R'? Ignore thepresence of the ammeter..o5o A simple ol l-Qttmade by connecrin \y\hflashlight battery ina resistance R and .ffithat reads from 0 to R /

)shown in Fig. 27-56.Resistance { A--R is adjusted so that when the FlG. 27'56 Problem 50.clip leads are shorted together,the meter deflects to its full-scale valueternal resistance across the leads results10.0%, (b) 50.0%, and (c) 90.0% of fullmeter has a resistance of 20.0 O and thethe battery is negligible, what is thevalue of R?..51 (a) In Fig. 27-57, what doesthe ammeter read if ffi : 5.0 V(ideal battery), Rr : 2.0 O' Rz :4.0 C),, and Rr : 6.0 f)? (b) The am-meter and battery are now inter-changed. Show that the ammeterreading is unchanged. lLw

..52 When the lights of a car areswitched on. an ammeter in serieswith them reads 10.0 A and a volt-meter connected across them reads12.0 V (Fig. 27 -58). When the elec-tric starting motor is turned on, theammeter reading drops to 8.00 Aand the lights dim somewhat. If theinternal resistance of the battery is0.0500 0 and that of the ammeter isnegligible,, what are (a) the emf of thebattery and (b) the current throughthe starting motor when the lightsare on?.o53 In Fig. 27-59,, a voltmeter ofresistance Rv : 300 C) and an am-meter of resistance Rn : 3.00 Oare being used to measure a resis-tance R in a circuit that also con-tains a resistance Ro : 100 O andan ideal battery of emf V - 12.0V. Resistance R is given by R -Vli, where V is the potentialacross R and i is the ammeterreading. The voltmeter reading is7', which is 7 plus the potential

of 1.00 mA. What ex-in a deflection of (a)scale? (d) If the am-internal resistance of


difference across the ammeter. Thus, the ratio of the two meterreadings is not R but only anapparent resistance R' : V'li. If R :85.0 ,f), what are (a) the ammeter reading, (b) the voltmeter read-ing, and (c) R'? (d) If Ra is decreased, does the difference be-tween R' and R increase, decrease. or remain the same?oo54 In Fig. 27-60. Rr : 2.00R.the ammeter resistance is zero,and the battery is ideal. Whatmultiple of 8lR gives the cur-rent in the ammeter?.o55 In Fig. 27-61, R, is to beadjusted in value by movingthe sliding contact across it un-til points 0 and b are broughtto the same potential. (Onetests for this condition by mo-mentarily connecting a sensitiveammeter between 0 and b: ifthese points are at the same po-tential. the ammeter will not de-flect.) Show that when this ad-justment is made,, the followingrelation holds: R'. : R,R,/Rr.An unknown resistance (R,)can be measured in terms of astandard (R,) using this device,which is called a Wheatstonebridge.o.56 In Fig. 27-62, a voltmeterof resistance Rv : 300 C) and anammeter of resistance Ra : 3.00f) are being used to measure aresistance R in a circuit that alsocontains a resistance R6 : 100 Oand an ideal battery of emf V -12.0 V. Resistance R is given byR : Vli, where V is the volt-meter reading and i is the cur-rent in resistance R. However.the ammeter reading is not i butrather i', which is i plus the cur-rent through the voltmeter. Thus, the ratio of the two meterreadings is not R but only an apparent resistance R' : Vli'.IfR - 85.0 O,, what are (a) the ammeter reading,(b) the voltmeterreading, and (c) R'? (d) If Rv is increased, does the differencebetween R' and R increase, decrease, or remain the same?

sec. 27-g RC Circuits.57 What multiple of the time constant r gives the timetaken by an initially uncharged capacitor in an RC seriescircuit to be charged to 99.0"h of its final charge? ssM.58 A capacitor with initial charge 4o is discharged througha resistor. What multiple of the time const ant r gives the timethe capacitor takes to lose (a) the first one-third of its chargeand (b) two-thirds of its charge?.59 A 15.0 kO resistor and a capacitor are connected in se-ries, and then a 12.0 V potential difference is suddenly appliedacross them. The potential difference across the capacitorrises to 5.00 V in 1.30 ps. (a) Calculate the time constant of thecircuit. (b) Find the capacitance of the capacitor. rLW


F$G. 27-&1Problems 55 and 11 1.

<-ozFrG" 27-&2

Problem 56.

FtG. A7-s8Problem 52.

;Slicling contact

irA.

Problem 53.

Chapter 28 I Magnetic Fields

0.010 T. The electron goes through ahalf-circle and then exits region 7.,

headed toward region 2 across a gapof 25.0 cm. There is an electric poten-tial difference A,V : 2000 V acrossthe gap, with a polarity such that theelectron's speed increases uniformlyas it traverses the gap. Region 2 con-tains a uniform magnetic field di-rected out of the page, with magni-tude 0.020 T. The electron goesthrough a half-circle and then leavesdoes it leave? €$

FrG. 28-43Problem 32.

region 2. At what time I

".33 A particular type of fundamental particle decays bytransforming into an electron e - and a positron e *. Supp___ose

the decaying particle is at rest in a uniform magnetic field B ofmagnitude 3.53 mT and the e- and e* move away from thedecay point in paths lying in a plane perpendicular to B. Howlong after the decay do the e- and e+ collide?..34 A source injects an electron of speed v - L 5 x 107 m/sinto a uniform magnetic field of magnitude B - 1.0 x 10-3 T.The velocity of the electron makes an angle 0 : 10o with thedirection of the magnetic field. Find the distance d from thepoint of injection at which the electron next crosses the fieldline that passes through the injection point.

sec. 28-7 Cyclotrons and Synchrotrons.o35 Estimate the total path length traveled by a deuteronin the cyclotron of Sample Problem 28-5 during the (entire)acceleration process. Assume that the accelerating potentialbetween the dees is 80 kV.0.36 In a certain cyclotron a proton moves in a circle ofradius 0.500 m. The magnitude of the magnetic field is 1.20 T.(a) What is the oscillator frequency? (b) What is the kineticenergy of the proton, in electron-volts?..37 A proton circulates in a cyclotron, beginning approxi-mately at rest at the center. Whenever it passes through thegap between dees, the electric potential difference betweenthe dees is 200 V. (a) By how much does its kinetic energyincrease with each passage through the gap? (b) What is itskinetic energy as it completes 100 passes through the gap? Letr16s be the radius of the proton's circular path as it completesthose 100 passes and enters a dee, and let rrct be its nextradius, as it enters a dee the next time. (c) By what percentagedoes the radius increase when it changes frorl r"roo to r1e1? Thatis, what is

percentage increase - rrct - \oo rco%?ftoo

..38 A cyclotron with dee radius 53.0 cm is operated at anoscillator frequency of 12.0 MHz to accelerate protons.(a) What magnitude B of magnetic field is required to achieveresonance? (b) At that field magnitude, what is the kineticenergy of a proton emerging from the cyclotron? Suppose,,instead, that B - 1.57 T. (.) What oscillator frequency isrequired to achieve resonance now? (d) At that frequency,what is the kinetic energy of an emerging proton?

$ec. 28-8 Magnetic Force on a Current-Carrying Wireo39 A 13.0 g wire of length L:62.0 cm is suspended by apair of flexible leads in a uniform magnetic field of magnitude

0.440 T (Fig. 28-44). What arethe (a) magnitude and (b) direc-tion (left or right) of the currentrequired to remove the tensionin the supporting leads? rLw

.40 The bent wire shown in Fig.28-45 lies in a uniform magneticfield. Each straight section is 2.0m long and makes an angle of I -60' with the x axis, and the wirecarries a current of 2.0 A.What isthe net magnetic force on the wirein unit-vector notation if the mag-netic field is given by (a) 4.0k Tand (b) 4.0i T?.41 A horizontal power linecarries a current of 5000 A fromsouth to north. Earth's magneticfield (60.0 pT) is directed to-ward the north and inclined downward at 70.0" to the horizon-tal. Find the (a) magnitude and (b) direction of the magneticforce on 100 m of the line due to Earth's field. ssM

.42 A wire 1.80 m long carries a current of 13.0 A andmakes an angle of 35.0" with a uniform magnetic field of mag-nitude B - 1.50 T. Calculate the magnetic force on the wire...43 A wire 50.0 cm long carries a 0.500 A current in thepositive direction of an x axis through a magnetic field E -(3.00 mT)i + (10.0 mT)t. In unit-vector notation, what is themagnetic force on the wire?..44 In Fig. 28-46, a metal wire of mass nl : 24.1 mg canslide with negligible friction on two horizontal parallel railsseparated by distance d - 2.56 cm. The track lies in a verticaluniform magnetic field of magnitude 56.3 mT. At time / - 0,device G is connected tothe rails, producing aconstant current i : 9.13mA in the wire and rails(even as the wiremoves). At t:6L1 ms,what are the wire's (u)speed and (b) directionof motion (left or right)?ooo{$ A 1.0 kg copper rod rests on two horizontal rails1.0 m apart and carries a current of 50 A from one rail to theother. The coefficient of static friction between rod and rails is0.60. What are the (a) magnitude and (b) angle (relative to thevertical) of the smallest magnetic field that puts the rod on theverge of sliding? @oooQ,$ A long, rigid conductor, lying along an x axis, carries acurrent of 5.0 A in the negative x direction. A magnetic fieldF is present, given bV F : 3.0i + 8.0x2j, with x in meters andF in milliteslas. Find, in unit-vector notation, the forcc on the2.0 m segment of the conductor that lies between x - 1.0 mandx-3.0m.sec. 28-g Torque on a Current Loop.47 Figure 28-47 shows a rectangular 2O-turn coil of wire, ofdimensions 10 cm by 5.0 cm. It carries a current of 0.10 A andis hinged along one long side. It is mounted in the xy plane, at

X

FlG. 28^44 Problem 39.

FIG. 28-45 Problem 40.

Itrlc. ?8-46 Problem 44.


your potential is greater than 100 V you could ruin the com-ponent. (b) How long must you wait until your potentialreaches the safe level of 100 V?

If you wear a conducting wrist strap that is connected toground, your potential does not increase as much when youstand up; you also discharge more rapidly because the resis-tance through the grounding connection is much less thanthrough your body and shoes. (c) Suppose that when youstand up, your potential is 1400 V and the chair-to-you capaci-tance is 10 pF, What resistance in that wrist-strap groundingconnection will allow you to discharge to 100 V in 0.30 s,

which is less time than you would need to reach for, say,yourcomputer? #72 An automobile gasolinegauge is shown schematically inFig. 27-69. The indicator (on thedashboard) has a resistance of10 C). The tank unit is a float con-nected to a variable resistorwhose resistance varies linearlywith the volume of gasoline. Theresistance is 140 f) when thetank is empty and 20 O whenthe tank is full. Find the currentin the circuit when the tank is (a)full.Tieat the battery as ideal.

across the cable, and a currentof 50 A. Which part is defec-tive? ssM

78 Figure 27-70 shows a por-tion of a circuit through whichthere is a current I : 6.00 A.The resistances are R r : Rz :2.00R1 : 2.00R + : 4.00 g1. Whatis the current it throughresistor 1?

79 In Fig. 27-77, Rt: 20.0 O,Rz : 10.0 ,f), and the ideal bat-tery has emf,'8 : 720V.What isthe current at point a if we close(u) only switch S,, (b) onlyswitches Sr and 52, ?nd (c) allthree switches?

80 In Fig. 27 -72., the idealbatteries have emfs Zt:20.0V 8z: 10.0 V' 8t:5.00 Vand Et: 5.00 V and the resis-tances are each 2.00 O. Whatare the (u) size and (b) direc-tion (left or right) of current i

1

and the (.) size and (d) direc-tion of curr ent i2? (This can beanswered with only mental cal-culation.) (") At what rate isenergy being transferred inbattery 4' and (f) is the energybeing supplied or absorbed bythe battery?81 In Fig. 27-73,, R : 10 f).What is the equivalent resis-tance between points A and B?(Hint: This circuit section mightlook simpler if you first assumethat points A and B areconnected to a battery.)82 In Fig. 27-74, the ideal bat-tery has emf.'8 :30.0 Y and theresistances are Rr : Rz : 14 f,),R3 : R+ : Rs : 6.0 C), Re : 2.0f), and Rt : 1.5 O. What are cur-rents (a) ir, (b) io, (c) i

', (d) i3, and

(e) r'? FlG. 27-73 Problem 81.

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83 In Fig.27-75, the ideal batteries have emfs %1 : I2.0 Vand 8z: 4.00 V and the resistances are each 4.00 ,0. What

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empty, (b) half-full, and (c)

73 A controller on an electronic arcade game consists ofa variable resistor connected across the plates of a 0.220 p.Fcapacitor. The capacitor is charged to 5.00 Y then dischargedthrough the resistor. The time for the potential differenceacross the plates to decrease to 0.800 V is measured by a clockinside the game. If the range of discharge times that canbe handled effectively is from 10.0 ps to 6.00 ms, what shouldbe the (a) lower value and (b) higher value of the resistancerange of the resistor? ssM

74 (a) In Fig. 27-4a, show that the rate at which energy isdissipated in R as thermal energy is a maximum when R - r.(b) Show that this maximum power is P - '8214r.

75 Wires A and B, having equal lengths of 40.0 m andequal diameters of 2.60 ffiffi, are connected in series. A po-tential difference of 60.0 V is applied between the ends ofthe composite wire. The resistances are RA - 0.I27 O andRn:0.729 f). For wire.4, what are (a) magnitude / of thecurrent density and (b) potential difference V? (c) Of whattype material is wire A made (see Table 26-7)? For wire B.,what are (d) / and (e) V? (f) Of what type material is Bmade? ssM

76 Figure 27-63 shows an ideal battery of emf Z - lzY,a resistor of resistance R : 4.0 O, and an uncharged capacitorof capacitance C - 4.0 pcF.After switch S is closed, what is thecurrent through the resistor when the charge on the capacitoris 8.0 pC?

77 The starting motor of a car is turning too slowly, andthe mechanic has to decide whether to replace the motor,the cable, or the battery.The car's manual says that the 12Vbattery should have no more than 0.020 0 internal resis-tance, the motor no more than 0.200 C) resistance, and thecable no more than 0.040 f,) resistance. The mechanic turnson the motor and measures 1I.4V across the battery,3.0 V

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your potential is greater than 100 V you could ruin the com-ponent. (b) How long must you wait until your potentialreaches the safe level of 100 V?

If you wear a conducting wrist strap that is connected toground, your potential does not increase as much when youstand up; you also discharge more rapidly because the resis-tance through the grounding connection is much less thanthrough your body and shoes. (c) Suppose that when youstand up, your potential is 1400 V and the chair-to-you capaci-tance is 10 pF, What resistance in that wrist-strap groundingconnection will allow you to discharge to 100 V in 0.30 s,

which is less time than you would need to reach for, say,yourcomputer? #72 An automobile gasolinegauge is shown schematically inFig. 27-69. The indicator (on thedashboard) has a resistance of10 C). The tank unit is a float con-nected to a variable resistorwhose resistance varies linearlywith the volume of gasoline. Theresistance is 140 f) when thetank is empty and 20 O whenthe tank is full. Find the currentin the circuit when the tank is (a)full.Tieat the battery as ideal.

across the cable, and a currentof 50 A. Which part is defec-tive? ssM

78 Figure 27-70 shows a por-tion of a circuit through whichthere is a current I : 6.00 A.The resistances are R r : Rz :2.00R1 : 2.00R + : 4.00 g1. Whatis the current it throughresistor 1?

79 In Fig. 27-77, Rt: 20.0 O,Rz : 10.0 ,f), and the ideal bat-tery has emf,'8 : 720V.What isthe current at point a if we close(u) only switch S,, (b) onlyswitches Sr and 52, ?nd (c) allthree switches?

80 In Fig. 27 -72., the idealbatteries have emfs Zt:20.0V 8z: 10.0 V' 8t:5.00 Vand Et: 5.00 V and the resis-tances are each 2.00 O. Whatare the (u) size and (b) direc-tion (left or right) of current i

1

and the (.) size and (d) direc-tion of curr ent i2? (This can beanswered with only mental cal-culation.) (") At what rate isenergy being transferred inbattery 4' and (f) is the energybeing supplied or absorbed bythe battery?81 In Fig. 27-73,, R : 10 f).What is the equivalent resis-tance between points A and B?(Hint: This circuit section mightlook simpler if you first assumethat points A and B areconnected to a battery.)82 In Fig. 27-74, the ideal bat-tery has emf.'8 :30.0 Y and theresistances are Rr : Rz : 14 f,),R3 : R+ : Rs : 6.0 C), Re : 2.0f), and Rt : 1.5 O. What are cur-rents (a) ir, (b) io, (c) i

', (d) i3, and

(e) r'? FlG. 27-73 Problem 81.

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83 In Fig.27-75, the ideal batteries have emfs %1 : I2.0 Vand 8z: 4.00 V and the resistances are each 4.00 ,0. What

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empty, (b) half-full, and (c)

73 A controller on an electronic arcade game consists ofa variable resistor connected across the plates of a 0.220 p.Fcapacitor. The capacitor is charged to 5.00 Y then dischargedthrough the resistor. The time for the potential differenceacross the plates to decrease to 0.800 V is measured by a clockinside the game. If the range of discharge times that canbe handled effectively is from 10.0 ps to 6.00 ms, what shouldbe the (a) lower value and (b) higher value of the resistancerange of the resistor? ssM

74 (a) In Fig. 27-4a, show that the rate at which energy isdissipated in R as thermal energy is a maximum when R - r.(b) Show that this maximum power is P - '8214r.

75 Wires A and B, having equal lengths of 40.0 m andequal diameters of 2.60 ffiffi, are connected in series. A po-tential difference of 60.0 V is applied between the ends ofthe composite wire. The resistances are RA - 0.I27 O andRn:0.729 f). For wire.4, what are (a) magnitude / of thecurrent density and (b) potential difference V? (c) Of whattype material is wire A made (see Table 26-7)? For wire B.,what are (d) / and (e) V? (f) Of what type material is Bmade? ssM

76 Figure 27-63 shows an ideal battery of emf Z - lzY,a resistor of resistance R : 4.0 O, and an uncharged capacitorof capacitance C - 4.0 pcF.After switch S is closed, what is thecurrent through the resistor when the charge on the capacitoris 8.0 pC?

77 The starting motor of a car is turning too slowly, andthe mechanic has to decide whether to replace the motor,the cable, or the battery.The car's manual says that the 12Vbattery should have no more than 0.020 0 internal resis-tance, the motor no more than 0.200 C) resistance, and thecable no more than 0.040 f,) resistance. The mechanic turnson the motor and measures 1I.4V across the battery,3.0 V

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angle g : 30o to the direction ofa uniform magnetic field ofmagnitude 0.50 T. In unit-vectornotation, what is the torque act-ing on the coil about the hingeline? ssM

o48 A single-turn currentloop, carrying a current of 4.00A, is in the shape of a right trian-gle with sides 50.0, 120, andl-30 cm. The loop is in a uniformmagnetic fleld of magnitude 75.0 mT whose direction is parallelto the current in the 130 cm side of the loop. What is the magni-tude of the magnetic force on (a) the 130 cm side, (b) the 50.0cm side, and (c) the 120 cm side? (d) What is the magnitude ofthe net force on the loop?..49 Figure 28-48 shows a wire ring of radius a - 1.8 cmthat is perpendicular to the general direction of a radiallysymmetric, diverging magnetic fleld. The magnetic field at thering is everywhere of the same magnitude B - 3.4 mT, and itsdirection at the ring everywheremakes an angle 0 : 20" with anormal to the plane of the ring.The twisted lead wires have noeffect on the problem. Find themagnitude of the force the fieldexerts on the ring if the ring car-riesacurrenti - 4.6mA...50 In Fig. 28-49,a rectangular loop carrying current lies inthe plane of a uniform magnetic field of magnitude 0.040 T.The loop consists of a single turn of flexible conducting wirethat is wrapped around a flexiblemount such that the dimensions of therectangle can be changed. (The totallength of the wire is not changed.) Asedge length x is varied from approxi-mately zero to its maximum value ofapproximately 4.0 cm, the magnitude rof the torque on the loop changes. Themaximum value of r is 4.80 x 10-8N.m. What is the current in the loop?..51 The coil of a certain galvanometer (see Sample Prob-lem 28-7) has a resistance of 7 5.3 O; its needle shows a full-scale deflection when a current of 1 .62 mA passes through thecoil. (u) Determine the value of the auxiliary resistancerequired to convert the galvanometer to a voltmeter thatreads 1.00 V at full-scale deflection. (b) Should this resistancebe connected in series or in parallel with the galvanometer?(c) Determine the value of the auxiliary resistance required toconvert the galvanometer to an ammeter that reads 50.0 mAat full-scale deflection. (d) Should this resistance be connectedin series or in parallel?.)52 An electron moves in a circle of radius r:5.29 x10-t1m with speed 2.I9 x 106 m/s. Treat the circular path asa current loop with a constant current equal to the ratio of theelectron's charge magnitude to the period of the motion.If the circle lies in a uniform magnetic field of magnitude B -7.10 mT, what is the maximum possible magnitude of thetorque produced on the loop by the field?

L




Problems

..53 Figure 28-50 shows awood cylinder of mass m -0.250 kg and length L - 0.100m, with N - 10.0 turns of wirewrapped around it longitudi-nally, so that the plane of thewire coil contains the long cen-tral axis of the cylinder. Thecylinder is released on a planeinclined at an angle 0 to thehorizontal, with the plane ofthe coil parallel to the incline


plane. If there is a vertical uniform magnetic field of magni-tude 0.500 T, what is the least current i through the coil thatkeeps the cylinder from rolling down the plane?

sec. 28-10 The Magnetic Dipole Moment.54 A circular wire loop of radius 15.0 cm carries a currentof 2.60 A. It is placed so that the normal to its plane makes anangle of 41.0" with a uniform magnetic field of magnitudeI2.0 T. (a) Calculate the magnitude of the magnetic dipolemoment of the loop. (b) What is the magnitude of the torqueacting on the loop?.55 A circular coil of 160 turns has a radius of 1.90 cm.(a) Calculate the current that results in a magnetic dipolemoment of magnitude 2.30 A'm2. (b) Find the maximummagnitude of the torque that the coil, carrying this current,can experience in a uniform 35.0 mT magnetic field. ssM

.56 The magnetic dipole moment of Earth has magnitude8.00 x 1022 JlT.Assume that this is produced by charges flow-ing in Earth's molten outer core. If the radius of their circularpath is 3500 km, calculate the current they produce..57 A current loop, carrying a current of 5.0 A, is in theshape of a right triangle with sides 30, 40, and 50 cm. The loopis in a uniform magnetic field of magnitude 80 mT whosedirection is parallel to the current in the 50 cm side of theloop. Find the magnitude of (a) the magnetic dipole momentof the loop and (b) the torque on the loop..58 A magnetic dipole with a dipole moment of magnitude0.020 J/T is released from rest in a uniform magnetic field ofmagnitude 52 mT. The rotation of the dipole due to the mag-netic force on it is unimpeded. When the dipole rotatesthrough the orientation where its dipole moment is alignedwith the magnetic field, its kinetic energy is 0.80 mJ. (a) Whatis the initial angle between the dipole moment and themagnetic field? (b) What is the angle when the dipole is next(momentarily) at rest? y.59 Two concentric, circularwire loops, of radii ,, : 20.0 cmand 12: 30.0 cffi, are located inan xy plane; each carries aclockwise current of 7.00 A(Fig. 28-5I). (u) Find the mag-nitude of the net magnetic di-pole moment of the system.(b) Repeat for reversed currentin the inner loop. ssM

.160 Figure 28-52 gives thepotential energy U of a mag-

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.60 In an RC series circuit, Z - I2.0 V R : I.40 MC), andC - 1.80 p.F. (u) Calculate the time constant. (b) Find themaximum charge that will appear on the capacitor duringcharging. (c) How long does it take for the charge to build upto 16.0 pC?.61 Switch S in Fig. 27 -63 is closedat time / : 0' to begin charging an ini-tially uncharged capacitor of capaci-tance C - 15.0 pF through a resistorof resistance R - 20.0 C). At what timeis the potential across the capacitorequal to that across the resistor?..62 A capacitor with an initial potential difference of100 V is discharged through a resistor when a switch betweenthem is closed at / : 0. At t : 10.0 s, the potential differenceacross the capacitor is 1.00 V. (a) What is the time constant ofthe circuit? (b) What is the potential difference across thecapacitor at t : 77.0 s?

..63 The potential difference between the plates of a leaky(meaning that charge leaks from one plate to the other) 2.0pF capacitor drops to one-fourth its initial value in2.0 s. Whatis the equivalent resistance between the capacitor plates?.o64 A 1.0 pF capacitor with an initial stored energyof 0.50 J is discharged through a 1.0 MO resistor. (u)What is the initial charge on the capacitor? (b) What is thecurrent through the resistor when the discharge starts? Findan expression that gives, as a function of time r, (c) the poten-tial difference V 6 across the capacitor, (d) the potential differ-ence V p across the resistor, and (e) the rate at which thermalenergy is produced in the resistor.fo65 In the circuit of Fig. 27-64., Z - l.zkv, C - 6.5 p.F,Rr : Rz: R: : 0.73 MC). With C completely uncharged,switch S is suddenly closed (at r - 0). At t:0, what are (a)current i1 in resistor 1, (b) cur-rent i2 in resistor 2, and (c) cur-rent h in resistor 3? At t : @

(that is, after many time con-

FrG. 27-66Problems 67 and 97 .:5

FlG. 27-63Problems 61 and76.

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+stants), what are (d) ir, (e) ir,and (f) t3? What is the potentialdifference V) across resistor 2at (g) /:0 and (h) t-q? (i)Sketch V2 versus / betweenthese two extreme times. ssm www..66 Figure 27-65 shows thecircuit of a flashing lamp, likethose attached to barrels athighway construction sites. Thefluorescent lamp L (of negligi-ble capacitance) is connectedin parallel across the capacitorC of an RC circuit. There is acurrent through the lamp onlywhen the potential difference across it reaches the breakdownvoltage Vy; then the capacitor discharges completely throughthe lamp and the lamp flashes briefly. For a lamp with break-down voltage Vr:72.0 V,wired to a 95.0 V ideal battery anda 0.150 p,F capacitor, what resistance R is needed for twoflashes per second?..67 In Fig. 27-66, Rr : 10.0 kC), Rz: 15.0 kC), C - 0.400 p.F,

Problems

and the ideal battery has emf V -20.0 V. First, the switch is closed along time so that the steady state isreached. Then the switch is openedat time / : 0. What is the current inresistor 2 at t : 4.00 ms? €*o r rS$ Figure 27 -67 displaystwo circuits with a chargedcapacitor that is to be dischargedthrough a resistor when a switchis closed. In Fig. 27-67a, Rr :20.0 'C) and Cr :5.00 p,F. In Fig.27-67b, Rz: 10.0 O and Cz:8.00 pF. The ratio of the initialcharges on the two capacitors iseozleu : 1.50. At tim e t - 0, bothswitches are closed. At what time r do the two capacitors havethe same charge?ooo$Q A 3.00 MO resistor and a 1.00 p,F capacitor are con-nected in series with an ideal battery of emf 8 - 4.00 V. At 1.00s after the connection is made, what is the rate at which (a) thecharge of the capacitor is increasing, (b) energy is being storedin the capacitor, (c) thermal energy is appearing in the resistor,and (d) energy is being delivered by the battery?

Additional Problems7A What are the (a) size and (b) direction (up or down) ofcurrent i in Fig.27-68,, where all resistances are 4.0 C) and allbatteries are ideal and have an emf of 10 V? (Hin r: This can beanswered using only mental calculation.)


71 Suppose that, while you are sitting in a chair, charge sep-aration between your clothing and the chair puts you at a po-tential of 200 V with the capacitance between you and thechair at 150 pF. When you stand up, the increased separationbetween your body and the chair decreases the capacitance to10 pF. (a) What then is the potential of your body? That po-tential is reduced over time, as the charge on you drainsthrough your body and shoes (you are a capacitor dischargingthrough a resistance). Assume that the resistance along thatroute is 300 GO. If you touch an electrical component while

angle g : 30o to the direction ofa uniform magnetic field ofmagnitude 0.50 T. In unit-vectornotation, what is the torque act-ing on the coil about the hingeline? ssM

o48 A single-turn currentloop, carrying a current of 4.00A, is in the shape of a right trian-gle with sides 50.0, 120, andl-30 cm. The loop is in a uniformmagnetic fleld of magnitude 75.0 mT whose direction is parallelto the current in the 130 cm side of the loop. What is the magni-tude of the magnetic force on (a) the 130 cm side, (b) the 50.0cm side, and (c) the 120 cm side? (d) What is the magnitude ofthe net force on the loop?..49 Figure 28-48 shows a wire ring of radius a - 1.8 cmthat is perpendicular to the general direction of a radiallysymmetric, diverging magnetic fleld. The magnetic field at thering is everywhere of the same magnitude B - 3.4 mT, and itsdirection at the ring everywheremakes an angle 0 : 20" with anormal to the plane of the ring.The twisted lead wires have noeffect on the problem. Find themagnitude of the force the fieldexerts on the ring if the ring car-riesacurrenti - 4.6mA...50 In Fig. 28-49,a rectangular loop carrying current lies inthe plane of a uniform magnetic field of magnitude 0.040 T.The loop consists of a single turn of flexible conducting wirethat is wrapped around a flexiblemount such that the dimensions of therectangle can be changed. (The totallength of the wire is not changed.) Asedge length x is varied from approxi-mately zero to its maximum value ofapproximately 4.0 cm, the magnitude rof the torque on the loop changes. Themaximum value of r is 4.80 x 10-8N.m. What is the current in the loop?..51 The coil of a certain galvanometer (see Sample Prob-lem 28-7) has a resistance of 7 5.3 O; its needle shows a full-scale deflection when a current of 1 .62 mA passes through thecoil. (u) Determine the value of the auxiliary resistancerequired to convert the galvanometer to a voltmeter thatreads 1.00 V at full-scale deflection. (b) Should this resistancebe connected in series or in parallel with the galvanometer?(c) Determine the value of the auxiliary resistance required toconvert the galvanometer to an ammeter that reads 50.0 mAat full-scale deflection. (d) Should this resistance be connectedin series or in parallel?.)52 An electron moves in a circle of radius r:5.29 x10-t1m with speed 2.I9 x 106 m/s. Treat the circular path asa current loop with a constant current equal to the ratio of theelectron's charge magnitude to the period of the motion.If the circle lies in a uniform magnetic field of magnitude B -7.10 mT, what is the maximum possible magnitude of thetorque produced on the loop by the field?

L




Problems

..53 Figure 28-50 shows awood cylinder of mass m -0.250 kg and length L - 0.100m, with N - 10.0 turns of wirewrapped around it longitudi-nally, so that the plane of thewire coil contains the long cen-tral axis of the cylinder. Thecylinder is released on a planeinclined at an angle 0 to thehorizontal, with the plane ofthe coil parallel to the incline


plane. If there is a vertical uniform magnetic field of magni-tude 0.500 T, what is the least current i through the coil thatkeeps the cylinder from rolling down the plane?

sec. 28-10 The Magnetic Dipole Moment.54 A circular wire loop of radius 15.0 cm carries a currentof 2.60 A. It is placed so that the normal to its plane makes anangle of 41.0" with a uniform magnetic field of magnitudeI2.0 T. (a) Calculate the magnitude of the magnetic dipolemoment of the loop. (b) What is the magnitude of the torqueacting on the loop?.55 A circular coil of 160 turns has a radius of 1.90 cm.(a) Calculate the current that results in a magnetic dipolemoment of magnitude 2.30 A'm2. (b) Find the maximummagnitude of the torque that the coil, carrying this current,can experience in a uniform 35.0 mT magnetic field. ssM

.56 The magnetic dipole moment of Earth has magnitude8.00 x 1022 JlT.Assume that this is produced by charges flow-ing in Earth's molten outer core. If the radius of their circularpath is 3500 km, calculate the current they produce..57 A current loop, carrying a current of 5.0 A, is in theshape of a right triangle with sides 30, 40, and 50 cm. The loopis in a uniform magnetic field of magnitude 80 mT whosedirection is parallel to the current in the 50 cm side of theloop. Find the magnitude of (a) the magnetic dipole momentof the loop and (b) the torque on the loop..58 A magnetic dipole with a dipole moment of magnitude0.020 J/T is released from rest in a uniform magnetic field ofmagnitude 52 mT. The rotation of the dipole due to the mag-netic force on it is unimpeded. When the dipole rotatesthrough the orientation where its dipole moment is alignedwith the magnetic field, its kinetic energy is 0.80 mJ. (a) Whatis the initial angle between the dipole moment and themagnetic field? (b) What is the angle when the dipole is next(momentarily) at rest? y.59 Two concentric, circularwire loops, of radii ,, : 20.0 cmand 12: 30.0 cffi, are located inan xy plane; each carries aclockwise current of 7.00 A(Fig. 28-5I). (u) Find the mag-nitude of the net magnetic di-pole moment of the system.(b) Repeat for reversed currentin the inner loop. ssM

.160 Figure 28-52 gives thepotential energy U of a mag-

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1.. - fisicadcyt.files.wordpress.comouestions 1 for each circuit in fig. 27 -i8, are the resistors...

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