A compass needle is not always balanced parallel to the Ears .;pte v/)v00lcta0+dty alvth’s surface, but one end may dip downavav0+ vtcp0d.;/t)lly0es t ward. Explain.

Draw the magnetic field lines around a straight section of wire carryin.o xi9y 1rvej2 nx2at7g a currenvn2 9ti1eor .2yjx7axt horizontally to the left.

In what direction are the magnetic field linesz)l ksz y255tn surrounding a straight wire carrying a current that is moving directly away from y 5lz5stnk 2yz)ou?

A horseshoe magnet is held vertically with thveavj zlfu( gh08q0z+)- j6yie north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, f+0)(ah u6z8vz-g ijvyeq0ljcarries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those ;a0 ux657 kru ixllaju.y :pd5made of iron? (Try it and see.) Why is this;y5 xau6k 5 u 7ljixladru.0:p so?

Two iron bars attract each other no matter which ends are placed close together. exy e)10 9/lia ,e3hde a9ak,e3zmovh Are both magnets? Expla1k3zad,e9 0m a,he ex)iv/y3h9eloeain.

The magnetic field due to current in d02zm)7k 9qhy s*f cjqwires in your home can affect a compass. Discuss the 9kfy0j7dh z s2q*qc)meffect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnv-d1mx (hv au s8y4zx;etic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric fielhvzxv; usad(-y8 m4 x1d.)

In(Fig. Below), charged particlesfznr/b ,w oc j21myx:7b)5p mi optn-5 move in the vicinity of a current-carrying wire. For bf12xnoc ,t)75pro/5y m:m i-bpjzwneach charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, annl;xq. e5gvibauja5c ovy;z/ l,w(il + )p4 0cd c, enter a magnetic field as shown in Fig. 20–46. What can you say about the charge on each partico;y,v 5zai(lcbe 4n5+pgj0 lv.a;) x iuclw/qle?

A positively charged particle in a nonuniform magnetic fajn7pe 88,ntt 3djg4 sb1b(quield follows the trajecto tdba(18,jnqet psjug 34nb87 ry shown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron roxypf(0 ,nq12 meq+vkhd? What must you consid f2 yhxqpmv0e(+ ,n1kqer to answer these questions?

Explain why a strong magnet held near a CRT televisnd6 0h*yw v,rg)-i hgxw81fchion screen (Section 17–10) causes the picture to become distorted. Also, explain why the pict vhhxr)c0hf w8ni ,1 y-d*6ggwure sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which ares gn6 6pi: 9+sv9xllao magnetized but the third is not. How would you determine which two are the magnets without using any additiosgnxs+9l6 a:v p6l9io nal objects?

Can you set a resting electron inghq 9)89 mk,aorz,isz :jvc -ato motion with a magnetic field? With an electric fields9j,8z-avkm,: o)rz qgaih 9c? Explain.

A charged particle is moving in a circle under the +4np ith3td8a influence of a uniform magnetic field 4i3n+d8thap t. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is zr ld,f mp ndn+rp;a,;yhi1i6k )6e7v4wh ho0the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodnmid)dpye +i,oz k hrr0;46,av;6n1p hlf w7h ium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is dire :3wqn 9z ybsw/q:omj. f*bxj*cted toward a horizontal wire carrying a current from left t3sf:: jq9*nzb xbow w/*yjq.mo right
(Fig. Below). In what direction is the beam deflected?

Describe electric andbu9yu 8*v8y e y6hh-fr/or magnetic fields that surround a moving electric charge.uyhbvf y89y *-8ueh 6r

A charged particle moves in f 8*):fhvx;uvmji)7g- *hv7g or yax da straight line through a particular region of space. Could there be a nonzero magnetic fielgxj* yvf8r-oamx))hv 7vf7uh i* :gd;d in this region? If so, give two possible situations.

If a moving charged particle is deflected si9.xkk f3my7 +fg ji ;(dk2leordeways in some region of space, can we conclude, for certain,kl.k joe2dim+fy97f3r( ;k gx that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fieldd +3a.m6a u5kwwc,sn:4q vjrs $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain region of space 7c xryhjh/y80dgrk7.xk aqj r1:5,3uew pmd- are being deflected by an electric field or by a magnetic field (or by by/djrh g35:q ,yxjdhxu re km-7c wpr07.ak18oth)?

How can you make a compass without using iron or other ferromagnetic materiab 2dd f bq+fsi40arfypnh-9 x)* w19ngl?

Two long wires carrying equal current94min3pylme d1 p3-ies I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on ye9m - epil m3p34ni1dthe other.

A horizontal current-carr s,mh5 w2/q2l ;jukw7luc8cr dp(fp:qying wire, free to move in Earth’s gravitational field, is suspended directly above a second, parallel, curk225 rpsc:8lhjw, uqwdm /f qu7plc(;rent-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet opuuw*ps 77v -7w- wbdattract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Howeve4cg/3sucz fut 5 ;fuao h qq58.sqk-5mr, if one end of the nzcusqo /fa;q38uqm54c f5-ut gh5 s.kail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but oneoipo qugk854wz0w( p5 is singly ionized and the other is doubly ionized. Hog55pzupw o8wi4( oq0kw will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long soh3g qrr1 d:n+nlenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid ,l i4b - ;k.kjjnl7 qhs,fxsai9t g(/ypl1lo1is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large curs(.ijbls h g,o j -qkny4/ft;l k1i,l1a9xp7lrent but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straigpdp w2 p(/734 fmi;pj zgm8wdyht wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magneti7(8w m2p4j fwp/p3zdyp gm;d ic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude 8 is3+bv+lgfbi8;ys ua) r-y vof the magnetic force on a 160-m length of straight wire stretc8fsb+l 3ruvg)si +bvy8a ;i y-hed between two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m lwyb am0dm/ wj+i*mm0.ength of straight wire stretched between two towers carrying a 150-A current. The Ea*mm/.+w0 0im mab djwyrth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.zcczv ;:umd f/pf;-jel57fq .80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800- 5;mfqc.vl;puc:z zf- ef/jd7T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At ta0 bmw pmgxhwp0:odt 1)ubl 22;3.q ithat point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle b3g;hlpo p2) tma 1qi dw.bm:u20tx0 wof 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A i w)nmyh3k/w3mmsh5( kuc;6 xns a maximum of 1.28 N when placed between the pole faces of a magnet. If t3n5h u ;h/mmwn6ck )wmx(ky3 she pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of itss uhxiupoo00k9/5rdl5n:d t:: du rl( maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle betwexls / 5u0kpu:ho :r0rult dn5 o9d:(dien the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum of9ia1g e in/lkso -d6e; $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diam- qefvv4gjcklbxs7, r:g49 5 veter copper wire could just “float” horizontally in air because of the for f9v v5q -,7sr xkbgel44cvjg:ce due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chs6fr+zr,zq)gu/ sqqnnf))g5p x99 bqarge $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of :g ./tjd*cf7 xux69icofy*ltthe force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of theqnu3o 3 xko6 fpo5 ;afe8fa5d1 force on a negative charge for each diagram shown in (Fig. Be85kfpfa16feqa ;onou 3 o35xd low), where $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direction ok 5alys +an5g8v1,,h:irk gvnf $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projeca 5x.hr8f+it nv( w1x )q/ukeuted vertically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plane perpendicula-eso,dn c6d +or to the fie o6cd-nd,s+e old. What is the radius of its path?    m

  An electron experiences the gffk tie0h - 4- u -4*bshzfp)*z5ieogsreatest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of elexx0c u*n:s .nmctrons that go undeflected when passing through perpendicular electric and .x0su:*cnnxm magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium. a5mv j(bq*7aanty3gek44 sm atom whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

  A proton (mass $m_p$), a deuteron $(m=2m_p,Q=e)$, and an alpha particle $(m=4m_p,Q=2e)$ are accelerated by the same potential difference V and then enter a uniform magnetic field $\vec{B}$, where they move in circular paths perpendicular to $\vec{B}$. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton. $r_d$ =    $r_p$ $r_{\alpha}$ =    $r_p$

Show that the time T requiredku1v 4fv*rls:-k7 ncfzb:z .d for a particle of charge q moving with constant speed v to make one circulcr :kzv .ns *u :1vff7z4-bkdlar revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r nku4 vqgbp8zj**: 6wzin a uniform magnetic field B. Show z qvu*pj4 8bz g6k:nw*that its momentum is p = qBr .

A particle of mass m and charge q moves in 0evek *0hf./ibo6yj3b1 uir6:o syxia circular path in a magnetic field B. Show that its kinetic ei b:yi6r x0/yesfk0ho1iuje6o 3 b.* vnergy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular mom9kdyy8e ybv:1yn cu:t ma023hentum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with amxkp m 1it1t/qxbu)6n 2j9(j i speed of 160 m/s perpendicular to the Earth’s magnetic9u2itj pk1(m t6nm ij/ )xxq1b field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s ma)jw15 lvosbz5p .ht 47s5h bqignetic field at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with s1id fa7,78 -k2xyjci,rv p ccdpeed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65sck-71; bn*/zesxrsx -A current. How strong is the magnetn-c/s; kzxrb*7 sexs 1ic field 6.0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to p.d;/z4rihhw7 k:ada vroduce a magnetic field no larger than that ozi dhd7.hakav/w r;4:f the Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of thl ve6zxp4j*cn7 :) 9iejcv8cxe page toward you. Indicate, with appropriate arrows, the dirxc nje8 c9x:lp * 4)7cvzi6ejvection of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A current vh6dhf3e9ywh ,99m ucexerts an attractive force per unit length of dwh9hf9em, c63u9hy v $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the force betweenxvx d 6o*nyya. 39*afxlom)i8 two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same dire. d i*)xfo8*vyao39amxl xyn6ction.    N  ----待选择----attractiverepulsive 

  An experiment on the Ej 074hng bz5mbarth’s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to beb zj7ng0m 4h5b accurate to $\pm1.0\%?$    A

  A power line carries a 0+w ge6jssplh/l4,hw current of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this w6 glhel 4+p,w0h/ssjwire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.(a(oal0unz0hsi;9au/,bxk ;7 p kq yx0 cm apart carry 25-A currents in the same direction. Determine the magnetic uqzhaxk aly 7iu9((0/x;o b ,s0apkn;field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due6gpq*yzpqzq zlrkk,9 8 el2 +9hgcr3*wyt) ( d south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle )(qzp* gc6zdre*+,29ptk kqg9yrw 3 lylqzh8point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due zj eah;1*,f e/ rn xfytrsj4 mpw934)wnorth. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north t49 w3;zmfpf1r*waj n y)ers4/,e jhxbut downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of rfyppky6,k ofu 3k)n z(3:9bzz i1j:eprotons passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field 3cqg zr oc:ecz- w3vjflefg/++f61 9g midway between two long straight wires 2.0 cm apart in terms of the current I in onefcef+ 9v + f:- l13ocezr 6j/wq3ggczg when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, an i7 tktti2t66y xnstrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field itky67tt 6 tx2of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. Below), para** c dza.2xvimllel and just to the right. If it carries 25.0 A upward, what force per meter of length d.d*mixv2ac z* oes it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points 6(a 9xsmxr7w-mupc+l23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straight wire, alj3s xai8 :wws9o e0v3w01rth s shown in (Fig. Below). There is a cu3390he 1v os0:ilxt wwasr8wjrrent of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A seco z8z(d7v 6ueucnd wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetu8dzuezc 6v( 7ically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so tgx 9v3c(omo*ej.j*y y nq; m+c;ay0 qn8s jdh5hat they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one car 350mhqa ( d;8. y+vesyxjc*co9m*q ;njynogj ries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cmg66ns7a */miqd eiik( apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 (k 6q6 sigaeni*md7i/A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looko2f755eai cf ying along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magneti efycf55a72oic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine theg1 3 9m)2vksuqwd+:ww xnfhah62.pa cih 4*ud magnitude and direction of the magnetic field at the midpoint of the side of the t:w 9a6fxd1 awmq.u2hu d3ihkg+ w vpn)ch 42s*riangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I in thewas; 27cop- ro same direction. One wire is at x = 0, ap;co-2so rw7the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 4qjcm) m:xw+4d.n;op6oz 5 wiju o7ka.20 turns of wire and carries a current of 2.0 A. Calculate the field dmnjw a;zj.+c wum6oko: 45q o.7)pix inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diam y:7+6.o qmuhjj4qopaw ef ))/ce7hwqeter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turjae/w. q hymo7ho4p)c q7euw:+j)6q f ns of the wire?    A

  A 550-turn solenoid is 15 cm long. 9m)e m t3cc//tvk wm-dThe current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and m //-ttw)v93kcm e dcmis connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoi;5hko 7eua m.rd that produces theo7m;k 5u he.ra greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’s law a 6ktdpfim32+7awgn05z) i x fzlong the circular patkf2x 0 atiidfm5 wg+z7 nz3p6)h, shown dashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that thl))k9pb0 pphke magnetic field between the conductors of a coaxik)9p) phkpl0 bal cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a s+(t ctpjq(sc5 ide is placed with its face parallel to the((c+t5pq jsct magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale zz16jvd-yd97b-p2hprw9 hzw2 zgyt) for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% over the years, what1 lxer(i4w 7mqcp-r f93vjy49 o fzn6xejz9)l current will give full-scale deflectiorq z41 )fc9l9x79ijxr o-6e3 fj(zy wnlvepm 4n if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torque ci3l(*6meyx *4 xvddmq ha qyl*6dx v4meimd(3*xnge?

Show that the magnetic dipole moment M of an electron orbiting the proton ,blm0 gt8d4y(xw mo0 qnucleus of a hydrogen atom is related to the orbital angular momenxt,mw0o0bym 4 qd8g( ltum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flat on 9bmbyyswm+vp; ( 6u5y)2 qbv wthe ground. The Earth’s magnetic field at this location has magniy 9v ys6pu) w(w+qbv5yb;bm2mtude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circls 4h d(j(9t,aal0aww)u5nw pge of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction must it pad4ww)sj0nt 5alg((,9aph w uoint?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvatuetchd:tnd/ l7m9c )4)a di2fore equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radica:hdm idfndl)2/t )7o9ect4us corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectromet t 6jsygz.yvf+ppcsic*)j2+w n1gs 18er of (Fig. Below) is sfy+i6 vt. +ss*c)g 8 2jnwcyzpgj11p $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air polludqpuiwk(4 l*0r mx f5+tants. It is difficult, however, to separate molecules with nearly equal mass such as dm5i 4( f*0prluwkx+q CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelgg fkkxc2km7jnaru2,f53u g zw : 1e9;erates ions by a voltage V before they enter a magnetic field B. The ions are assumed to s;mkw7 zuen kjc3,k2f12a5:xf 9ugg rgtart from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A cu8 tzf)eu4: roprrent flows through the wire. If the permeability of the ireopuf):rz8t 4 on is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in dip-qxut3*me9bert-n 9 r;d ch- ameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is -c rp-q txrd-eu99tbh3 m*en; the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumwv(94 twuu-6h z(hg-zd vtav 7 $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic edtuo9pq .-z i9nergy upon entering a region of constant magnetic field. What is the ratio of the radii of their circular pat9i- up9.d ztoqhs?   

  The power cable for an electric trolley (Fig. Beo5k .qc34t cddlow) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field hqdt4 c3ko.5 cdas a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which haibv d*ou,q 3s2s acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic fk.v w q8x:6wqqield points almost horizontally to the northw:q k 8.qwqv6x and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helizo;08on-kys n um atom, whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Beldax; 5 ofvf9fig*oj;+)iff/ q ow). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar /;+d9 g ;f5vfij fq foix)aof*from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and is b 1cij0hsw)lyw 8xk ,ov qo0-;suspended in air due to the two yw80so q,;iojhkw lv x)- 0bc1magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane actgk-f1 )1r lemmpg;d) g as rails to support a light metal rod of mass m (perpendicular to each rail), 1;kg- mlf1g)dre) gmp(Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection ofgt0 som+0 g 6m6tu,vdi the electron beam near the center of a TV screen dmid0g m v 0t+sg6ot,u6ue to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate raglj;p g,t2ba7/8y s elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time theyp,a; l/b trjy 8gsa2g7 pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight paran wdwim 3 ; bwg89;7u8x0m/masytz po(llel wires, located at the corners of a square of side l, carry equal currents wwum atzm mxoi0w n(7; d3 8/b;gp98ys$I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in partp7aa1fhvx ,1micle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its ,1m a1f7ah pvxspeed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrldz );k1g*gsc ying a current I (as in Fig. Below k;cldg s1*g)z) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnr1qd:+zxqn/ *:wsvev etic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produce -k9b/r)rrn crd by overhead power lines. You estimate that the two wires are each about 30 m above the ground a nrc9 /b-rkr)rnd are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of electrons,6qz r94n( blwv traveling to the ribzqn946 (rv lwght at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of bclgcxvk*,ic4m f,h+2wg (r50.010 T, perpendicular to g,+5 hc,bglcc (wv*r 2xkfmi4the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetm od2:hq5gvzyq/3ap8 -a)gxgic field at its center. If the maximum current is 5.g-3amqag: x dy qvg2o5)zh8/p7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wire4tq2o: *svjabwb /kr9s, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings a bso v/bkr t92*jqw:4as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B bbm8hu;estvt x-)t0 lhr.c2 , = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$