A compass needle is not always balanced p0 3qdbsul7 r8(/mwk mharallel to the Earth’s surface, but one end may dip downward. Exkm(q387/0 lbsuhw rmdplain.

Draw the magnetic field lines around a straigjnqyo j/sirn( pyb x5,v4oiv y /-0.n9j up0f)ht section of wire carrying a currenosn/ .v 90 jn(uqrio yb,4)j 5p0inj-yyfp/x vt horizontally to the left.

In what direction are the magnetic field lines surrounding a stra607gandw );z6la1vqb aw e5 uqight wire carrying a current that is mozlqan 5d1w7 au0g)wb6;6qev aving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left and south boe:zek .h;0qsq3fr ) pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In wha3o sk zqhe:)0e rbf;.qt direction is the force on the wire?

Will a magnet attract any metallic objecq+ lygi8847mcxtjl; pmj8 6 unbj lf),t, or only those made of iron? (Try it aj)lm4fg x8 6ub c li8jq+n7mt;8ljp,y nd see.) Why is this so?

Two iron bars attract each other no matter whicx:wqv1us+g :*l oc qr8+wewa 9h ends are placed close together. Are both magnets? Expu91:q +8:o*wvlexc rqwwg+sa lain.

The magnetic field due to current in wires in your home can affect a cowk g:j h.hb,d(mpass. Discuss the effechw : (,khjb.dgt in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic fu(tcw iu p2i* c, b gsm+9w;)5avlso7aield which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, lb;7* p, c)uwasi5osvgi2wamu(9tc+ decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-cqy. .yzu55rwp *obr7aarrying wire. For e5ro7yyu*r.abz.q w p5ach 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, and 4tz38-n4cv*egvh,nh p:n ohe10rb 1nzd znm* c, enter a magnetic field as shown in Fig. 20–46. What can you say about the charg4zntd,ebcvnhmrng :31n p*e *0 h8vh-z 41znoe on each particle?

A positively charged particle in a nonuniform magnetic field followsk2qo;zc-g0 u ,f*.x ywtp* pkn the trajectory showg.ktp wckn0;y o fx*q-,p2z*un 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 rod? What mub;tj,c)(slx 7 8gfbtx /2gqlist you consider to answer these ques(gtb lf7, tcx jl2qbg); i/8xstions?

Explain why a strong magnet held near a CRT television screen (Secn5++- m ,wse -dzydvgetion 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. e5sm-e - dyvg+w,zn+d [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 ir-7 4poq-)zu:ttpj ng)q -mgfmwcdril3,* + uron rods, two of which are magnetized but the third is not. Howpfotq,7l*)--)g3rm cwj+urgu m- :nitpz qd 4 would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnz v 35ytijs9j; n9)emcetic field? With an electric field? Explain. en9vj9syj zc35)m;ti

A charged particle is moving in a circle under the influencda4kk7w y3 d)be of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe thykb dd)34 k7awe path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromagneticu5: bm1azlr)0:0z qrtrgr5w v pumping. It rz bw05ulv:5gqt)r0zr rm:1ais used to pump metallic fluids (such as sodium) 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+rf a4yn8- b4s tnxeu;q:rai-cted toward a horizontal wire carrying a current from left to r4 qn-nts-iabyuea;+rr48 : x fight
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fieldsb..j w ki5 z9qil6ckug0k-r0 z that surround a moving electric charge. k0.6r ziczk- qk9ul.bgiwj05

A charged particle moves in a straight li 9la p7k,fxuz6fn,7:ftm q+kl ne through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give twq6ftufk a,9n ll,mzpxf7k7+ :o possible situations.

If a moving charged particle is deflected sideways in some region yr p viccqp7-lf5os7p *c3-7k of space, can w rv y7pq7ic5o kl*cfp-s-p3c 7e conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fiel0mf77jplk v+i d $\vec{B}$. 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 spachv/-hn ;x.e 4n 5o3fqpvz*tmwe are being deflected by an electric field or b .twpvhhn;xo5mq*z3/4 -ne fvy a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic *d xjdb5xx tb/c) /t,amaterial?

Two long wires carrying equal currents I are at rig:p.n5lsdl. z*p *xc p46wmigfht angles to each other, but xip zl 4dw.gp* fs*5:.cpmln6 don’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying iqcq, 3pte4n+wire, free to move in Earth’s gravitational field, is suspended directly above a second, pari,ne 4 q3pt+cqallel, current-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 attract an unmagnetized piecg6b-. jm;/ahvxzl p m-e of iron?

An unmagnetized nail will not attracte+2c (to .gfn a0m,jkb an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paof+ . ,cbj2gek0(antmper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubly ika z)xnft- 3 nzy-v(k-oniz n3ztyak-kn-()x-z v fed. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect: 2htn g6d srna5c2 j k-:bpxzt,v7v*i on B inside a long solenoid 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 is a relay . /j.ip3bzbo3:zt x k/n) ie:uwA relay is an electromagnet (thew/3ip :bb u xoenti3j:).kzz/ 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 current 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 op ccfl *499aann a straight wire carrying an 8.40-A curre9cl apnf*c 9a4nt when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic fl jc9)fl7c( 8kxtem5h0 1 jsnirak6 6force on a 160-m length of straight wire stretched between two towers carrying a 150-A7kfl0ra(c) jltc6en516m ks i9xh8j f 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 forcg( /p,fj6z gxge on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The E/ gx,gzj 6fpg(arth’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 4.80 m long if tha:bzsip;- vsnu;89k+ ;zryzi e maximum force on it is 0.750 N when placed in a uza :-szik9u+ bizv;s ;prny;8 niform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current isxdny)d1fdyu91tc 2 sxfkw5b*q4) )ta oriented horizontally. At that point on the Earth’s surface, the dip angle of the ya)wfq sy4)n59ktdxf *t xbdu1)cd21 Earth’s magnetic field makes an angle of 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 mncm)+/+wj-zn3 musbis a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 5 jmz++ ms cb/)un3-mnw5.5 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 its maximumu0e 3r4 lpg:me 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 between the wire andl3egmu p4r: 0e the magnetic field.    $^{\circ}\,$

  The force on a wire is a m(e 6b 7g.tn aiz ,hd(im*byq(kaximum of $ 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-diameter copper wiri)p) vbkjb:/s e could just “float” horizontally in air because of the force due to the Earth’s magnetvb :s k)/)pbijic 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 charfcnuz:cka-82x 4bzuxq7:7 vl h*pa r+ge $q\,=\,+2e$ 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 anp9 v6xmz+kod(z f.zb;d direction of the 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 the force on a negative charge for each diagrs5u2jx ) thx l8d4xdvy7i+-zbam shown in (Fig. Below), where 7x82t h)54xzu -dxdvlj+bysi $\vec{v}$ (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 directio xchz)o++:cx kn of $\vec{B}$ 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 projected vertically upward-, ie1+f/pl y2iqbyqa 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,jltu :x-9- ppkzz54rhuf0 aa7 in a plane perpendicular to the field. What i:rux-5azlj0af7z htp pku9-4 s the radius of its path?    m

  An electron experiences the greatest force as it travels gvsj69uc p1g0,jwh w2 $2.9 \times10^{6 }\;m/s$ 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 beai 4,ry*;mxqrcm of electrons that go undeflected when passing through perpendicular electric and magnetic fields of magnqx ,c 4*yi;mrritude $8.8 \times10^{3 }\;V/m$ 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 atom whose masu /7xoxz9.v x3m/prp ys 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 rhn t.w gh n0i2dnj xic)h;.qrgc8025 qequired for a particle of charge q moving with constant speed v to makj08nictn i.5gq0) wrhgd 2qhnx 2;c.h e one circular 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( 4 nlnbh.ru)8wkr/cw circular path of radius r in a uniform magnetic field B. Show that its momentum is p 8wrbk4.nu hnl wr(c)/ = qBr .

A particle of mass m and charge q moves in a circular path inm0zb p (k032 dv8zyusx(x,,teycx 4 th+kv5wx a magnetic field B. Shy38 ,x4esv2zx(wy05hvd+bp(x k tmu zt xk0c ,ow that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of thej,tye t 9km.0o particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s magtfc9l90kiwn3dsys v8 64q u2 fnetic fi 8w6y c9dsiu0f 9ts 3fnlkv24qeld 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 magnetic field at the equator(c ;7hzjqr 4fn 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 s)m( ugs1y.mg+ n7p,s5ilx aqipeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 stm tl wz jimj3h;df6)3woio0 7)art a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? i7fjjwz i) 6 th)dwol33mom0;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 produce a magn1 a6 y2zr5tz, sooo jlo8yyk/wc8b+ 3getic field no larger than that of the Earts tzjbzo3,yo k c8yo /ly86og21+ra5wh $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a loo g4m .t9 pj+s:9bfunay(m +sdd:fs .gng straight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the dir.b(otps9fn+ gd9s4 dmgay.u :smf+j :ection 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 exerj9v7mp,7i 8fb 2esp ddts an attractive force per unit length of id7,pvp8f j29ed7sbm $8.8\times10^{-4}\mathrm{~N/m}$ 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 between two pu3o :ao zik1b/v7c1 fio6ik)qarallel wires 35 m long 7c/3afz: 1ookii1qko vb6ui )and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carrs;8/rh a0nntms/: 0a7m.yzc wg kylp/ied out 1.00 m from an electric cable. What is the maximum allowable cth z:0gm8kys.s/ar7/y/ nlm pan w;c 0urrent in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a cur cm3z3nuk .4a k5szyf+,h3ekcr*li4 grent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare wit3g5un,zis.3kh femc cz+ y4 34a *kklrh 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 wawu)s15,c or lires 13.0 cm apart carry 25-A currents in the same directwu s,olra)c15 ion. Determine the magnetic 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 due south from a straightiqqgsu5u* *6tdk 9k y+ vertical wire carrying a 35-A current downward. In what direction does thi65uk*9 g+*kq yt sqdue compass needle point 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 n: r(s0jx;tk 2zv3mg zof current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but g;m rs0xz zv2(3n:kj tdownward, 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) * b6up.6j:rdsoqvx q protons 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 midway h u)vb r;wvs;v(ejgw 5a05b:ubetween two long straight wires 2.0 cm apart in terms of the curr;s:bv)gve5ua( w bju 0rv5w;h ent I in one 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 t6wb 36bsyihh q n+e7-instrument. If the insulated wires are of negligible diameter but are 236bbt7 +n eh wihy6s-q.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of 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 i2;kwxrp8bu.zoj/ o-xn the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carrie 2xbzo; 8kx.jpr -wuo/s 25.0 A upward, what force per meter of length does 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 pointo,cmk j /vw:m*. nkeez,b 7ha8s 23$^{\circ}\,$ 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 s,e eje :hqvow17g1 jwqp f 3hzyd339i2ame plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magniqfe,wyhp3 iw79vej o:1 e213hgjd qz3tude 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 curresh ewm:)21mb nnt of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetic :whenbmm1s) 2ally 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 that they are d7lc)u73l3lsi u xd9wperpendicular to each other. At their cwu3llu9i7 sc)xd 3ld7losest, 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 carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel w zs(2y 7:uqhigires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current :zqiys7 h(u2g is 4.0 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. d tgu15 0broxb:(l;ow(Looking 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. ( lo: tbxgbowr0d51 u;Below). Determine the magnetic 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), deterjr38n 1sae-pk e:4ox umine the magnitude and direction of the magnetic field at the midpoint of sja8 e oxn3r1e u-k4p:the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equap,ux jk6w5bae4zd+1 el currents I in the sam 1bz6jed,uw5 +4pk xaee direction. One wire is at x = 0, the 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 19rff s7p ofh,ulw4)2 n9rkbyhas a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside near the center. o l4s f91,yw)nhb7rr pk2f 9uf   $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.385 T bbkp,f 9yt hi9)l ixv4 : ,/jqtdlx0m+at its centet:lbl/,m4d )v +fh9tx xp 0,q9iiykbjr. How much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm6q-pkuv.;f 1k-uyop m-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the f1;yf-qovupu .kk pm-6orce on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practicp gvd5x1:-wph al solenoid that produces the 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 so 1h- d:pwvpxg5lenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circlesa e1naf*i9 f0 (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to de *1a9fans ief0termine 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 shhol795 yqj;b6wz( freipn.5p ow that the magnetic field between the conductors of a coaxial cable (Fi.5rq; wi95 67z bhonpelf(jy pg. 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)n 9ytuhi00djpxs ki6;gtp1a( jl,r;l u d 9c* wire 22.0 cm on a side is placed with its face parallel to the magnett cd*uuid pi t0;kyl1h)9 s(x,6jrgp0an 9jl;ic 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 fulp* ,p:p ;-px mlkv.0 npa1eg/0dhg htdl scale 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 galvanomete.bjmhp/: cxea 6fu1o hk3e,g5r weakens by 25% over the years, what current will give full-scale deflection if3 5 ja.xc, h:u/k6ee pg1bhfmo it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torque c229crbyi 1 rqdhange?c2 ri2rq1d yb9

Show that the magnetic dipole moment M of an electron o qtxq;hyr kt3sg;:).erbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the elec:ktq ;) qh .gexy3trs;tron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 if9:4 nke5gho cm in diameter and containing nine loops lies flat on the ground. The Earth’s magnetic field at thi:5ifeok9hn4 gs location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ 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 circle of radius 5.10 cm in a 0.566-Tz h/ga, ;53dimot( bucun3mh, magnetic field. What value of electric field could make their paths straight? In whatd,(5m,to muuh b a3 ;z3ch/ign direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal to/z ec jul4g.6z 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The lar.ljez4/g cuz6 gest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the+ae:df5qjcl56 zc xt/ 3*t jtk electric plates in the mass spectrometer of (Fig. Below) it xa+tf/*jj cclq ke6 55t3:dzs $2.48\times10^4\mathrm{~V/m}$ 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 xfxnf *b:( d x1mkv08cv/lh: abeing used to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as C1hn d/:xkc*xa 8 xb fflvv(m:0O (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 accelerates ions by a voltage V before they entewppzd) 1lm2)h:s34oe 8o hnvtr a magnetic field B. The ions are assumed tvenl)32: msp4 oohtz1)8hp wdo start 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 loa 0a; kla0jsi1ops of wire per meter, and a 25-A current flows through the0ka; 0saja li1 wire. If the permeability of the iron 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 diameter, and has 640 tu j b(;c7j2xbttc9v8ferns of wire. vj9ebj8(; cx7cbtt f 2The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu2j*nq89 u b uxn/(eedhm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 sxqd*cto yt08 y(9j/ pl6k6 vfnhzx.*n ame kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of theiy0zdn66 (chytvtpn* / f.8 x9jxoqk l*r circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal curre2dbvr/ wu n1ss*c 4tu(nt of 330 A towar/vuu s(crdn*24 s tw1bd the east. The Earth’s magnetic field has 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 whicmi bj;)uifw .5h has 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 field points almost horizon. dyj,d-mkd+ qahk43mtally to the north amydak4.q-,d3d+h mk j nd 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 heliu .i: oqd9tqqq1m 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. Below). A (7nift o,zq0 f8;*jzzj l6+5gnk2 jfahf 4i qplarge 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 pe + k zf fo(;5z2jjqj6gznfhn0 fqt74i8,i*lparpendicular 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 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 to s;asrhvq/6by4a sm6 8p wire is 1.00-mm-diameter copper wire and is suspended in air due to the t8ss/rs6q a 4ma b;h6yvwo magnetic 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 act as railsqc b0-7(3hcf7 19ntzue lur jn to support a light metal rod of mass m (perpendz7j3(b c- nqcul r0u971fhtneicular to each rail), (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 *j0 xl -vbehv/maximum deflection of the electron beam near the center of a TV screen due to th0bx-e l/ h*vvje 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 sz moackn62c- xz;yhl ;ea :4-a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the mag ;lz :2chsn -me4ya-z6;akocxnetic field B. The particles are accelerated to higher speeds each time they 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 parallel ws1dymn /9 rs5yd(i3mb ires, located at the corners of a square of side l, carry eb/ 1r m9(simydy5dn3squal currents $I_0$ 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 particle accelerators for cnc3cc8/w e ;tg(gnc ;“beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. Whatecc(;3g8 n tgcwc;/ nc 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 coic8:idh4(y7fnd j3il+ngq o bde*7sr 5l of wire carrying a current I (as in Fig. Berei4n y3sqo7cdj b7id+ h8(gd:*f ln 5low) 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 magnetic field iom9dnsmly ;6)s 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 magnitu bdk+b o68g5unde of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and 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 curgbk68 u5ob+n drent, 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/l 1un:by6cc d rk1xr2 field would make a beam of electrons, traveling to the riry 1bcn ck/x21:6drlught 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 sp :thr70n) p7 beidq+mkiral path through a gas in a magnetic field of 0.010 T, perpendicular to the 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+k7 pmb) d 7iht:0qnre. 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 sry2 errt /w)howa3sbz j70hlh;4e g(y0ck+;to produce a 0.30-T magnetic field at its center. If the maximum current is e g;rhstw/;7) w sh3ya ohr4 (zcyk+2br0lj0e5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of du e1d5phwi a1pk 54f;piameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. pp51 ;ek5 4ph iau1wdfBelow). 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 u6gi:)ieul 99kfkmpf ; niform magnetic field B = 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$