A compass needle is not always balanced parallel to the Earth’s surface, butdz .p:efyd9x ad sm3ospg162j)wo(i875eg to one end may dip downwa 7d9.x)3d8ogtwsm2 :fyo ap1idzpe5s(jo 6gerd. Explain.

Draw the magnetic field lines around a straight section of wire carryihi:zf3s*z83uz 8h cpdng a current horizontally to the iczdp 38*hs3f8zh zu :left.

In what direction are the magnetic field lines surrounding a straight wirqv,vkrp (cv*8tmxpx s/ kv+9l5+ wmj-e carrying a current that is moving directly away from y s(rv kvxq +-m5l pk8*/9t+vvpcjx,mwou?

A horseshoe magnet is held vertically with the north pole on the leftra 0/3ero,b tr and south pole on the right. A wire passing between the poles, equidistant fromabr e otr3/r0, them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic obja 2l2 vx-q0kwzgq cgt r;9,qf0 6fb5ecect, or only those made of iron? (Try it and see.) Why is r 0qce2;5f,b lqq- k2fgcvz6 9at w0gxthis so?

Two iron bars attract each other no matter sziz xlaa*c 4x49e+x; which ends are placed close together. Azxza9 l4 e+xxa ;4is*cre both magnets? Explain.

The magnetic field due to current in wires in yo)ngreuj;gi3a k 6qq nnw-c09lxl2i+0ur home can affect a compass. Discuss the effect in terms of curre ;g -llai 3ennrqu)k9w0qj n+i62gx0cnts, including if they are ac or dc.

If a negatively charged particle 1(8fli,(m t*p gsmdc senters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the par (*lit c8 1fspgmm(,sdticle increase, 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 oy 9+p,2cgoypcw /rsm8f a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For eachcy g9+ 8pyo,w/spr mc2 of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown i tlnp,k( / ow;uoh;f3qn Fig. 20–46. What can you w(oh n3uklqop f;t;,/say about the charge on each particle?

A positively charged particle in a nonuniform magnetic fie2ww3xg ot 0qcm tbm(*;ld follows the trajectory shown32oc;bxt0*gwm(qmw t 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 must bbpv (zg5 9u(pyou consider ub9(pvgbpz 5( to answer these questions?

Explain why a strong magnet held near a CRT television screen (Section r bnid/ uas(p;v9 ah.xqg8t 4517–10) causes the picture to become distorted. Also, explain why the picture 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 thiqhn ( 54gb su.x ta8pdrai9v/;s.]

Suppose you have three iron rods, two of which are magnetized but the thir., ckq,ezzdvbq8t 4z2 d is not. How would you deteq.4d2,zz 8bvcztqe k ,rmine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic fr-1n (sb5/(wztuabf mield? With an electric field? Exnf1(b5uwt /b(srz-ma plain.

A charged particle is moving in a circle under the influence of a uniform magnefi; + ikxw92iki)*z 37efza2o4 0dua7n drtvatic field. If an electric fielzi72i) vazx f3rud24ek0;+*nika 9d aiwtof7 d 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 the ide )dnh,0 p 9vsqbbdd3b,a behind electromagnetic pumping. It is 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 per b d9s0 d,pbh)v3ndbq,pendicular 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 directed toward a horizontal wire carry:+)w4v3 erojtmn+m-8n rar9jhtcv8f ing a current from lero89 jrtt83++wn4mvc:a he mnj-frv )ft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric char 5jam8 74mn-cgn vx,:0l ktlevge.mlexmg84ln 5vv :0t k,janc-7

A charged particle moves in a st c y u8g,erxh3vrkeq7irr r;n* x2b0:3raight line through a particular region of space. Could tr30rqk br;ihuxec e 2,n:7 x*vgr8ry3 here be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is defle4poljs+48 pt9dsw1r it2cko* cted sideways in some region of space, can we conclude, for certaindl k2ort w8pc*4pi9tj o s+s41, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic yq/yjhcv67z 5field $\vec{B}$. 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 whethss pr/mjw8tx1m4ter;n;t-n ( er moving electrons in a certain region of space are being deflected by an electric field or by a magnet p/ n8;st (srt ;n1wmextjr-4mic field (or by both)?

How can you make a compass without using iron or other ferromagnetic mate hf*;tg;ds1jl rial?

Two long wires carrying equal currents I are at r ph;isn2 vc u-s/so967(bx76hjs v demight angles to each other, but don’t quite touch. Describe the magnetic force one exerts on the othe(miho7h6sjv / 9upvc ; besxdns 6s72-r.

A horizontal current-carrying wire,e9zd;:p o)ks iv pkhb 2:1di0;oviht9 free to move in Earth’s gravitational field, is suspended directly above a second, parallel, currk21vpo shk)pi; 9etio0: h;:zvi 9bddent-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 unmagnetizuk* rhnp, /13qf5ss lped piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if :pap,/b4 cqrgone end of /ar:pqcbg4 ,p the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly qqzy3hf7tbhm8 w/6 5g 0udgt7ionized and the other is doubly ionized. How will their positions on the filmmt87g 5by7d q / wqz3hftug60h of a mass spectrometer (Fig. Below) differ?

What would be the effect on B into:,: 0szo6oq; acxp yside 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 . +x-s3fw kcr xx aoyj+;m;z *bpo:89opA 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 cfapo yc38j* x; +obxp-szwr mk:o+x;9 lose 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 on a straig-i-h. hp oiir(.39ap fuqere9e 6)yms ht wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field?sou9h 3rfih 6 9rp-(eqy-pi.a)ieme.    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of straight wirbpqy+ 0 +,bv bz3kt8ebe stretched between two towers carrying a 150-8+bz ,tb0yvbbpk3 eq +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 length of straight wi +opxphy g** rf 3mr0/uvxi-6wre stretched between two towers carrying a 150-A currx0 rwpxv6ypo3 f m/g+ rih-*u*ent. The Earth’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 the maximum for0/jjo ceprrup)f u 2,- t9ny06za;rbgce on it is 0.750 N when placed in a uniform 0uozn,;et6 r pgu29 0 /rjj-)0r pbafcy.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented zz p8 5 7ijxcok7b*il9horizontally. At that point ok9p5x8i7zibo*7 zj lc n the Earth’s surface, the dip angle of the 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 ca z53p21qo nch-o/r.8/3bdhebfu qxnorrying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approx.qod o eq/8nufhpn3h2bo 1xc/53rz- bimate strength of the magnetic field?    T

  The magnetic force per meter on a wir,ch q951rq-j xwlr: kue is measured to be only 35% of its maximum possible value. Sketch the w,-ckr q9rql5:x j h1urelationship 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 and the magnetic field.    $^{\circ}\,$

  The force on a wire ikg oe.qbr *g99s a maximum 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 coppergr5v(;,pu-yzyl rsa*i-o ;ai wire could just “float” horizontally in air because of thei (py za ,5o-sv-;uri*lg;rya force 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 charnak ffqo,74r)g elxr-/na)- zge $q\,=\,+2e$ 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 the fojns8uc+f s,f* rce 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 ozs+bwr:*1:9gyvj4 og 0ab qnr f the force on a negative charge for each diagram shown in (Fig. Beloqz bj 9b4rwn*:s v0:gyao +1rgw), 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 directida17tywfe1 nqket 2,nydf .kt-(7 b0ton 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 u3 97zpu;s,wq-ag b krnwz*db3pward 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 r*izzj8l bwdc9 g9*f 0 6qg9vl0.20-T field, in a plane perpendicular to the field. What is the radiuz9 9 j wzgv0id*f*lb 9g8c6rlqs of its path?    m

  An electron experiences the greatest(,5aocsu./ smrjjk -p8p,ybbfeno1 w zir, ( 6 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 electrons that go undeflected when passing thry8zemmzu ; l k-oe1+.i94fd5 cfg4lvjough perpendicular electric and magnetic fields of magnit-m+;z el yc48lf 1 zeuv4kgo9jdfmi5. ude $8.8 \times10^{3 }\;V/m$ 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 w k) ;.1 xi y:kdfmnxfgk8.3zmml 0k6qnhose 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 required for a particle of charge p6 /byyvtkuh8gb(y4+q moving with constant speed v to make one circular revolution in a uniform magnetic f/ky8 h(bybpvtu6y4 g+ ield $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular patrl t j*4pykxy hy*(z4a dk(82rh of radius r in a uniform magnetic field B. Show that its momenr4ypxd4y r (kly*h*8jz2t(a ktum is p = qBr .

A particle of mass m and charge q moves in a circularbo8yl kkiuz163 g t-pcn),) bq path in a magnetic field B.3 )plku8bt- yigo1kqn,6bcz) Show 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 the particle ih6da,hugg, my vu8 9o ,wmz3)bn Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with3etb0)xq.df4a tuk,k a speed of 160 m/s perpendicular to the Earth’s magnetic field of .)e ,xukq4t03dt afkb$5.00\times10^{-5}\mathrm{~T}$, 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 has magefeiwfrdw +dkxgmyg*he *6+ 1719d(onitude $0.40\times10^{-4}\mathrm{~Т}$ 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 spe,zrxy qv 6bn5sx,pbp 8gt2f 0ck1b2o2ed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 eyng(cac zv 7+i, 17fua 65-A current. How strong is the magnetic fieldve ig fzun 7+y7(,c1ca 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 produce a magnetic field no largp nrc2+: a3uoyer than that of 2aprno+3ycu: 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 bq)ab 47yh h+1ces r.l6nw:v)1icl vfcurrent I out of the page toward you. Indicate, with appropriate arrows, the dire)cqa cb)yh6n:hf. r1+ l w1 i4lvvse7bction 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 exerts an attractive fp hox8v* c-w2*impvn)orce per unit length ofwoip*p) hv 2m*8xc -vn $8.8\times10^{-4}\mathrm{~N/m}$ 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 for gsxxpqu37z.ta 57mw+jb9)ib ce between two parallel wires 35 m long and 6.0 cm apart, each +bqw.7iz9 majgs 3 )x5utp7xbcarrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earwj6d)ju3yd ( i5j6yvath’s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable ij5v3wdy) d ajiy6 u(j6f the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-hiadkz7bg ( -*usy5op at9. gyi:gh poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earg-*5aiu. yt s (bozdak:yg 97pth’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 13.0 cm apart caxx7v3j0je v(p4 k5y dhrry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm frxykvde j 5v3hj px704(om the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is p4.zmb(aca:m ivu5:pjvt:r /klaced 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the hori4r5k:ajzm/v a:ivt ucp. m:(bzontal 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 north. What is the netsf2yea9,usjx *.6crt 5.lq 7+z zoxp z magnetic field 20.0 cm due west of tfq7.zje2,y.lsor pz9ts+*u65x x z cahe wire if the Earth’s field there points north but 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 protons passes a given point in space at a rajljh q43o4,fb te 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 between two long strl.qsatei7gyw ) j7c 3y4j1x)h ajv27dk d;f1zaight wires 2.0 cm apart in terms of the current I in one when the other carries xfay4j7ds;h12y7jdl 7kjva 3q )1)e w.itgzc 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A ofltnc1gzf9i1vli wo:6kyk )+ 1 dc current to, and from, an instrument. 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+cvn )klz 1io 1kf9w: yi16ltg)? 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 in th2:/i/r 5 ko, x7rym)voztblgxe plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 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 neare://)vg2r5 o , yokxx z7bmrtilst 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 2r bldonhv. )/+3$^{\circ}\,$ 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 )tgj/r+q)xf5 +kb p 2zr joymmp2 )t0eu86mw jplane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitu20f jz6j 5gytm+b u)xrp82e )tkp/mw)om r jq+de 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 second wire, made2g5y5 dd pl1po of 2.5-mm-diameter copper wire a5opg2pddly 15nd parallel to the first, is kept in suspension magnetically 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 perpendicular to each 7 vx ivd84r,zgother. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field atgdvxrv 7,4iz8 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 wires are 15 cm apart. s(*yb1zs; dg,xr.ny aew wc)) .njc p7Wire A carries 2.0 A current. Wire B’s current is 4.0 A in thy()c *we .r)ga1;n, zjbws .cyp nd7xse 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 ano ,6iia ah ksrrd3+09ryther. (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 i69, sr+ra i30kdhia yrs opposite to that in wires N and P (Fig. 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), determine the m* bzv42ca:a tr;oif4bagnitude and direction of the magnetic field at the ma co2 ;bbt4i:f*a4 rzvidpoint of 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 o aki-uj7o7(6x;r /vkxxb4gu distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below).g6 oubov-j 7a(/ 4xi7kx ;xkru 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 420 turns of wire and carries a curr 2 .glf8;oslcy sg)yf1ent of 2.0 A. Calculate the field inside neascoyllf.g8y2 f gs) ;1r the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.253g. z ko.swij) cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoi3oki.) j wgzs.d carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is tblwgz1nx ;h71e g5j r ()iwy,idt r+4sr*de533 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameterr;ger1n7 *zhldix 1jyr dt(b s iw5wgt+,45 e). This wire carries a 22-A current downward (and is 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 avo;lw16 qwc* :9bbho c practical 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 variableowvo*h1 :b bc9w;lq c6s, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape ofy9o6x; kr7 qfl a circle (Fig. Below). Use Ampère’s law along the y x 6r9k;qo7flcircular path, 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 the ma gst-am/ f-;ymgnetic field between the conductors of a coaxial cm-tmg; asfy/- able (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 akbw 75b)ez,fk side is placed with its face parallel to the magnetic field between the pole pi,)kkfbezwb5 7 eces 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 fu3 4: cffuh7wy(zn*v bull 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 galvanometer weakens by 25% over the years, what c*mpie01ys 0y ;nw:n xwurrent will give full-:* 0w0in;nm sex1yw pyscale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does thv3u3og lv8tz1gvl-.ae output torque chanza vu8v.-l1tg 3g l3voge?

Show that the magnetic dipole moment M of an electron orbiting the proton nucleu yqh9i rebsczj4v9-/ege o+gc *g8.*us of a hydrogen atom is related to the orbital angular momentum ciuvy4q9- +rbe*gs.g9jze /g h8e*c oL of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diamzqbu0qe.2q er+okh7 9z0h -eq eter and containing nine loops lies flat on the grouoqeh-. 9qebz rehzk70u+0qq2 nd. The Earth’s magnetic field at this 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 qd0-cav66i5+ dt5bxoj ee) kx in a 0.566-T magnetic field. What value of electric 05a6t ekq xbi-dxjd6oe)+c v5field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms /8/d/w tc*;znbr jgjx,u0qqahave radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22jb;/wzuc*, /0grtq 8x /aqdnj .8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric p4-rv;po7 m fam* w)59k ve3bwnsdhao9.uvu g:lates in the mass spectrometer of (Fi-a avdvb .wu3k;f7 *so n u emw99phv:o4g5)rmg. Below) is $2.48\times10^4\mathrm{~V/m}$ 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 ahjwabsy7 jzwi s6*0iw3z61)( cb u9rused to monitor air pollutants. It is difficult, however, to separate molecules6jczbh9a1azr*)w7ii (6sswbwyu 0 3j with nearly equal mass such as 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 accelu ,vo83.ky kaeerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that th3kyv8ko. e,ua e 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 current f,m+ouqr;jglz tx-t:z h bu941 lows through the wire. If the permeabilitom9rz l4ttb:g zh-;uxjq ,1+uy 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 hvqyqa1h8o7 7q6 (g7pzmtxq- vhn *8q mas 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48qv78qq7ya8mh6( x7v g-qqp z1 no*tmh 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 momentum1u. ho2 ghj-icorvq.0 $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 ene*x9 uzm+j; ;yjtj/dvp;cfkf: rgy upon entering a region of constant magnetic field. What is the ratio of the radii of the*zpm xdvjf;cuft:j;+ 9yk/ ;j ir circular paths?   

  The power cable for an electriv .a3h 9 r0xq4ltxpdf5c trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic p3vthxd.4af5l x r 0q9field 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 ciki j4,08(/pgw5nio , afmlgan airplane which 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 hormvqo 66mi5ld 0izontally to the north and haim6 50lo dv6mqs 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 hel+ rna+(f ex8+vc px+qsium 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 mfdy ciad2.ed7o::74,j pvzh in (Fig. Below). 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, am2dv:h 7:de7c ai.pfzyd o4j,nd 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 top wire is 1.00-mm-fjd zioc89x0abw24v peg)3 -ddiameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the read f-d3i0gw4cze9xvj 8op 2)bquired current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act as fwpi2 3it(va,so d:8arails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnaiv32t ow:asf8 (p id,etic 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 t7j4 :yh/ i:yycm+dnemaximum deflection of the electron beam near the center of a TV screen due to they: +y i mchny4de:/j7t 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 eleme7c1m 7pvifdw6(4dll antary 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 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 directildvd fm(pi 7a7c4l 16won 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 paralledi-s38 ;e urhpwq k:xpvu0 2q1l wires, located at the corners of a square of side - uvkis ;830uhwq2p :xq erp1dl, carry equal 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 “beam steeo nhb48cefv,47gep2r ring”; 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. What happensnr7p ogb2e v4 ,8efh4c 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 3lk8fnz;rcwr ,yvd 8oc . n 1*, 2ocqqemarr96of a circular coil of wire carrying a current I (as in Fig. Bmolq ;rzqrkn 96o.1vdcef r8can,c8 r *w3y2 ,elow) 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 t z;9 zm/awp0jeyso(e1he magnetic 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 of3:qeunx5t cr)m wd-fc,7 8 4st kum .evx;nma1 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 provid,mx;ec8 5a-mn )ck urxu3t1dvt fn sqmw7:.e4e 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 og/ /gtma i942fa8xqmh f electrons, traveling to the right at a speed ofm4q t2 /aggi8a mhx/9f $4.8 \times10^{ 6}\;m/s$ 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 so ;.z ok4kw-kzpiral 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, kk kwozz.4o ;-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 ujkf. pp9m0;j 0ia6njto produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, 9;pjnf6 kj0j m. ui0aphow many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50t;fx m3 0kovqh4nf(8o mm, carry the same current but in opposite directionqm no(h 8fx;0v t3of4ks. They are suspended by 0.50-m-long strings as 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 = 0.ypdx1j7;)opjjua0 g723 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$