A compass needle is not always balanced parallel to the Ear(-vxuq4t u-p rgmy q 2e* )l7da61irqqth’s surface, but one end may dipm i6*rdqt2rv7l eq )u(xq-4 -a1ugyqp downward. Explain.

Draw the magnetic field lines around a straight section of wire carrr;88kqp l m ej,av c)y0u,s4nxying a current horizontalseunk)4c m0,8l vjq yxr ;,pa8ly to the left.

In what direction are the magnetic field lines surrounding a straight wire cae0)wheu2r qj.rrying a w0)2jqu.er ehcurrent that is moving directly away from you?

A horseshoe magnet is held vertically with t2sf hhi1n, k. eynb78dhe north pole on the left and south pole on the right. A wire7 s, 1iekyh2dnhfn. 8b passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any md.0 m3vy:aqagj. 3wryt- ckk 8i4zf* tetallic object, or only those made of iron? (Try it and see.) Why is thaqvz 4.wycaiyr -. 8t3 j3k*g kt0fmd:is so?

Two iron bars attract each othel9 (2dz-sr oywr no matter which ends are placed close together. Are both mag-w(ld92rs yzo nets? Explain.

The magnetic field due to current in wires in your home can affect a compass.8bb . 1e bhga3x;rll,s Discuss the 8.e;a xgrl1bbl3b,h s effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field which xu9tc8j8si, 3+tkhuc 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 aks cjiuh938t8 u+x, ctssume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a curreyi7e 4 ip46uwknt-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, ekiupwy7i6 44and 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 c, enter a magnetic field as shown in Fickqg1 v ;7dtrda9:bs2 g. 20–46. What can you say aakqt91:7bv 2c; rgddsbout the charge on each particle?

A positively charged particle in a nonunw nelgg8/mmf(m19 t/niform magnetic field follows the trajectory91m(gge/nt/nw m f8l m 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 2b7*zx lk1r75em bpr5n nm;kb z: e-khmagnet? Can a magnet attract an iron rod? What must you consider to answer these quxz5 r*eeh1r2z mk5-b; np:bmkkl 7nb7 estions?

Explain why a strong magnet heldyiz a k2ubuc8x3:ffzu469p t* near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, exp8t 4a z3uzfi629pybuk:x*fcu lain 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 this.]

Suppose you have three iron rods, two of which are mag rrek9omyj, tyu y/,:r(ybx ; 38hw6jgnetized but the third is not. How would you determine which two are k6,yt: yjm,yjrrow(8 u9/e 3h;g xrbythe magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an elect)j87kdx psy. c3vsh ee08dd8 qric fielde sp3c7q )0e8dv8.jdhk8 xsdy? Explain.

A charged particle is moving in a circle under the influence of a uniq+i6h4h8ni;fouzx x xxf4mriv1-,y l* fnp 74form magnetic field. If an electric field that points in the same direction as the magnetic fiel 7ium,-l xvfin ;r +14of*4hxxznp86qfxi4 yhd is turned on, describe the path the charged particle will take.

The force on a partii o;(hhc::7 vsq,eecd cle in a magnetic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart (,vc7 eso c: dqeih;h: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 dio oe61o;jnbb+scro (s4,mh c ;rected toward a horizontal wire carrying a current from left to ri 6ms r1oonb cb o4,hs;(+ecjo;ght
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields thaal1w -2fg ka+r1sg;o2bfyt8dt surround a moving electric charge.as2b2lfg8rdko1t w+ya; 1fg-

A charged particle moves in a straight line through a partij b13s-s ip(vdzlcs8*cular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible1*c-38vdb p j lzssis( situations.

If a moving charged paryrnz3z-1rn9p p-y1f lticle is deflected sideways in some region of space, can we conclude,- 1y31ylnzp9rnzfrp- for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magn:l3/f spf wqxeq4-5 7vvsw 6oaetic field $\vec{B}$. 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 certn72zb7 a9hxjb ain region of space are being deflected by an electric field or by a magnetic field 7 x9bj2banz7h(or by both)?

How can you make a compass without usingqtgq ru30o;m/ iron or other ferromagnetic material?

Two long wires carryij ; rtq9ohj;r9u9 8zqvng equal currents I are at right angles to each other, but don’t quite touch. Describe the magnetij h;9q vtr;98oz qjr9uc force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational fiez(s :65 dbl+ yewq(scald, is suspended directly above a se(cqeybz5l sdwa s +:(6cond, parallel, 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 bp+udnk 1tuj* lyml * 2t8;+bsunmagnetized piece of iron?

An unmagnetized nail will x(w(x(ofkd; v8q rr:aszt,.p not attract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet( (:r ( rqoxap.x8kvf w,dszt;, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singl)gap5 2l0mty ay ionized and the other is doubly ionized. How will their positions on th20l)5ag m yptae film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid if ql m;jp p)+c1i2 1eg4)qpyako
(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 . A r8drsoka6 ,0e8 ppna0f71 zbrxelay 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 c8pond0ef7s0 ,a pkbz 8ax6rr1lose 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 magnitux/)d 3:zvbnan rc1 z3c:a;frv de of the force per meter of length on a straight wire carrying an 8.40-Ac/rn1fa r:v;a z:z 3 vcdbx3n) current 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 force on a 160-m length of strai;lezbr9 k 5nuy4skr 85, c,za8rnfl6vght wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field ,; erlk y5b 6s95r88unar4,vlzn cfzk of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on xw4b)o8 pyv90zr h dk;aj j(2sa 160-m length of straight wire stretc; x8w9) ypdsbv( hroaj2kjz4 0hed 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

  How much current is flowing in a wire 4.80 m long if the maximum force on it is -b l4 +q;ujtln0.750 N when placed in a uniform 0.0800-T fij4nt b-;lq +uleld?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. Arfge o:pzq5-z)( qqu++e/ygh ri 9s1jt that point on the Earth’s surfaczzqrgfh:y iep+e/ujso -5 q)(q1r9g +e, 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 carrying 8.75 A is a maximum of 1.28 N when placed between jga jj)x4j dy4r6ca,132i nolxaup7)the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnea)6)1xirxu ag 3 l oj 72,apnc4yj4djjtic field?    T

  The magnetic force per meter on a wire is measuredffvdmojc*h v07rws:x86 9- xx to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum,6 0s xv9fxh*j o-rm:cv8dw7 xf and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maxiti r.r8q)buovh; g 86gmum 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 3buwnlwa+5 e1k. r7glq(lsb2 copper wire could just “float” horizontally in air because of the force due to the Earth’sbb ls72 (3+gr nwuw5.ll kq1ae 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 charhq /t.6 do8a1axnf-m*h/ a cqwge $q\,=\,+2e$ 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,ncqjx9sqzrh tr8m si3( xw2( )9 ebo/ 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 negativqc3 uaw4s .u0n-3. nht hxfa0ke charge for each diagram shown in (Fig. Below), knfa 0s4wu3c0. u- 3h. htnaqxwhere $\vec{v}$ (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 oftza x5(r297-.(c fgllj ,n,dbjkdoff $\vec{B}$ 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 vertikn sc2+xx4 ybk4/kk i2cally 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 enhnj5(2q mqt4p 73ivofters a 0.20-T field, in a plane perpendicular to the field. What is the radius of its path7 jmfh 2v5n34iqto (qp?    m

  An electron experienqt4 kuaa(r98z ces the greatest 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 passicf1 .oqo/a4 s:h/sfl zng through perpendicular electricfsqosc4 : ./ zoa/1hlf and 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 atom 8u usv9ujt bpd 1b74dfsc:a:2 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 required for a particle of charge q moving jy 1bi jen ..7 e,enbgq4+b*gxwith constant speed v to make one circ+x . , ngbjie .e7bqgnj4eyb1*ular 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 pat /qm9y(lev w/hh of radius r in a uniform magnetic field B. Show that its 9lhwe m//(vqymomentum is p = qBr .

A particle of mass m and charge q mo,dl7.8 l pm*qaiw7gyaves in a circular path in a magnetic field B. Show that its kinetic energy is pro.lm a a*pyq8d7i7w,glportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of tr7x i m0l;kn dr,hw(6lhe 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 perpendiculaoyp8t1s u b-rxj2 :hr,r to the Earth’s magnetic field hr, yu8po2rs-:j 1txb 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 magnetg*h)mf0i -h mr y0zqr6ic 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 spee jb9*gb +zb0ecdyt28w d $\nu=2.0\times10^5\mathrm{~m/s}$ 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 6fwfzd+:)704hzvf(k- r 4+yaq c jysls 5-A current. How strong is the magnetic field 6.0 cm away from it? Compare to ty wac+sf4yd f) -zvhz+jf 7kr0(q4sl:he 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 3328hv c r nh yr;rnjtq;l ytsd55rt7+allowed to produce a magnetic field no larger than that otl;jnv+yc5;t7rrn3 dtr2hhr3ys5 8 q 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 wid:i.fjw5 p,fn 0 i9niw/x*wtqre carries current I out of the page toward you. Indica5/xw. j0*dwt ,fn fw:in9qiipte, with appropriate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrymhmj17l o 8z58zs onb2ing an upward 24-A current exerts an attractive force per unit length omn mzjb78ooh15l 2s 8zf $8.8\times10^{-4}\mathrm{~N/m}$ 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 direct(xqoem idf pt6;9xy93 ion of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in thxy;o m(d i9f3tq xpe69e same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 5 +* ufrllvm-sm from an elev lu-frl5m+*s ctric cable. What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A alongidmbb l hets;-+v2mf 10vv:du,3g *xh the tops of 8.5-m-high poles. What is the magn+gbt 3f:0db1 mm ,uiv d;le-h*h2vsxvitude of the magnetic field produced by this wire 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 13.0 cm apart carrydttal s i r 86l a4ak0sp-8;oc5.v)lox 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm fraxla l5rts6 4 valt o)c;pksoid.-088om the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wire cl:b1svy-xv . zz;p a0iarrying a 35-A current downward. In what direction does the compass needyz:.lv0-bz;vp1 siax le 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 of curvpxrd+o i,9z,xm :/4yc:tzpgfx ,m3irent 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 downway+t:dm, g 4 ,mx,ipf/:9 rxxczpoiz3vrd, 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 pa1s3x2pp 08pzyued2 pe sses 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 between tw79k-utwt0orn )v g f3ao long straight wires 2.0 cm apart in terms of t7rwto0 u3v-)gn f9 kathe current 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 curvy6x/ju )j1*ihiujzu 03ig)grent to, and from, an instrument. If the insulated wires are)j 3u/0 zuxg6hy 1*vi iiugj)j 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 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 the plane of the two wires shown in (Fig. Below), paraile*iooicrf +yl n92l60f 8p) llel 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 nearest wire, cenf) yfl9*il2ce pi6i o0l +orn8ter 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 poic0 uzh;-g6s mrin0ll 3m : ;-pywlof aus11uy:nts 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 lm1 j7 mw*hv2lv29hzmf7 ixx d1ies in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 m jzm2lh7dix9m 1hvxv7w 21*fA 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 carriesyusut0b+j m l5j6+wng) 7a gl) a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 wub6tgg )+jj50snyul7 )+almcm 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 ,ab*-rx /kslnv j r)-tperpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Bes,)ktb/- rlva xn -r*jlow). 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 wires are 15 cm apart. Wire A carries 2.u8do( 33rv 8g ,glag6ci3lk yh2 oypy*0 A current. Wire B’s current is 4.0 A in the same directigo6 oa2 3clg(g dyukli 38py,vh3y8*r on.
(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 /c) k.t ag2immwires are 3.8 cm from one another. (Looking along them, they are at three corners of an equilaterm2tgak. i/m)cal 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 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 magnitude and directio6v n3la3 v/yvw3r rmv9n of the magnetic field at the midpoint of the side of tvl3n v 9va3 6vw/3yrmrhe triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long paralle4 q.wb jc*il5vl wires, a distance d apart, carry equal currents I in the same d4q iwj. lc5*bvirection. 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 has a total of 420 turns of wire and carries a cur;k8 cy0izb12 pubo9lp au05 sgrent of 2.0 A. Calculate the field inside near 002au8;i uoy b p9 1cgzplbsk5the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 qps2k41m rvqad:2*xzmcd5 q:cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if i1r5mdmdc x4 qs2az*p::v2kq qt 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-cm-lons,s,,,a ysi g :qegve)g 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 force on this wire assuming the solenoid’s field pos,qs, egy :i,v)ga,e sints due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that prtyivwl42 cxgf65x.j )oduces the greatest possible magl ) i2gy cx5xf46twjv.netic 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 hzuq;x h9l3d :f8yn5b along the circular pa 9zlh:b x5hd3;8yqfun th, 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 magnetica ) wny3l(d8 4ce.+pzrx/k0a:wxtxah field between the conductors of a coaxial ca+wa03 8xxk.rth / pdzeywa:4an )xcl(ble (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 side is placed with its face parallel (m jgglq-*b9;qvj (iray3p-b to the magnetic field between the pole pieces of a ab-3 v-blrmq ;(igq*9pj j(gy 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 form mq1z.f0 )q jtmo bdv8m35)t7a6tuhe 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 spr40)g gfr ky3bxo29g lqing of a galvanometer weakens by 25% over the years, what current will give full-scale deflection if it originall2qf 03xg bg4 oyrlgk)9y required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the outpunjcwok - u5 hr in32e7)-,8o gde2irict torque changudcno82 e w hir-rgni,2-3 i7j5ekco )e?

Show that the magnetic dipole moment M of an elecwc.1zt 2, 7,xm9qaw g8vpxymvtron orbiting the proton nucleus of a hydrogen atom is zw x g,2m.vmyq vx8wp9c7 1ta,related to the orbital angular momentum 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 th;n,1a1 t5r4 dm y7ejdyfg*w jbe ground. The Earth’s magnetic fie5jf1;j y7a4ydde*1m t b nrwg,ld 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 in a 0.566-T magnet2h z,mqk6cp lp -k, ::(zmninhic field. What value of electric field could make their paths straight? In what direction must mzpz:lmqcnkh,nk 2h6, -ip: ( it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germaniul l5 +3ndn fvsl03i4hzm atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u3il3nlfv+h n z4ds50l . What are the atomic masses of the other isotopes?

  Suppose the electric field between the electi85ekfzn,s (a ric plates in the mass spectrometer of (Fig. Bek8n aszf 5ei,(low) 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 used to monitor air pzs1v eip32-d1xizam4 ollutants. It is difficult, however, to separate molecules witm4iax2spzz1ev -di13 h 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 accelerates ions by a voltage V before they entew8 tn6a 7b hy;p)iv2nrr a magnetic field B. The ions are assumed to start from rest. Show that t27 bvn8;6intpy h)awrhe 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 flows dl6 2wtt2m 3lwpna m+.r+(ixz 0b+d nsthrough the3l+nza bit 2+ dmtw sx6(d.np+2 r0mwl 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 diamet1p,1(jaxzaemy zkp/ tks7m * 5er, and has 640 turns of wire. The mes5 y *kj,mz1zmp/kx7a1(p taagnetic 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 momentumw 5q63wyl d97y8 oy3f vwcm*qc $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 energy upon entering a rekzw v.0,/s5caw3zrk* e 5jcbf gion of constant c/rz0 v a3,wsc 5.jwfek*zbk5magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electrimqzas;i3ewc. +-. wwdc trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a +a-e qs.zdw;c.wm 3wi 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 has acquiy)x 7sl//ce7 ag3uflu1 qh:jw red 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 horizontally to the:hvvkgzp3 - r1-a8 sst3+l;ia 1wnxzb north and has magni 3za w-ibvz;a811 ghlsxnr3+ksv-t:ptude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 helium atom, whose m 2xmo(im9gz 1iass 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)ycbo8b -yg.; fyq/h.5 h( eywi. 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 web5b yh8h.fcoy;/.q y(gi y- 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-diameter copper wire and is iu. 8i) 6(hjyx*xk;ckuyh n;ssuspended 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 required curhch* 6 ); ji.8kysnxkyu i(xu;rent flow in the suspended wire.    A

Two stiff parallel wires a distance l apart inav rznuno04s8 6hj6q; a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. a; j0zrsqno6hv6n 84uBelow). 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 of the electron beam n yd()yw7jb/ h)vqx jj:ear the center of a TV screenj)/:jxy dh7vq y b)w(j due 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) j- 2t2mbpnr*a-qb 8ydis 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 magnetic field B. The particles are a- -ypm8btjr 2 bq2nad*ccelerated 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 wires, located at the corners of i5/ncvv 0e ;xy vnx1z n1sv,7;m s7oxcb2tm0g a square of side l, carry 1i n5s7nc2m b,xxe c/7n;zvsxm0vvvo 1yg0;t 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 partinul3g7 y, + 69xzzzcskcle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction with7,l3 z6gnx+k9ucys zz out altering its speed (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 40 u2nzr yxnmt8css4) of a circular coil of wire carrying a current I (as inrm2n)cnxz44s0u y8 st Fig. Below) 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 5 8x ,bq: mngf7v-j7rvvrs+qk 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 of magnetic fields produced hf93y57-f gyokrfn9q 3xl 4ty3r-xl hby overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. Th-k5lgy x r f74nth yx39f3rflhqy-o 93e 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, traveling to thz8dv3te9lrdo0,l f 1te ro t dlz3ftldv1re, 809ight 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 fielii9e( h4u1n/ foek -xwd of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two succ /nfi iw4h9e(1x ueko-essive 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 diamete6t,h01xaotuu /8 1efozj 4bomr, is to produce a 0.30-T magnetic field at its center.1aho j /e8tz4 oxt1,m 0ofu6ub If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, ca3w(e4) mj) s24pmnke w2m6 wfe a*zmaerry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Belowsan *m pa mww) 62emwf(z mekj)4e24e3). 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 f /dyf-a4:kx.;k (d.akrn h fhqield 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$