A compass needle is not always balanced parallel to thex+w0 /2ai)m4 tpph yc;dcmb r(bpr7y/ Earth’s surface, but one end may dip dow(xcmb a pwm7h;b/0rpcy i)t/p+4ydr2 nward. Explain.

Draw the magnetic field lines around a sqw8c-ks ;x. --whv nbztraight section of wire carrying a current horizont-vbnc qz .ws -hk;-wx8ally to the left.

In what direction are the magnetic field lines surrounding a straight )zotz + j5hn/wwire carrying a current that is movit) hwnoz+5 j/zng directly away from you?

A horseshoe magnet is held vertically with the north pole on the left0y9m 6je wqcd(o7jgn3sdi--8hz1p o y and south pole on the r7o h o9yn013qjiz mdcj(-w8- dgs6peyight. A wire 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 merlvhy/5dya 0 7tallic object, or only those made of iron? (Try it and see.) Why is th/dy lv0hayr75is so?

Two iron bars attract each other no matter which ends are placed close tt*vct vc.k g)xb/9wt 1ogether. Are both magnets? Explc /1 .twv)xc *vtb9kgtain.

The magnetic field due to current in wires ins fr8 oh :8kvecpyy;q.-bdg f,1/hb 9z your home can affect a compass. Discuss the effect in terms of currents, including ify8v -hyprgb .1dckzeos h,q:98f/b;f they are ac or dc.

If a negatively charged particle enter1w8 : -.oanono;emhkss a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer :sakm1 8wnn;oe.-o ho. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinityrzhc9 g ib/2i( of 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. g cz/h(9 bi2irFor 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 sh.ch)wqbodr -(6-- se r :m1 jqtpv2dooown in Fig. 20–46. What can you say about th- od(. r)q:w6trhc1b oeq -dpjv-o2 mse charge on each particle?

A positively charged particle in a nonuniform magnetic field follows th51ecz5ik 3(id+.lo lr ctwvoos e +11ie trajectory shown1+3e k1o( wirizt5o5ls1co il evd.c+ 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 199 pccs3y us/6uxiexhu*xu 9iron rod? What must you consider to u9 6i9p9y1 cc 3usuhxx/*sexuanswer these questions?

Explain why a strong magnet held near a CRT television sz wr/w/unt0. kcreen (Section 17–10) 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 yw tw0/ un/.rzkour TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have threx6iezo u)0.f ce iron rods, two of which are magnetized but the third is not. How would you determinf)0uxe i c6o.ze which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? Withc6bf-:4qzhgc sd8o9w an electric field? -cs 8bg c :4zdwh9qfo6Explain.

A charged particle is +bkwlo)bbdb3s(a 3b,.b 3e famoving in a circle under the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the paafbe3.a)b b b3d3w so+b k(,lbth the charged particle will take.

The force on a particle in 1 .)gcb8shai:behe3z -y fmg9a 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 machines. The basic d ga9hy) emfhz b 13:ebg-si.8cesign 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 issjb 2yld ks7jifg,c,7jp 1+ 4vd0k 2tn directed toward a horizontal wire carrying a current from left tolsjj b n10iy, k4fs+cp22kdv7,gtd j7 right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or mag0tz )7pvn-w.v;e2y) uzq x*, fucgmaknetic fields that surround a moving electric charge.epf ny7kw0v;mztq.acx,))v g- u* u2 z

A charged particle moves in a straight line through a particular regio c;uvc kf52;lb3mrt4 pn of space. Could there be a nonzero magnetic field in this l4 tk3v2rb cfcupm5;;region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, can4lz a ;xmce1;dw w7g4.9toub a we conclude, for certaibad4x u;.7w1;wglm4ate9oc zn, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there i-q+v1vbhc8e fs a uniform magnetic 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 certain region of space avy4 jg./f,bq ore being deflected by an electric field or by a magnetic field (or4. f/ogj vy,bq by both)?

How can you make a compass without using iron or otherg6.djuveh /7 d ferromagnetic material?

Two long wires carrying equal currents I are at right angles to 5:hzm78zp aixeach other, but don’t quite touch. Describe the magnetic force one exerts on the otpz 7ha iz5x:m8her.

A horizontal current-carrying wire, f41nz9tlmukbdv1 o al,4 -li 3rree to move in Earth’s gravitational field, is suspended directly above a second, parallel, current-carrying wire.b, lidkn3a11z ltou-lr9 4 4mv
(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 piece of noiv u 2ly0 +h3wy0r,.nrucl3iron?

An unmagnetized nail will not sxhf0) x .sqdhk:hpb1 :r)7n4gml 2t)xn3 fpvattract an unmagnetized paper clip. However, if one end of the nail b.rn3dx t nh:g :ps1hv mq)f7fsk ))0 2hxxpl4is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is s(refd 8.r 0meajtu( v*qaj/k+: bo 9kfingly ionized and the other is doubly ionized. How will their positions on the film of8b.+( v 9o mf0(d*/fkeeajrkruqatj: a mass spectrometer (Fig. Below) differ?

What would be the effect on B pzf,:4 pl1 ivyq,p9fu 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 aj3*ff vu+.*7 niifw(dd frr(r relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit urrin(i7 .j*w f rf+*ddf3f (vcarrying 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 magnitudenyvsvcm:ibv a/ w3s3gq(. i 4l.fk-n+ of the force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic v:4ika (vg.3l q+.ci wn/-vn3msbs fy 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 straigh.c 9lj-xcoq l-t wire stretched between two towers carrying a 150-A current. The E.-l-olcxj9 q carth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude ofs) rws,uk, jw.jm79)f li 3bxdhy,5br the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetb9 ibjflj,h ,.k))5 37 ,dwswyu mrrsxic 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 theb3+ sd+ndd3hk1 k:t/ 2yksoge maximum force on it is 0.750 N bd ht1+sk:yokds3ek/3 2g+dn when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is akos6g (qj)iqz k mkwnfw8 *5d60;b 7toriented horizontally. At that point on the Em6sqn;ojwtb6qg 5 w(7fk i08kkz)da *arth’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 carrying 8.75 A is a mawd7fer// :zjx du3 ;poximum 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 approximate strength of the magnetic fieldo:3 jx;p rd w7f/zeu/d?    T

  The magnetic force per meter on a wire is measured to be only 35% of itsgq-okug )1 l.0c b7ag)lq pk-s maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the r-q.ogb7gkck)sp )qal0 1u-g lelationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire i,c vo gt+j bq21 9fwsr9r69b1b mjtey6s 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 copper wire could just “float” horizontbn ma4h9j6 d s4*hsmd1ally in air because of the force due to the Earth’s magnetic fiels4h9anbmsm41j d6h *d d $\vec{B}$, 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 chargk:0gu r;:xd+*qfp bo1 nk +doqe $q\,=\,+2e$ 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 7vjyz9gug(9l 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 each0zukkz 4dj)b7 diagram shown in (Fig. Below), k)kd0j74 z bzuwhere $\vec{v}$ (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 directhw aeqx.bc+ koi0*g*2 b5 6vrqi rz)a3ion 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 with a speezbn oop37r9 .td 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 f91jpqa4d ae pjy+/pvl y+fg58ield, in a plane perpendicular to the field. What is the rale8 d yj+4fy g9/+pjv1qapa p5dius of its path?    m

  An electron experiences tqils2 fsai:km ;ezt3rk -q5 (*wexw 8+he 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 .5 l4jq;dx efppassing through perpendicular electric and magnetic fieldd p.;4je5x lqfs 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 whose masscoxk:n)4b*l (49gvpi9mo ux s 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 requiredefq . s/7g9syp for a particle of charge q moving with constant speed v to make one circular revolution in a. q p7ssfe/y9g uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of rls (ipnf kqh07d :.s,)i ym8t 3qyeom-adius r in a uniform magnetic field sy7t.qfqpye)s(-i3m ln dk 8m,0oh:i B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetiuxz ,7qcc4a8b c field B. Show that its kiz,x 7cqua4 8cbnetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem hc+9dg07ox p l21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/*saee:xoqy/jbcm90gue *c 1y x6vd .- s perpendicular to the Earth’s magnetic field-ecy:09*e aqx jg/1um s6v o.ebx*cdy 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 has magnitu 7py7b5r1fg xfde $0.40\times10^{-4}\mathrm{~Т}$ 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 p :a sd8fwup6h 1-amn5speed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 65-A current. How str3w*oj7+:fp chc ma s9fs*7zxl ong is the magnetic field 6.0 cm away9c* w fsl *jafxsz+3:hc7 o7pm 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 allih +o l nwt*st8slm5o:,lwwz)dm,6okbyl)0 *owed to produce a magnetic field no larger than that ofm,tho*d,t km)lyo6w)lzl*bw: sl wo +i8n 05s the Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of * gionbgc :x;1+a2d vsthe page toward you. Indicate, with appropriate arrobani :+*cg v12sox dg;ws, 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 carrying an upward 24-A oc 0 aqv8la52 rrsw-a--jwl *xvqv 6*jcurrent exerts an attractive force per unit leng 5j c-6l-alvjo*8w0v2x*waaqsq-vr r th of $8.8\times10^{-4}\mathrm{~N/m}$ 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 di4g 0h-ymxo lu83cf zc5,qs .h)qlfu+grection of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same dil3 sc qxg,5fgfyqu )+ ml 08hh-.4zoucrection.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being cayb 1ny sdr,bknl:062s,vpfq9 rried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if t,9 n6bn b0f:l q vdspryk12s,yhe 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-high poles. W)quu7jjgeh:u1u ;e3ig 9cm7q hat is the magnitude of the magnetic u;e:q9 g 7cq1ig )h73 umeuujjfield 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 wirefk5 -cn9e+ vzyzp 7ux(s 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic ficz yeux 75k -pvnfz9(+eld 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 sou, 6du.gtq 7ammth from a straight vertical wire carrying a 35-A current downa.qmu, dg67m tward. In what direction does the 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 of curreaow*ffw 9 (efz;dvp+r rj0j.0nt due north. What is the net magnet p+wfz*j0vf r;.er0 dwjo9(afic field 20.0 cm due west of the 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 w 7-et+ba7z jny 9wfi4at 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 two long straight i)sa: 65: a);utvy ogfg 0amytwires 2.0 cm apart in terms of the current I in one when the other a )yag6yvg5m 0 :ots);u:tiaf carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25yk7efsi c hy*le7-4x sbh)( j+.0 A of dc current to, and from, an instrument. If the ins) ki s+7-cblfh y7jy *4(exhseulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field 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 d(s9verd0ma .s v/6ta(Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert sa.amvdrvde0 9s(6/ton each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points k ;7zj9er wi4m23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a str-tdhui g5ruxyhkgp0a98 /c 8 9ksi.k(aight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the ac /kurk-ptykh 58 gg9h .u8 s0idi9x(loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire, vne yp qo,)l x7an ,cm)ka+,*umade of 2.5-mm-diametero,a nx yupmvkeaq n )c+)7,l*, copper wire and 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 t,-mbcyasm)0 3okks j3hey are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between k,bc3)ams3soj 0m- k ythem 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 wm)63ngq* i(vckdkp w5m*yc, i ires are 15 cm apart. Wire A carries 2.0 A current. Wire Byp 36ckic5mki q)dmwg**n(, v’s current 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 a9 jbt+jp.cfdshgj6m;i8wuq.h l2c+ x 1-m- x wnother. (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. Below). - +1-lsg+ .9jcjj;p ih8cx6 fwm mb2hxwt dq.uDetermine 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 mag yi8w x00.zdddnitude and direction of the magnetic field at the midpoint zd0 d0ywx.d8i 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 distance 9pfopfm g763 d 1g) j)e5ztvwhd apart, carry equal currents I in the same dgo 9f 7vd6tjp )) p5f31gzwehmirection. 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 c vemb8l thzzv,)2 0(bhhflq (juz.:2zurrent of 2.0 A. Calculate the fiv z( uz(8el0 qf,.zh:2hb)z bj lthmv2eld inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is*/ s03zu sg3qdo )yrag51bl3-fjq juz to produce a field of 0.385 T at its center. How much g zjz5q u3/s 01g-3osyda)fu3lbrq*jcurrent 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 33d 8 7c-vv xh/;m8t ct*c08gn(hx6kwua/gbxia A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wireshvm6*n tix/g8bwv-cx8kxtd 0c( ug;a8c7h/ a that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that ( s9dap7ktqm mz2*cbfnl*4 v0produces the greatest possible magnetic field for a given voltage. Should you make yd7kv c* fm 4(s 2bln0pztma9*qour 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 Ampfdmln8s.0au nu62xdf )7 rpz.ère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnu2).d6na7 l0 ffrpxsn8 m.duzetic 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 q::)qq+ tk/ 3ik3fm5sau bv qwmagnetic field between the conductors of a coakv+i5)m f: qbu:s 3/qkq3qt waxial cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed wi684 of4 bzhcxi4d h1p8td4(xd)roobm th its face parallel to the magnetic field between the(1 8 bbt4mdhrf84 )iph do6zoo4d xx4c pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full spc4mg.v 87lxkxb*h9odn1mp )cale 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 thecpl :95d,ga:a. ru 4 7on/cvhzjwt-dd years, what current will give : v-dn:cpd7ujwr/tlo,zc 9agdh a.45 full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by whatjpdqd tdcp6,w*gg7; 5 factor does the output torque cha, dg 7dw;pgp t*j6cqd5nge?

Show that the magnetic dipole moment M of an 0 hah/qpe3qh9pr8ky;9fv n x)5zk 6 voelectron orbiting the proton nucleus of a hydrogen ato/v0 nrqhe3p85k9hh)qya po f69;xz v km is 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 loe *khy74bizaz+xi5 )uops lies flat on the ground. The Earth’s magnetic field at this location)*z4iyha+75zk e x bui 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 magnetic fieldp0f -9wt xpy( 2bw6 gvv+vf+an3y7gnr. What value of electric field could make their paths straight? In wpbf7ytwf gannvw+r3x g+20y(9 p 6v-vhat direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometr;aqd*n/r ky. ai(gk3er, germanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest 3kqgr* n .aayk(/ d;irradius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric)aq,4uci mppxs(d .-g field between the electric plates in the mass spectrometer of (Fig. Bpcua)d xq.i-p ,m4gs( elow) 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 yc:2p u0tus34vcvrks- ds33 io-hb+eused to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (28.0106 u 3yh4+cp tb-isuvok3s-: dseuc2v3r0 ) 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 azk,fe ;gai(3( pjax0enter a,( pf jaxika eg3(a0z; magnetic field B. The ions are assumed to 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 loops of f (i-6ohiw6dx(yi ck5/zu3s or 7lf7ywire per meter, and a 25-A current flows through the wire. If the permeability of the iron -chfsk6wx 7(yri/d3f l5i7 io(y6u zois $3000\mu_0$ 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 tmq/no) l5 6 xhi7*ss82 xj69nnzwbl neurns of wir* eb hw56n9i7xnn / oxqn8)sm ls2z6jle. The 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 momentumd.cssc-: c zww);x -qm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 ek9oinzm6s:7/xzg-v h 7us;/ wp ugw4region of constant magnetic field. What is the ratio of the radii of their circularwewup7:s mzh9 zu47k/;v i-gn6os /gx paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizo*vewn(ub g: l,ntal current of 330 A toward the east. The Earth’s magw:*( vlue g,bnnetic 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 ana.slfc6agm q04 v58 f0bl:pue 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 fwobwyjx 6:/ 5eield points almost horizontally to the north and has ma6ybx 5:wowe/jgnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 heli-7 /qhx.t0*- addhliv hrw9na um atom, whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A large current *sq8rd 6a; mcmvasz*7moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnv r*z7dsa ; cam8s6*mqetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar 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 b1wa)j. ; oawbm3pt bmki,r:.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 required current flow in the suspended wi.;twrjkm) p b,.13 amow: baibre.    A

Two stiff parallel wires a distance l apart in a horiz ghr/qo0l1sg .ontal plane act as rails to support a light metal rod of mass m (ph/r0l qo1.gsg erpendicular 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 maximum deflection of th mudur(q ;+*uy;+zsn de electron beam near the center of a TV screen due to the+udy(;u zmq*nd+us; r 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 accelerauvrcqk /evl68k e-m50te 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 accelerated0r/u5eevk mqvl6 -k 8c 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 co2jv m* v5c/qgvrners of a square of side l, v2 qg/ *5jmvvccarry 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 gh8-,r/8i hphabj 3ewju0r o;useful in particle accelerators for “beam steering”; that is, the magnetic fields can beh3uwgab r iho 8r;-pj j,8/e0h used to change the beam’s direction without 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 of a circular cr,e*4q tsb:m sl zl5u)v3q6bhoil of wire carrying a current I (as in Fig. Belob3lemu:4 s q,bv6t)5s *zhqlrw) 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 itxzl2a2gm+ g-x .ifm/ 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 magnitude of magnetic v)4(l ja9tw* wjkf9a hfields 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 current, values are rms, and the magnetic*vk9ltafhjawj( w9) 4 field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic :xf9y)znbs .-g yl4 u8sue0utfield would make a beam of electrons, traveling to the r98:yxsun yg uz- uf0tle4s. )bight 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 sp2 et.qdog7:5qfo ubk8cf 4yz,,v mxr3iral 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. Calculate the change in the kinetic energyeo,coyf43f x75t mk ,2.vg bur8d: qqz of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in d*bomfpb h.kf(na;6-g vjy:rc dp+8 ;aiameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how ma -8gnabfpdy:p(6kc.av h ; ;bjorm+*fny turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameteru 8eos bk6v)ni.bu0i* 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension so in6)*b .sub0ivku8etrings 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 = 0.23 T rb 8v( hn*y4fkqm 8gn vn1:,9l pyca,jat 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$