A compass needle is not always balanced vk8,jefd :egz-pu;8p parallel to the Earth’s surface, but one end mk,f; p:ev8-gpu8z e jday dip downward. Explain.

Draw the magnetic field linexue *+ jag,c1ih sc;+ts around a straight section of wire carrying a current horizontally to thei c*ga ++ h1eu;xtjcs, left.

In what direction are the magnetic field lines surrounding 6e3ryxceo)r o(d.ki*wo( fs)cv6+ ewa straight wire carrying a currc) r3de(efwoev)s* +ok.ocx66yw(ir ent that is moving directly away from you?

A horseshoe magnet is held tkvhl khxdw c4 om2tp. 40*z5/vertically with the north pole on the left and south pole on the right. A wire passinkm thv x/lop0*4z.2h twk c4d5g 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 metallic objectx xq(k+ us0p+j, or only those made of iron? (Try it and seq uxxsp++(k0je.) Why is this so?

Two iron bars attract each other no matter which ends are plac (ehgtmh5cy-z;9a1t38 cp)xp ploukl8 79 qxfed close together. Are bo1cte57 c8p ;(m8xo 9zghtp)qkpflah9ux3l-yth magnets? Explain.

The magnetic field due to current in wires in your home can affectq3; dv(s4z4i0b4 3cehluc tjz a compass. Discuss the effect in terms 3zs4ub;tlj z0i c vc 34e4(dqhof currents, including if they are ac or dc.

If a negatively charged particle vk(xx *4i2bo53rqukoenters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, dec5iobku4x kvxr*23 ( oqrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged pa6 b9 tq.vlf -ms05q;rpbz5 qagrticles move in the vicinity 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 pbfbq. 9-;vqtlmsq5az6 g5 r0 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 Fig. 20–46. Wha+ xsg+/ nv7 zsoem*3aet can you say about the3s g/*xn ee+m so7+zva charge on each particle?

A positively charged particle inue6 q1h(ej ifs5prb vb1)*cy 0 a nonuniform magnetic field follows the trajectory shpj sbvb6 (u0yee15 *h1criqf) own 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 atw3 ppke23f 1j d3l9zijtract an iron rod? What must you consider to ad323j1ppiez3 w9klf jnswer these questions?

Explain why a strong magnet held near a CRT televisib56sscymj j9y -br 9+uon screen (Section 17–10) causes the picture to become distort+mbyb-s9y 9su jr 6cj5ed. 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 this.]

Suppose you have three iron rods, two of which are magnetizev) d*c.+:;gak kazcha d but the third is not. How would you d .vcha:d;*g+kac)z ka etermine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an enehw (*s+lm a 7*jhth9lectril * eh7h+m(*9ash tnwjc field? Explain.

A charged particle ih.al c0 o*+oxjs moving in a circle under the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic x o*c+hjao 0l.field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electr)stsn48i-,i v)kam z9ajf j c)omagnetic 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 perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative fi-) vjmcak8 j n,a 9st4i)sz)ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a current from jd55:npbksl 3va pm/.r8cow. left to m pn:kdp.5w8r5ba.jl v3soc/ right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electrigf v2y+bwq)xb.x df25cxk(f 5c charge.5d)g.2f (+fwq bxyb f52xxvck

A charged particle moves in a straight line thr67s)/xjpb xi 7v kj9smough a particular region of space. Could there be a nonzero magnetic field in this region? If so, gmx/ijv p6sx77)jbsk9 ive two possible situations.

If a moving charged particle is deflected sideways in s7u55tq(o 0zr rggqi0+b ;wtwhome region of space, can we conclude, for certabqoug( 7hr 05;g ztqi0r+w5wtin, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is aqsa5s6p7laz 7+x x2 )vu99 uk2lxphfw 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 wh)jchssg ;cinf*nv,+ h0 *cm;oether moving electrons in a certain region of space are being deflected by an electric field or by ac; foci;m)nsjs+ n*vhc,g 0h* magnetic field (or by both)?

How can you make a compass wc0qw5thw ) mtv,cza1: ithout using iron or other ferromagnetic material?

Two long wires carrying equal currur1 kw ,uf9u9bents I are at right angles to each other, but don’t b u,fwr91 kuu9quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carryijonx 33s5blu2 72paz ing wire, free to move in Earth’s gravitational field, is suspended directly above a second, parallel, current-carrjnoza2s235up3li b 7 xying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized piece of irayxn kmfy1 0tt 2rjpn)0(v*z8on?

An unmagnetized nail willc)r7yst +vp z f599yyx+e9plnjt va-+ not attract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper pr+7fsycy+zjx v95-y ttlp9ve)+ a9n clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubli4 yq:pn s-lu.n )pa:cy ionized. How will their positions on the film of a mass spectulci4p )anqp:ny .s- :rometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid ixmxtpr / 3y-yecp.e0+pz e2t. fe*7gkf
(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 relw-qr f/b buz3c(7 zqe2ay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivqzbczqwf-r e3 (/b72 uot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of cde)rcnvt7 sp3 9vy9)c,6 fxq length on a straight wire carrying acvptr dsx cyf,n3 9ec6v)9)q 7n 8.40-A 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 magnitu0r5 7-3yjvalr3yylffbza0. puw )e vag(u ) p1de of the magnetic force on a 160-m length of straight wire stretched between)ujyeapy0 z7)p0vagf f5-u1r r v (llw.y33ab two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of straight widc5(ecklck/ 8j wz 7s9re stretched between two tower895cl ek(wcsd7kz / cjs 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 p qr4b o,o/gs34.80 m long if the maximum force on it is 0.750 N when placed in a uniforo4o,pg/s bq3rm 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.p) 3r0 5job8op tndt3 tn1)ycu5 A of current is oriented horizontally. At th1n)buot3j8 d0typ)c5 nro3pt at point on 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 carrying 8.75 A is a maximum of:jg w7j)7n fpy 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 j7pf g:)wny 7jstrength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of its maximu.)ri1ya beo,om possible value. Sketch the relationship of the wire a ai,ebr.yo) o1nd 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 is a maxip yvzi;vq p lzrj+76x +9n/h0ymum 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 qp 5j3w c:sk6y.c xj-vwire could just “float” horizontally in air because of the force due to the Earth’:ypjj 3s x- 6c5kc.vqws 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 ch8c3ailqi v hq9n889bbarge $q\,=\,+2e$ 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 force on abqcwx q1+ne0tre j621 n electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for each diagram shown in06evz e ob )gg,x+e-me (Fig. Belzbe, eo gge0vm)e x6+-ow), 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 directikwha6:)jjw*;n qrh/(3 ur4+qamf obz on 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 projecta vvur-efvu ol/ is5t2)k y.4-ed vertically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in aj fcxdf+(mco+y gl,,-wxj4a 9 tdp3az rc 4x;: plane perpendicular to thej3xm,cxjpdo :;,4wad9y f4ac+ f lr+tcx-gz( field. What is the radius of its path?    m

  An electron experiences the grf wqfm;nwca: 09:/ lqa8ta pr-eatest 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 passuql/ g lx3c -mn0f.yu8ing through perpendicuncm-xu0fug/l8y3l.q lar electric 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 w+owoj4gy0 2pwhose 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 ack c qw-dftg+iy/, z88 particle of charge q moving with constant speed v to make one circular revolution in a uniform magnetic fieq,wdkfctiyzg/ 88c - +ld $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uniform mage6 gx9s+a jab3netic field B. Show that its momentum x 3sbjaa69ge+ is p = qBr .

A particle of mass m and xf2, qwcfjzf5( aul71charge q moves in a circular path in a magnetic field B. Show that its kinetic energy is proportion5f,qx2 fc w1zjl 7(aufal to $r^2$, the square of the radius of curvature of its path.

Show that the angular momen bfsx.) .db9.cb swb+btum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular -tom9n)h0vp/y e(qakto the Earth’s magnetic field p0 yh9n(-/vtae ko) mqof $5.00\times10^{-5}\mathrm{~T}$, 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 magnituo/ d;ij(irelrh7,ca 4de $0.40\times10^{-4}\mathrm{~Т}$ 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 sz:ws.qlcv uj ;/(nk4twem ujcx53 k.z/8* pespeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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/e g 15qbzeow(-A current. How strong is the magnetic f/eb 1qe g(5ozwield 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 producwnum xq1q *a9:yfl 2)u+ pjd7he a magnetic field no larger than that of the Ea1 fxq)jywp:d7 uhm *+n29auqlrth $(0.55\times10^{-4}\mathrm{~Т})$ 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 the page tjh.wt xejryy 2y-99pbmu6b 4 -oward you. Indicate, with appropriate arrows, the direction r2. x jy49by-h6j-9e uytbmpwof $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wirfd/s3 3zt/5kb al1c0ndhik0xe carrying an upward 24-A current exerts an attractive fobkhdlf 0 i n/153s zdak0/xt3crce per unit length 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 direction of the force bd76tflg+90, u tjretq .d t1vn - d3gvlegrb).etween two parallel wires 35 m long and 6.0 cm apart, eac dlf ed g7jevb1t3rv. t.rt-u0tg+ndq, 9g6l)h carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is bep0*jrn n v2 ip:j4 ca cu+leoc0by:c;*ing carried out 1.00 m from an electric cable. What is the maximum allowable current in the ccv4:0jja0;* neb*lco2 ipcyn+:prc u able if 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-higaa+;;oco1j 7g3*y ovf,x z xvyh poles. What is the magnitude of the magnetic field produced +gv,1ozj*x3;x7f yv;acaoy o 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 carry 25-A current/(t1jkbld l o:s in the same direction. Determine t ld:b/(ktj1lohe magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a s ,jq --h k7mvh*.rs2-ghdy1k: fjloiz traight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Ea ij7vk *m:s2yfdh.hz l,h 1--gokj-qrrth’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 tly 6o ivj*u(q9yzj* u:he net magnetic field ovz:qu 9yi*j y*(luj6 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 c;pdtvu4p*o xj7b 5- 7y: qixdgiven 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 bz*w+vo5oadb yf ,2a+p: l+crlu/i 5rs etween two long straight wires 2.0 cm apart in terms of the current I in one when thurc w,do:z +2oyilf+* lr/ pbav5+as5e other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires condee*g h75kwk2rvt - :ovucts 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8kovw -7:kg 2*5ht eevr 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)yr /m t0pha5k qb4vc*;, 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 wirvyarq5m*t0;k4cp h/bes? 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 poiks 28dl bp*dbsxh o f+,+/s0lrll3p2d 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 lies in the same pdy, 9mfg6l jua;+kgs4n1q j6llane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in bothsmdn;1+ yf 6agl4kq luj9g6j , wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire, mad;be-bl ckb k86h kb05ge of 2.5-mm-diameter copper wire and parallel to t50;blb8kc kek -bb6gh he 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 otybocn.l141 i gher. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a ynlgb .oc141i 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 w3j2rf5jj0v1en o uj/ jires are 15 cm apart. Wire A carries 2.0 A current. Wj j j3o0 fuenrjv1/52jire B’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 on+c 2ya viv1w8cow,vs d-a 8ult5h2nr4 e another. (Looking along them, they awatcoali+rw c nhv8 8-,syvu25 4d2v1re at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the 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 direct(8tkn1rxznudo,7i j8k ,wm) bion of the magnetic field at the midpoint of the side of the triangle between wire 8,n,tnoz( 1 7xukdjwk 8imbr)M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents Ig/qh c *(onqv3 in the same direction. One wire3/hq*n(cgq ov 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 has6y+g5.mw5btc3knh)4gg kah4 oavb5 p a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside near the center5g gh6+ta.3ob p44hwc5mnvygba k5)k .    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm 6m2p+z6wlz-n5yx kg din diameter is to produce a field of 0.385 T at its center. How much cumnl - zg2kdwpx5y6z 6+rrent should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current iw zzrtz8k/irj3f jt:r48s ;+en it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solj;izsw+tzz r 8er:3fr/tk 48j enoid, 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 points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that produ uvot2 xn/0t+eces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or somet/20 xtnute+vohing else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circ3wgt ,wc q65j v y-qliryt.t51s/1yb. ogg0t gle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. B g/ 0t5-.w1vc 5b1oq,g iyjwq3tyrgtst.y6g l elow 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 magnetic field between the conductors om0-f1hmpmnu1g nj( 3)ecxsa7 f a coaxial cable (Fig. Bnnmxh1 s-0mep m(f7c1uga)j3 elow) 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 vsytf lbzju *m6wg3+i q4n5 l80 f7j;zplaced with its face parallel to the magnetic field between the polz+3 fzjqsy fn5lbm6wu4 vlg; j*t80 7ie 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 needlep2f5e7dsiw5q vv(pl- deflects full 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, w;0t 8o+lxbffh c4 n9hdhat current will give full-scal ;b0dohtfc 89h+lx 4fne deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a bp1 /vq9nv3 j .6uk)z3vww1iuvs )kqtmotor drops by 12%, by what factor does the output torque chau.wp)nv911kvj3uvtvi/ bksq ) z3 qw6 nge?

Show that the magnetic diwx:emxj+ u*ka4 4: y 6 twppr)-urs9wzpole moment M of an electron orbiting the proton nucleus of y 4e4as6wpp) u:+- 9xj rkwmzr:w*tuxa hydrogen atom 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 loops lies flat on the)bg1d;mgl9 l2 zplhs- ground. The 9)b;p2ml d g-slh1zlgEarth’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 e-x0pt6 q en1l -szmk.of radius 5.10 cm in a 0.566-T magnetic field. What value of eqke- 0te. 1sx p-lmnz6lectric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature eq-i 06a jqdwq mx6p99kpual to 21.0, 210p 6qik6w9p dj -aq9xm.6, 21.9, 22.2, and 22.8 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 plates in the mass spectrom)vo5dx; yt )0wvnstv (eter of (Figsxwt y;))vodv n5t 0(v. 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 used to monitor air pollutants. It is diffr1(s9gwcbor y 4( wq0qicult, howeveg4 rwq10 q ysrc((wo9br, to separate molecules 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 accelerates ions by a voltage V before they entersc2r ;o/h d.yfxhc) 6c a magnetic field B. The ions are assumed to start fro .6rdshfo;2cyc chx/) m 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 loopcb p1)g (p8bwd.fq7l zs of wire per meter, and a 25-A current flows through the wire. If the permeability of the iron is 1pzb.l8)7g (fwbp cqd$3000\mu_0$ 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 hj w,)r4aqeg8v c3 0sdbas 640 turns of wire. The g0)wrjb 3s4, eda8qcvmagnetic 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 momentuq/ ymm2 c1m. bz uel iy/4pxbj;2f6q4pm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kine3jz tmuom5y m 4akk;:5tic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their c5a4 :k ky3om z5mj;umtircular paths?   

  The power cable for an el*le 1klqf46 hwectric trolley (Fig. Below) carries a horizontal current of 3wehl 4kf*ql1630 A toward the east. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a 8+ uo3)bk+jvrjh nfjm 0,zx)jyze4i0 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 ln3pmw3a(;r xu- .1mz; wf bwpEarth’s magnetic field points almost horizontally to the north anraz ;b;3wlp-w um3 (pwn.1xmfd has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atomwl4hdvnh( ix-l5s ;y-6vf7t)g0n pkd , 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 launc du ioq:8+aoq/her” is shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, q8a/uo+qido: a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar 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 suspend;8wrzs fp: usp3p4*j;s euar; ed 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 currenase3*;:upfr ;ju4 szw;s p8rpt flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act as wo 0ye3k88y.f b kl+hux-/s hfsg7ph3rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic .s 0hefl h 7wbs hg/k3y+y3upk of88x-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 deflecti0ipi6hq q+ m)lon of the electron beam near the center of a TV screen ) imh l6qpi0+qdue to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelera858hux a /drrtte 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 accexua/rtd85 8r hlerated 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 parallo+h5pre:.ymrs / dy *u +.sjsoel wires, located at the corners of a square of side l, carry .e:sys.+o up*hrdr/mo y j5s+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 accelerator38bak8zxto t5dxu) i:dv5*k vi5v:shs for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. 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 dk3:v v 5tv:it)shi x8auzd x *b855okangle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of w9jfajec2h*m: st pu 4 h25r1udire carrying a current I euc 4j9sdh2u5*fj 2mt1:hapr (as in 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 magneticva)w2p b pui/ nag3-i6 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 py1sd266nv5z7 c jae3.znlkl us3;l toroduced 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 experz;lcl3s usoav y2n3d l67.t j15nzk6eience 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 makexh90m 9k5ybf,r jvd2w a beam of electrons, traveling to the right at a speed ofjw f,99rbmy 5khx 0d2v $4.8 \times10^{ 6}\;m/s$ 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 m+a+gjqogv;-x +dqi w6 agnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successd+gg-++qi;6wjqvo x aive 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 di/a0 ikqg ;lf(wameter, is to produce a 0.30-T magnetic field at its0i;qkf/wa (gl center. 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 de z :u l btzuol8 g)7x(pt*1l4md,i(hwiameter 0.50 mm, carry the same current but in opposite l1ep8ut :o),gi(l lz7 d*btm4uz (xhwdirections. 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 magnea- kw0dq .4pr-k9 ,kxzg9fs sktic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$