A compass needle is not always balanced parallel to the Earth’s sj7ezkp3rkw0te5.x( purface, but one end may dippzp .50r 37wkjxeek t( downward. Explain.

Draw the magnetic field lines around a st+* ipnq-gg+d3:j5bad wqy1g+ 5 oybszraight section of wire carrying a current horizontally t15:3 oy dn wg+g*j 5bsyqg +iz-bq+apdo the left.

In what direction are the magnetic field lines surroundi-3mqua9ddijrup1 x q +0 48mzlng a straight wire carrying a current that is moving direct u4alp93r8xqzm+dd-q im 0u j1ly away from you?

A horseshoe magnet i x) byk;y1:;hzfqewvq: dte.3mh)gz 8s held vertically with the north pole on the left and south pole on the right. A wire passing betwy3fzx ew k e;t:g :q8)) dq.;v1zbhhmyeen 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 object, or only those made of iron? (Try it af6*xr mgj8 .7yuasf9 rsh 8k/sfrh s g7 6jrfy8asu/xkm* s89.nd see.) Why is this so?

Two iron bars attract each other no mattt 2xyqk6 f3zfab u9 ;ftxp*oq/ s:t:7uer which ends are placed close together. fax2futf/ :;*9qxtpyz o:t 3b 6kq7usAre both magnets? Explain.

The magnetic field due to current ikbko9f /-vy8aytqjf.ls1qc z/.5 h /nn wires in your home can affect a compass. Discuss the effect in terms of currents, including i nflo //qyf9 tcjb zks-. qhvk./ay815f they are ac or dc.

If a negatively charged particle enters a 9t5idnxnrmc 4o lmp/g; 4qp+ (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. (Neglepc 4r59nmo ;/x4+gdlpmn (itqct gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a curre dst(w 0b (d6z;qr5ifgnt-carrying wire. For each chargeq dtfbi(d5(0sgz6 r w;d particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as sh5nfp*kf -zghdfjh r 2to 4h/79own in Fig. 20–46. What can you say about the fho5j-rh z4792hd ff/gp tk*n charge on each particle?

A positively charged particle in a nonuniform magnetic field follows the trajegqac q4gga.wn 6*p a8+o4nk6pctory shown i4 qgacwng6 gk.p4q 6oaa+*np8n
(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 a0 4f -qslm,cfv magnet attract an iron rod? What must you consider to answer c4ff,l-v0q smthese questions?

Explain why a strong mpgsozc - lf, 3 q27ez-f)0ynjwagnet held near a CRT television screen (Section 17–10) causes the picture to become distore zcny)f0gq2-s zljp37 ,f-owted. 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 rod x7l .pq)zz-bss, two of which are magnetized but the third is not. How would you determine which two are the magnets without using any addition. -lqszbz7xp )al objects?

Can you set a resting electron into motion with a magnetic field? With an eleczf:wlm8d rssc fb4,1.tric field? Explaiz.drwssb8mc :f , f4l1n.

A charged particle is moving in a circle under the influence of a uni /w2lgb)qr*,hhw; zl5/8qs osbly3k dform magnetic field. If an eg y 85 d sh;/2)wqwlr3bzl*s,bkh q/lolectric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromagne-me ) 6b-rpqgetic pumping. It is used to pump metallic fluids (p m6)g-eq-rbesuch as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a c7vj2e co odk4ows1* e-urrent from left to right1vo2 s4owe-e *kjdoc7
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric chuvm pe8k25yig ,e z7))o yb1hzarge.mb)hz)g1py ,ukyiv2 ee8 7 5oz

A charged particle moves in a straight line through a particular regh:lub 3xlw atsw-m. *h8j1m/yion of space. Could there be a nonzero magnetiw: mshb l*xjwu 3/ -htm1ly.8ac field in this region? If so, give two possible situations.

If a moving charged pg/r(3 ,m 1cxmjq9 jnwbarticle is deflected sideways in some region of space, can we com mjn9cbqj 3(xw/ r,g1nclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fkj/-ad8m c. zpb0kz1k-lei q)ield $\vec{B}$. 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 el j1 zbn4ac3mj+rzzq ,+ectrons in a certain region of space are being deflected by an electric field or by a magnetic field (or by both) zrz +,j z4c3nbaqj+1m?

How can you make a compass without using iron or other ferromagx0rv)uqd( g/0w2p m yhky.;ggnetic material?

Two long wires carrying equal currents I are at rbiitb lspd9c.:p/5x2 ight angles to each other, but don’t quite touch. Describe the magnetic foid.l5/b i9xcb2 p:stprce one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s graceonbp. h027j vitational field, is suspended directly above a second, parallel, current-chc.2bojp0e7 narrying 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 y5cbl . vqbd20an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmxtpd4j w+(cb 9 wp0fy;f sk80nagnetized paper clip. However, if one end of the naiwp8 k 0db;wtf0xs+nj9 p f(c4yl is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the sa ewzu t2;-a7glr7n :bime mass, but one is singly ionized and the other is doubly ionized. How will their positions on the film ofztwuen gi27 a; l-b7:r a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a lox( *txkh 4wvmq14b,glng solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . A relay djdxyl.)c3j m6zg/y/ 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 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 switchj)z6d yj/3lcdg m. y/x.

  (a) What is the magnitudeg, **y3ryknn)f 9vqhc of the force per meter of length on a straight wire carrying an c)vh *,y9fn r3*gyqnk 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 magnitude of the magnetic force on a 160-m length of straight dh+o0jucrdw5sn:9 1uwire stretched between two towers carrying a 150-A current. The Earth’s magnetic 0 duuoj:n5csrh19wd+ field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the ml. wf rdu xv htts;,6a;5mc4:kagnetic force on a 160-m length of straight wire stretched betk5xac;hw .d;, fsuvlr :m6t4tween 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 wi;neeta9 s0e8 vre 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0a;n0svt9eee8 800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current iy s ufz t:nx yrau*2w599:il 0mcxd/e*s oriented horizontally. At that point on the Earth’s surfe fc ux2 0si z:tn5xw /uard9lmy*y:9*ace, 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 1.2go p7 j:iv0u*e8 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximatepjueo*vi 7g0 : strength of the magnetic field?    T

  The magnetic force per meter on a wiirm h63lv u:1s58 edogre is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and s6ih3m1 ro v5dle8:guthe 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 maxb6t pm)fr1dd5fs .4tzimum 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” hoo/ lkdq*mvsxs 5/8tx; rizontally in air bec;/8lktxx q ovm/*5ssd ause of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chargnee(+nljd wcl 7. +sr/e $q\,=\,+2e$ 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 ly l 6r.*t2hjdi3 dod1x hcc57on 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 ch 0ei7y8b,n9xt* vywcn-xh v2 qarge for each diagram shown in (Fig. Below), wherey9,x *inv-yt 27vhc qxe0b n8w $\vec{v}$ (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 directi ooaorml,u1.4,r 2t qyon 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 1a x1 4ailh7hko-edm 8wu;p9awith 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 (at gi7/x8l 8p7deedy0.20-T field, in a plane perpendicular to the field. What is the radius of its p 7xpg87dd(iyl /et 8eaath?    m

  An electron experienc: /js+y;cf)zz cw+ohi es 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 whh xr/c;8c,ipvh hr*2qkjr;g,en passing through perpendicular ele ;rj qi c*rrhh;cgx/2v8hp,k,ctric 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 whoserso*cpmunxsj d3j *ig;d)i-b(ey ;* - 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 )w2u2pd e*9fo m1gna drequired for a particle of charge q moving with constant speed v to make one circular revolunf 21o*mp g)aedw d92ution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge(b t.28 4 it1ewcylt l:zumg/w q moves in a circular path of radius r in a uniform magnetic field B. 2ec( b1mtltzw: wyi./ 48tgluShow that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetic fielst i,u ,yu(z kxkg,1,fd B.1,,ykksiuf,g( xu,zt Show that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particleio o)x,*p3k .vp jqo1a/abz+ p in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Eabl 5ew1cpcv 72tw6 :byrth’s magnetic fi2btww1cy 5 6:pv7l ebceld 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 equatorstlw/1k);z9ef h a1 at+hkh.x 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 withuz1 lzj+pg dcq:3mg )) speed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 str6/uuv3w0,inj l:x: tp be4bhaong is the magnetic field 6.0 cm away from it? Compvp:3/lejw t60uh:abibu, 4nxare 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 2dvsjf,qjb)(rfns(8e1r se .34q lrd to produce a magnetic field no larger than that of th 2rdbqjs 1s(rnq(l3e 8d).rv ef, fj4se 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 straight7v tu,) z2rxjs wire carries current I out of the page toward yort7zx2,)svu ju. Indicate, 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 carrying an upward 24-A current bc+bv kov i;/hg. 81ebexerts an attractive force pebkv8hg +ob e;bi/ .v1cr 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 between two parallel wires jf( nsun. 1qe835 m long and 6.0 cm apart, each carrying 25 A in th 1esu 8(n.njfqe same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magneti 5.zhdx g9koj1iy8v4r 1 puu+bc field is being carried out 1.00 m from an electric cable r5u 1zvobigx19phk8jy4 +du. . What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries wpm.8 sokmu vv0cbp9b2j+t,+ a current of 95 A along the tops of 8.5-m-high poles. What is thes 9jp.vo8tmb +pbw,v0mu ck+2 magnitude 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 carrzdb9m;)p/3vz k0-ckm1 ts 6io 2mq zmwy 25-A currents in the same directimzdb qip3 k6zm9s;omv2m) c tz0/1-wkon. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wire cak1ktoip 5p fi2m,,r9q rrying a qp2k,,kf9mt 1 iirop5 35-A current downward. 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 current due north bg;hm.tj38 gg. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward,bjm g;g.3 8hgt 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 protonske01fe j*y5ky f +bjs/ passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wiresvgn(6 mlp;qr 81(vg h; qm,gwv 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume th,vgn;lgmh8( v gm16qq; wvrp(ese currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc c*.y2h0. ij h9h xjipdt3uc rp7urrent to, and from, an instrument. If the i*xp yr tdjh7 .ch 9i.j2u03phinsulated 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 (Fig. Below), para/b/ 2k9dihig dllel 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 twokdg/h29di/i b 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 pointsuvab3 p:ms*b1 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 plane as a straight wire, as(/ +k cbuicaohgn-8y, shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude anny-ckoau b+8ih/ (gc, d direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carriklz p,3 x2g*61qhwxsbes a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire anb 1x32,s*q k6 xzpwhgld 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 theo -* 0hec(ylym*f9 o(d*ku ku*in-0nm3 nfy pat they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Belol*39(u0(-k yfn*dc ohmfpn*y0eno umie *y-kw). 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 b),ze;vo7/ ,xay h.h3i pfxkvA carries 2.0 A current. Wire B’s current is 4.0 A 3 y vx,)v;ihkbo.7ep, h af/xzin 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 fdiervi 1/h4 i4u1 nd1*t+mnp from one another. (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 annn+1*p idi 4r1muh e v/4iftd1d 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 direction of the magnetic field at 7hc )gnyeu4zi w msg 9887e6 i2ougrj)the midpoint of the side of the tz77i)hgu4j8g 9cm6nwr8ieu)og se 2 yriangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carngbz1n72-lr pry equal currents I in the same direlg-21 z7prn nbction. 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 mw0y,buh6u 5va current of 2.0 A. Calculate the field inside hmuw 5y6v,u b0near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in di99*p zzwdwf9x h6yg0yameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wirdyp 6*9yxg9w 9wzzfh0e?    A

  A 550-turn solenoid is 15 cm long. Thyz ;wh8(ji)wr vbhx8n y46qo2e current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a wbh 8nro y 4wjv(26h);zqi x8y22-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 solaj9aa5x dai /4nq89 qjenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, jiajx 9q9/q8dna54 aalength, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’ 8z3b2w1jeacgjwcdpw t.4 y o98p;wc)s law along the circula gwyw p)j2bzo .8 w1pcjte3a4wc;89cdr path, shown dashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law1ss5d p tst,;qswvb 2sa37*i )(kwvvb to show that the magnetic field between the conductors of a ts132 7( b vs5*qipsavd ,ww)tbs;kvs coaxial 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 dems p 0:v9,upside is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows s:ped0,pu9vm in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflectr (g;abcze;t3wk9iv,s 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 o d5;esbowpr - 3b:sid m)lc0;25% over the years, what cuci0rosowe)bpb3m;l dd- ;5 :srrent will give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops v33+w h 3w7(;:uc* dzqtkmp-mggbdhiby 12%, by what factor does the output torque chang3w*7d- (m3uwqd +vbh:3g mc gzk;piht e?

Show that the magnetic dipole moment M of an electron orbiting the proton na; onms;2pehof-fp 3 .ucleus of a hydrogen atom is related to the orbital angular momentum L of the electronf;n.f moshoe- 32p;pa by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loa aeg7(,fmd4 fops lies flat on the ground. The Earth’s magnde(a4f7ag,m fetic 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 ciz9 nce,uu; (vtrcle of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction must it poz,ne uu ;c(t9vint?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of cu*zv *rpkoum3 .rvature equal to 21.0, 21.6, 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 tkvr .p*3ozu *mhe other isotopes?

  Suppose the electric field between the electric plates in the mass spectromes: fy-z.klixp,vktso2y54 q 3ter of (Figys3 x.y:2 vsql-zkof4p5k , it. 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 monitoui13vb43tf hr xy fv;;r air pollutants. It is difficult, however, to sepa;yvb f3 ;f3t4 xiuhr1vrate 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 /;zo- /pmbw (gxv 7hs4gwo ;gnby a voltage V before they enter a magnetic-wgg moo/v/ 4hpgn;w ;b7(zxs 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 wire per meter, and a 2 )oiudpn /q+.lgobp542qs6 tqm eh7l, 5-A current flows through the wire. If the perlq7u5 t)e/ 46bp.hp mld go+sn2iq, qomeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and hia2s x y0fetmn426 ct.as 640 turns of wire. The magnetic field inside thcxy.i02t2se4 tnfa6m e 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 momentum ::(h iy7p wxzbdae+ ,l$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 ki o 2ok81g:elob w6tdn)netic energy upon entering a region of constant magnetic field. What is the ratio of the radii o8n ekgb:t6o dlo21wo) f their circular paths?   

  The power cable for an electric trolley (Fig. Below) carriesls*nx v0 -hnle/moy1l 8) n/8o kis)oi a horizontal current of 330 A toward the east. The Earth’s magnetic field han )ns -iol) m/eohoik8n sl1*v/y0l8xs 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 net charge wly0,x: ex ee/4rand* 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 : h(g i,gj k/,xic a2nqve;4wfpoints almost horizontally to the north and has magcxi w;n 4f/aq,e(jgk2:hg , ivnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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, vqlep wiki m*le(ei; t**53 k;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. Belowd7uv- hu k 2y7 alvvlcmhf,;22). 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 constany 2- hau ;ud2 hlvf7kvlmc2v7,t 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 wi7n: 6yzi) wjiyre and is suspended in air due to the two magnetic forces from the bottom two wires. 6i)ni j7wzy:y The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l7j6 e zs4sks2l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to ek7j62 zss4le sach 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 maximuocqv6/ pirk;0m deflection of the electron beam near the center of a ; q/opv c6r0ikTV screen 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) is a device used to accelerate elementaryh vlmnd*: /*eh particles such as protons to high speeds. Particles starting at point A with some initial velocity n*e /hhmvl:* dtravel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes 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 a squazp aq-k2kbcrdl( t j88f1d*lf5wx7y /re of side l,rl (*d kf2 z5aqc y8pkbl td1j7xw-/8f carry equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators fo4m:n9 a ai+spunne5* tr “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 pmsnti+nn *ue:5a 94 aof 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 coil of wire carrying a currg uxrco6 f 04z r3,sec*,xv9rwent I (as in F6u 4s,zorr ,rcgxef c 0w*9x3vig. 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 magnetic field is about 1i;j x),ayty +xG($ 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 mag 6y.jldu -gtp:h 0,vto5h 13srx;o tpjj81ubvnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field youpjvploj;v - 3yxj6ot1hu ,d8hrt0s.b:5 tg u1 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 magnetic4; w5jv/fv8aelxy 0tj k a m13aqxcs3k++:ect field would make a beam of electrons, traveling to the righ+ ve4am:xy c;30+w k5aj jk/ve3q8asct1tf lxt 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 field of 0.010 p16:m; afu;b;mpb mm hT, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P aup; a; ;:p6hmbbf1mmmnd 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 d ipqugms4dl: 9:0bl d+iameter, is to produce a 0.30-T magnetic field at its center. If the maximum curre9 dus: lqdl+0pgb4m:int is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameus9b: wow 3f4mter 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 t3wb m4os9 u:wfhe 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 fi dxigj(0)w zxu2 l5vfh3g3ga9b)o rq2k 5/bet eld 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$