A compass needle is not always balanced parallel to the Earth’s surft.hg 9e;p.akx) 7 mpkrace, but onega .h7p ;pkmxtr. k)9e end may dip downward. Explain.

Draw the magnetic field lines ep /m5 wc;8nnyaround a straight section of wire carrying a current horizontally to the left.wnme ;py85c/n

In what direction are the magnetic field lines surrounding aw)i / ntbeg5+pbjw6 fsap-a4:xq21 vk straight wire carrying a current that is moving directly away fr5wi)bsx4j -pa/ aw2 q:1 gv f6e+bktnpom you?

A horseshoe magnet is held vertically with the north pole on the left and slxg-c 6(6ob s*fysh0south pole on the ril-y xg*bc 6(fos6ss h0ght. 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 metallic object, or only those made of iron? (Trykj7la zm ;f.ou;)kwr wq7 s9(m:adn2d it and see.) Why is this mw7m f9)sq;2a;wzu r: d7k .ljn(ko daso?

Two iron bars attract each other no matter which end4 o7swlezg*;n s are placed close together. Are bogn;7eosz*4 l wth magnets? Explain.

The magnetic field due to p8+j1muvzr9vg -s0w tcurrent in wires in your home can affect a compass. Discuss the effect in terms of currents, including if they are ac or dc zv+9 s1jvgm rwt-up80.

If a negatively charged particle enters a region of uniform magnetic fidn h)76scsj-dp2 s ul;eld which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no ep) s d sjlu;-nhdcs672lectric field.)

In(Fig. Below), charged particles move in the vicinity of a current-carr7o0kva hsh81qying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. Forhvq1a8h7 s o0k each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, bere/z+q7+7fyguoe 1 e, and c, enter a magnetic field as shown in Fig. 20–46. What can you say about z/fee+rqee7u 1+7ygothe charge on each particle?

A positively charged particle in a nonuniform magnetic field follows the trajectimeagzf a8e3r:e, 9y.t qy6:iory shown in :: tz.y3ar,iym 8 6eeea fqi9g
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron rod? What muo-mr05v* j wkest you consider to answer these questions?0rj-k w*moe v5

Explain why a strong magnet held near a CRT television screen (Sv 7 5r,x*wwmfq jp.n, gnydd0-ection 17–10) causes the picture to become ddfyn0 ,w-g r7,.wnjx5dm* qvp istorted. 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 whi .kdoc.yr8a ivasi*0*ch are magnetized but the third is not. How would you determine which two are the magnets witiyi8kv *ar .d. *soa0chout using any additional objects?

Can you set a resting electron into motion with a magnetic field? Wi5hn8 l( kaumo8th an electric field? Explaikuna88mh(5o ln.

A charged particle is moving in a*q1d h9 4pae insbz)b:c*b3 qs circle under the influence of a uniform magnetic field. If anb*hn a9c s1b)qs4i *bzeq3d: p electric 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 fi1tu(,h oo+vw celd 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 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 causeo vch+1wu, o(td to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire cara *3fz:b:jbm0u zp kj.rying a current from left to j u:*pb f 0b.mj:zk3azright
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields thatgi lp/:sh/)h,r;xk/ds uqmj : surround a moving electric charge.m/ikupx/lj ;:hr s/ )h,:dqg s

A charged particle moves in a straight line through a particular refnanb46k4 19 uzfl h1ci2q: sogion of spacen1f4i khnlzfa2s u91c:bo4 q6 . Could there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sidewk0h imel) ,b9+u-mmm iays in some region of space, can wmii9-0m)em kmu,+ lhb e conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic 51k irl fabbo53n- 8.ibdtxi/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 mox732j,.ie77t kys3k d vrgehwving electrons in a certain region of space are being deflected by an electric field or by a magnetic field we,33r2kjvhe7i. s7yd gk7t x(or by both)?

How can you make a compass wit0ua(e6 3d d4aa: +8 lyebllhvohout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to each other5 f9,i / xzvqoh-nzhy4, but don’t quite touch. Describe the magnetic fn49zz/ -5qh xyhiv,o force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’f6aa z6aouc: c2 j92v fqsud.4s gravitational field, is suspended directly above :fu2 a4c javcuz2fqa9o.6d6sa second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attrz)j+c/)d4bo -kryvu g act an unmagnetized piece of iron?

An unmagnetized nail will not attract an ,7ygs: o-pr9is/eo cyunmagnetized paper clip. However, if one end of the ,ey/py9 oio:s -crg s7nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionizedgt b gcxq pnrb+;da.l02q889 l and the other is doubly ionized. How will their positions on the film of a+lqdrb8 ;tg8x.pag l0 9b2cnq mass spectrometer (Fig. Below) differ?

What would be the effect on B inside ai);;k2ksc fj a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a rp )ndx7 jtav*5elay . A relay is an electromagnet (the iron rod inside the coil does nn*jpxd7 )t5avot 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 switch.

  (a) What is the magnitude of the 5 ,yc(z*dooeid/ gr( nforce per meter of length on a straight wire carrying an 8rz,y5e/(nc g do(o*id .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 * bennu,/j)pk of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fieldu)kp /* ,nnjeb of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitud4gqm5nimqr -6e of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A curqi r mq-mn465grent. 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 wirej h( w+rzoy t;/mn,wg2r 0)cnem3ct s* 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fiznse2mywm ;jgr3)rn+o w,0c/ h (tc*teld?    A

  A 1.5-m length of wire y*01+;sky,ylk7fzrfscxl 0 vth; a k :carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic fifva*kkyr+s1z;0t c;s h,0xy7 :ylf kleld makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when placed bywdbj( o0y8q +etween the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of jd(qw0y +b8yo the magnetic field?    T

  The magnetic force per meter on a wire is measured to be onlmy2igwp7 -;lly 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic fiel pg7y2 ilmw-l;d.    $^{\circ}\,$

  The force on a wire is a maximlnv3)d/xgfg+lo x/ ;a um 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 a,4,w xht(fsh could just “float” horizontally in air because of the force due to the Earth’s magne4xth,s (fwa,h tic 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 ch p ey-d3,xq4baarge $q\,=\,+2e$ 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 forcec04y)cr5 p gbw 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 each diagv .os ol4+jzc(2a yty i;yvy7-ram shown in (Fig. Below24vz7vylycyi j( .t+ o o;y-as), 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 directak nd1ven fyc7t34.;ye7n- vvion 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 ;5kwzd:hr u y;wmr 2,h i17tsya 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 a plane perp0qv3x cd4b4p uendicular to the field. Whqcvdp3 0bu4 x4at is the radius of its path?    m

  An electron experiences the greatest for ev3emrzszy +l-u.2oz vbp;4- ce as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when passing *e5x: v87hlaji3b x t((hd sqgthrough perpendicular electric and mih8 he5l:7j d (s*q(bgxt 3vxaagnetic 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 whose mas rs7c5- vccc1*rpb:s ontb /)ts is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

  A proton (mass $m_p$), a deuteron $(m=2m_p,Q=e)$, and an alpha particle $(m=4m_p,Q=2e)$ are accelerated by the same potential difference V and then enter a uniform magnetic field $\vec{B}$, where they move in circular paths perpendicular to $\vec{B}$. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton. $r_d$ =    $r_p$ $r_{\alpha}$ =    $r_p$

Show that the time T required for a particle q/4fsp o9 v8dyof charge q moving with constant spee4qpf ysd/o8v 9d v to make one circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uvt.7 c 2tyai un3ecn9+niform magnetic field B. Show that its momentum is p = +n9tu7c. 23t iycvena qBr .

A particle of mass m and charge q moves in a circular path in a magnet6cxwdn+7 cea, ic field B. Show that its kinetic ener6ca+ e,7xwcnd gy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momen ey/m6z ;u/ysktum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speedf9;y x/i(sl yp of 160 m/s perpendicular to the Earth’s magnetic field of 9;(py yxlf/si $5.00\times10^{-5}\mathrm{~T}$, 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 hasxedo) xf(c h.+vpv12z magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with speo0fve f/* +o9yv a;em3fp5yoved $\nu=2.0\times10^5\mathrm{~m/s}$ 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 curre, iq2.xh0nbc j,mpkl ,m,d9 9;guzpd tnt. How strong is the magnetic field 6.0 cm away from it? Compare to thedmxpdc0jzitn h2g qu,l.,b; mp ,,99k Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic fi -0s fxngj7d,feld no larger than that of dxj0 nfs-,g7 fthe 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 the p.qh n3jw zde86age toward you. Indicate, w j3hn zqdw.86eith 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 z wase*3g jd)y**chh2pjpt.-/,gmm wwire carrying an upward 24-A current exerts an attractive force per unit lehj /wyd)he 2at.cpgsw g3m*-jm**, zp ngth 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 ,h/znb2dfug f+c d 0y e4n+ka835 m long and 6.0 cm apart, each carrying 25 A in thn0+cenbh8/, ug 4 2+fyka dfzde same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earzf,t9;rm 0.e btxtj 1xth’s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the er m1t t z9txej,0.fb;xxperiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A aloy/ gyp29 0fndxng the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by thi0f ypg/ ydnx29s 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 wir*2gku tivq*z xe4,n4des 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm fro4ued qzt ,4n* vik2*gxm 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 vero)c, n y/l1ntltical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the ) y1tnlnoc, l/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 no9 b6,j qj,xuep oz2226x4ykqbvk. j gerth. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north buzeeuvj4. jq q2,9x2b6p2,k gxyk 6jobt 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 e++:vs5u:-bjzdi z jfprotons 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 betwei1 rbq q bo;ybu4gy-b o:*4;dcnmb89i en two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume thbdb1b b-*4cn 9mu;4yir qq; y:io8ogb ese currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conductsr1p ezqnzw1po m: *.n- 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diamete:opp .q znerm n1*wz-1r 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 npch-cw)8(kz k vm 0,rshown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upwar )npzrk( k0-wvc8 cmh,d, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, 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 point3sdck)82sc o 8qhz*8ymc5t kls 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 samu 0oapbn n78ymmy;).oe plane as a straight wire, as shown in (Fig. Below). There is a current of)7y.0on nuompy8 am;b 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 4fh 7b g2+c b5nw,*otfa8 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically +a7fc2hbg*f5b t , won15 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 ykh0evo,(cd *q / :mfhother. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midwaydk(/h:mcvh* eofqy0 , between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A :xg o 7q/fo6k er3kr*ocarries 2.0 A current. Wire B’s ro7fgko/6ke : q3o rx*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 frn/+ueyfv( w 1pa mg6z;om 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 and P (Fig. Below). Determine the magnetic force per uni uyaz6pfnve 1(w;gm /+t 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 fielb446n1f.z+ n5 wrwpllabbtm3 d at the midpoint of the side of the triangle between wire M and wire3.fwb1m4 wb + zn 4pl5arntl6b N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I in the e65 *mln c,ivw *hub4hsame direction. One wire is at x = 0, the other is at x = d, (Fig. B w,v5lbnme u64*c *ihhelow). 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 turn+au;wo1pa hhf. g1d)9w/ kn gis of wire and carries a current of 2.0 A. Calculate the field inside neuwaapi gw1. h1g k9/)+d;fno har the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.385 Ta .t5zt ;z;3areh3tm1vvwm 8q at its center. How much current should the solenoid carry if it has 975 tut.r;8;w3a 5amt3th1q v zme vzrns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A.-ls9 le pz : ,hg94zlziibp:7m A 3.0-cm-long straight wmble-iz9g7zlzps 9 , l:h:4pi ire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practica9o2k+xxcbnlfsfe3 - 79pd ,w sl solenoid that produces thec7s + xd9-s 3bf,f2ekpwn9 olx 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, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig.(cu;.s-rtqq x Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic fie uq(sq;t.c- xrld
(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 be(m.kp zs07y3m9hd,k ibtqm s 6tween the conductors of a coaxial b3smt k970,d6i(mqkszhm py. 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 with its face paralle vbbvzn n75y7(4 hk4ztl to the magnet4vz v5b7(y4ntknz7h bic field between the 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 scali2p(s+.o * tn0a odolh0q /bqse 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 2tnf7ne.ynt9 5 5% over the years, what current will give ynet9n t57nf.full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 1chxy8 ;s o+ zjcxg:a * e75ntkj3qy3a62%, by what factor does the output torque chach:q 8a5s* 3g6yyoa xn;xj7c+3jtke z nge?

Show that the magnetic dipole moment M o59kh6 zgba2qpb.b++ djq uthtp/27 ouf an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the ejhhz+b7.tb26t5od+u p/ka2 q 9gbpq ulectron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies nd4um azh57 6txs4iv ua:g2j-flat on the ground. The Earth’s magnetic field2d s: -atz7v4xn6u a54ughji m at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0 sdtt+u y(/oy9zv* c0qcte96j)fl4kn .566-T magnetic field. What value of electric40)cyyetnlf ttkc +( 9v/69 dus*qojz field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germa 1mr2if;bpe ( yt4cb.attdhl,h f4nt4a kn13,nium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopmnafntdarkh thc;,3p 4bifel2, bt4(1.1y t4 es?

  Suppose the electric f;vuxix (/9bun 286/xe sgytuc ield between the electric plates in the mass spectrometer o2s 6(;utxgb8nx uevu c/x iy9/f (Fig. 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/ p5k a1d.dfoq97; qqo b+xlti monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass suchlq.p 75d +kaqb91tx ;ofioqd/ 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 acce .jw;b * azlpbbyrl67:ao9fsc+-: alb2kfm6e lerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rw b6sz:afa2 m ebr7l.lk-fab9j;* bl:ycop +6est. 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 25-A currew y.m3l qa/ir)z*q.6x.xa ovodcpdz 2lk48 s 6nt flows through the wire. If the permeability 6.z y 6/a )xvx3dazdmsk owp2 *qc.84ro. qillof the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long a+cfb-bkt zid)r s-nz9 3sq 5-9fo-azand 1.8 cm in diameter, and has 640 turns of wire. The magnetic -dsb9-i f s93 5z-z+qntkrc ) aoza-fbfield 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 momentumnydhv y,5q4cv,l 3f 5c $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 ( pk;oqn/gr 9yzmr.6q,4yew u have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circula y64k,wqr/u9nomgp(eq. r; zy r paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizg4d0 q+fo.v jhontal current of 330 A toward the east.d0j +fho4v.qg 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 a,jry 2qfu3heknl 8 aa k5vv23qfxd80-n airplane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almost horizontally to thraay71*igt,oy ; )wdz;p ;juve ndu7iao*1r;)yj ,y wg ;t;apzvorth and 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 hel +i0 gqwdhf **pw2:k:trqvl1,rhz a8eium 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 curr wp u9d;h+vcskq+)uf 2bfb6c- ent 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 lecf bbc wu+ph-q2+)kvs9;uf 6 dngth 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-diamete)bo/q 1 ag7mtlr copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is)otg /b7 malq1 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a t9ta5o x i 2w01xb-0ljutu*uoj+y9ma horizontal plane act as rails to support a light meta0 j xtxymio-9tja5b*au20tu 1 +9owull rod of mass m (perpendicular 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 approximtcclea 4m 5p*(ate maximum deflection of the electron beam near the center of a TV screen du54e(cm ap*tcle 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 r 3/ma);fbi byc*rc;o:oke 1 dr3w i(kto accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an elecy ;f*(kmc3ib3) w korei :o1;/bcarrdtric 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, l)g/gi jy mpw/(ocated at the corners of a square of side l, caijgwg)m (/p/yrry 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 particz1u)zqc oy8l cpeb2v*v (0)jmle accelerators 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 approx)bcv )q*1(m08 2zupcvzj yo leimately 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 cirwnc z.9yd89m*besadydj,3 x6cular coil of wire carrying a current I (as in Fig. Below)6jmse n89aybdd w,zd.*3yx9c 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 poleso5,1e-p oeeta p ad .z*jlv0o ;zfco74 the magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea 9 abyi08+fpmq of the magnitude 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 ti0pa q8bm9 y+fells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of elec00wl/fa xc 1n npnaay(nw.0i6 g7ab,ftrons, traveling to the gx (lf nwaba716nn ap0/.if0 ,cyaw0nright 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 xwa tdi7 8w9x1a 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 arexi d97w8a1xt w 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 cx- ad7,jy;vv4gbqr h +m in diameter, is to produce a 0.30-T magnetic field at its center. If the4 vvy,+d qx-bagh 7;jr maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each ob7lci *)cgko/o5z/ux ;itpk :f diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (F5ib/g ;cloptuz 7i o*xk:c)/kig. 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 magn6.+jp. ,vauhgx9 xd,:l dmabwetic 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$