A compass needle is not always balap/9qm jqo31 iqnced parallel to the Earth’s surface, but one end may dip qjmq3o1p / 9qidownward. Explain.

Draw the magnetic field lines around a straight section p tg4 mux;3l ;dc3:c ndgcf:j/of wire carrying a current horizontally to t4f3t/ 3 gjcxcndpumc;;gd:l :he left.

In what direction are the magnetic field lines surrounding a,uligwif6+a 4au r4r3 straight wire carrying alr i +,g4a3 ru4wafi6u current that is moving directly away from you?

A horseshoe magnet is held vertica2b0l nelln g1 )45j7rgv8jzmelly with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from4le 581 gvrz0jnje2) ng7mbll them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic o )j-4.dgbvao object, or only those made of iron? (Try it and see.) Why is bdj- )4.avogo this so?

Two iron bars attract each other j0,57m lhnc9uk g y-xd 8dkodg-81f id:ggz9uno matter which ends are placed close together. Are both magnets? Expladk i-dujd ygcno 9:90 7xkgf18glm-8hg5ud,zin.

The magnetic field due to current in wires in your home can affect a compass. mw*ftf:ej h6- av52/jk0z,rn)va qonDiscuss the efaj-*/,kvwmhzf ftn a5)re0 :nojv2 6 qfect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magneticov1oqejd 13iuqh:0* bzp8.r orlsw89 field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the samw8dqprh1 *9.1svr8lu0biz3 o:qo oe je? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-carryi)h-tslghsq4e)2 mo7 c ng wire. For each charged 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 foosmh l)e 2h7 sqc)t4-grce 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 .tsudw(8wwqnm 1*e u6. What can you say about the charge on each p.s uwu*e (wnmt16wd q8article?

A positively charged particle in a nonuniform magnetica1 m:0e i4m/pxprtga2 field follows the trajectory shown1er:m2gaaxip p mt /04 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 magq:/ -vegq pyced3xq.*net? Can a magnet attract an iron rod? What must you conside/3vg* c: -xy.qdqqpe er to answer these questions?

Explain why a strong cgt/k2+ t uhn,r8-dm7c (yofmmagnet held near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is h2d yt8-7tf mu rc(gm/noc+, kthe 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 thr//8yg n hxwz7coy6iv )zn,*a+fhys)ssce3 h(ee iron rods, two of which are magnetized but the third is not. How would you determine which two are the magnets without using any additional af,8z*h xwczg)in 3( cs/ hns)y yv/sy+6eh7o objects?

Can you set a resting ele;r-m o1x ;v+ctu2.up kq*h piectron into motion with a magnetic field? With an electric fieldmvphuetu i.; -x2c*; k+o pqr1? Explain.

A charged particle is moving in a circle um39 69bx ihh z8x1lhnznder the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged x 3 zmbl8xnh i1hz9h69particle will take.

The force on a particle in a magnetic field is the idea behind electrfq 1gs+ yq(1g*ksh0t 8hjaq*l 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 vesseljkshqt g*1 qyhs+lgq f(*1a80 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 towa n.r,c;ffw(ll -u-w nprd a horizontal wire carrying a current from lel.nwl; wf cup( -,nf-rft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/okvt g /6l- ikaf(b-npf4yp8x 9r magnetic fields that surround a moving electric charge./- p4plg8y f ikf9bn6(vka xt-

A charged particle moves in a straight line through abrbee .l k/3qgjk f-35 particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situ/qrk -5leb3.feg3j kbations.

If a moving charged particle is deflected sideways in some region of(hk/d 9 m/xa1tt (dikz space, can /h(td/atkd (x1m9z i kwe conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is avhi1m , d2i+qu/ 9x;44yh expo cfdq7e uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain re01fchbw te tf*4ncf81iyr 4o *gion of space are being deflected by an electric field or by a magnetic fiyer81f4fcbt w0 t *n4hoi1f* celd (or by both)?

How can you make a compass witjqrt xc90jae4,wb 9+dhout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to eac tf)po1im(u9 oh other, but don’t quite touch. Describe the magnetic fori1om(p )tf o9uce one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitationafkw:r.b,kc -j 4c 3dwzon*c4ml field, is suspended directly above a second, parallelk rz4-dkfww* nm c ,ccbjo.4:3, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized piece ofkew7t ukfuwhbq 6 t*j7gr +f6*0gx,hi)p7 o3k iron?

An unmagnetized nail will not attract an unmagnetiw) jr1kfrle7;m vro20,pto6o zed paper clip. However, if one end of the nail is in con0)e,r7p1f2oo ok rv tw;rm6jltact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly iona-j7+g)8p3 +a sdo3 f idhkqosized and the other is doubly ionized. How will their positions o3f++phsd )jdq3sigko 87aa -on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B p wq24ld6 (eqlz suhje3f4uda0t v042inside 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 relay . A relay isxdr -)+xoqb(c 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 co+ -(rocq)x bdxnnected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magni aai;iyf./p ra cipc0bcw.i43g+ f: y(vsi,8rtude of the force per meter of length on a straight wire carrying an 8.40-A curypr is+cpai i:0 8.br(i cfyv,af34iagwc ; ./rent 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 of50tw 41tmngpwd adc; ; the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field ofp t4dwwtm;1g;0ndc5a $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 16,95e*m bslj8kayh90ucg u qg20-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fiell bue5 9 j*ysu89qch0agg 2km,d of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowi,j:rwt)2u:jz *o ma4 hmshfrow378pp ng in a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-pt p)*8om::hj7 o arwmh3j ,rzsf 4uw2T field?    A

  A 1.5-m length of wire carrying 4.5 A of current isxh9 yjfmm7q 42 oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes xf4q y7h2mm9j 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 A6uomzbaf28r k*f w o4( is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 c* o6r kombf(fa82 wuz4m in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on qml3aq-assv h3ufmw)t3 v h;2y96ev 4a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if th6s 23f49eva3as q y hhtl;m-vq3) wmuve 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 maxizolmwzuu9swf. m56 ca /er r4f7,)q;xmum 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*)kddl*q ujr dnx .a(2” horizontally in air because of the force due to the Earth’s magnetic field *dra.( jd*d) lk2xnqu $\vec{B}$, 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 charge 5 4z*fym,lgc. bz* vwx sfp.f)7rzlg8 $q\,=\,+2e$ 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 an electro/s kwd,cw ;zwya m bc/61da)4bn 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 forc(d0b+n/iq ou10-vfyef 8x-:swc eu yxe on a negative charge for each diagram shown in (Fig. Bxdy8q 0fsnv u:(oe/ic+0b-x ufye1w- elow), 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 directy.k,p4 m b:wj;s 0hxdaion 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 ver nolk ,8c:3jh8vhxhvgp 7sui )+hj)h1tically 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 0.2kg,jc,8i o -ue*idz(f0-T field, in a plane perpendicular to the fikz ig,e(,cfi -d*u8joeld. What is the radius of its path?    m

  An electron experiences the grov9q*yfb84ipx/ vg rwx1e:o *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 elect7(jj08h0r*at0jf q,kcu3 qn . ;lqxa5 xugfzyrons that go undeflected when passing through perpendicular eltjzh3a xc*yrquu qlj70f 0fgx;q.nj(,08ak5ectric 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 whose massjf ed xi0za-+.d9-xrq r.l ca6 is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge q moving wirsu( 88vsa:fi u/qy1wtz4 hp 9th constant speed v to make one circular revolution in a unifowafy hp: tsv9r/4qiu uz18(s8rm 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 unifogwel- 37mv/-j 8ycb 8l,npq1kb / gyh)1dr rstrm magnetic field B. Show that its moment3 r/v/bys-r8blj7lgtyqk18,mc)dn 1p -w eg hum is p = qBr .

A particle of mass m and charge q moves inp /t z,yji1n*n a circular path in a magnetic field B. Show that its kinetic energ iy1pnt/j,nz* y is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of t 3jy0:vpri j 7r2gh3ozxai02 nhe 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 to the Earth’s7jc d5gstgrqs+ x j:h*zi g*70z(ww g1 magnetic fie1jw7z rqxc +std 5j(hg:z*gg7siw *0 gld 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 magnetr)n th;u v/h;dic field at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with speedlptu9 k r456eg0dxq0d $\nu=2.0\times10^5\mathrm{~m/s}$ 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 curr p gdo(12s(gnrent. How strong is the magnetic field 6.0 cm away from it?(n d2 (1ospgrg 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 produce ak:up ;j/ty7 l8fvf/jy magnetic field no larger than that of the El8jpjv :f/ yyt7 ;/fkuarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carr -n8v8.t opdwse a8ug)ies current I out of the page toward you. Indicate,w p os.na8)dvuet-88 g 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 2(/pno*y6m ztq4-A current exerts an attractive force per unit lem/*tyzn6 o p(qngth 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 t /l z3mehs;zw2he force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same direc2sz;wlz/ e 3hmtion.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magneti.g g aipul5::oc field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accurat:g5pga :.io ule to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high py:lrd14gpq2 l3n5b hl7 gho-qoles. What is t 2rd:p olg-qqhn14bl5 gl h7y3he 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 carry 25-A8viub9y :*l cf currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire ab:8ulyc fv*i9 nd 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass isa 1/r 1uf(z musr(fscqvx7 r/8 placed 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle 8/ c1a 7 zsxufq(ru(m rvrf1s/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 wir1 b4jzm cmo9 b7p9wugd+zz2ud*6;jdhe carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward, 37pz71b*zd 2bud c9w+mh4j;9 6z mjgduo$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given p0)zdn.op(klf*cj qh jp m93)) uf)8ycnvr t7roint 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 p) n hek3+wn8ulong straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currentue+w8p)3hn k ns are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc cyhvmie1o 7usot /u) ;3urrent to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm aparvu3yo7/ ie;1sh o)mtut, 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 wiren d1rhnechl/4p 663cns shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert onhehr /pnc6c 1 4n6d3ln 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 poinz7q.udb.l9p(lf g k ,f,ak (wrts 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 shokkim0bg:u* + a4xk od3.,vxdnwn in (Fig. Below). There is a,bkmi kxx :k+v34 *dd.uog0an current of 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 48 A. A second wire, made of 2n4 -1qnza;lz- ;vapok egn )t7 ifg/nlxb)m+3.5-mm-diameter copp;n+7km nng f-axp3av1;n4o -bzli/ zl))tegqer wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicuuip5c8v5hv;o3p0mc*0 96b twc vjyjxlar to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point mi0;5v 90mbtcv6c xwjo hjy5 cpp*vi 83udway 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 paq 4 kiu,kt)d-cm53 hpmfw5 p;wrallel wires are 15 cm apart. Wire A carries 2.0 A current. Wi p3kft ) h;m 4-wu5d5wckmpi,qre 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 one another. (Lookin; q f)ji6ptcwfz/rg** g 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 *pg6j;zf*)iq f twr/cforce 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 magnitudeem3nocy61iu0 i 05 1if-szorr and direction of the magnetic field at the midpoint of the side of the triangl i ors-5m03ir1i0cn f6zeyu1oe between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, cam ja ;n.tdv3 s1u,spb:rry equal currents I in the same direction. One wire is at x = 0, the other is at x = m p;un b.sa3:j,v std1d, (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 of5cqlw ;rsxw90g*jfr*w; a m(t wire and carries a current of 2.0 A. Calculate the field inside near t*gf95c rtw*j( 0sx q;wmr; awlhe center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.386(a 2gtk zxxt45 T at its center. How much current should the solenoid carry if it has 975 turns xgxt6 z2(t4akof the wire?    A

  A 550-turn solenoid is 15 cm long. The current in ity,(io d f qu;x*vg+.hkv)po4 c is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming tho;,(ykfv)q+* gh .vop4udi x ce solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid th 8-pen:-dqub zat produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or som ezu--d n:p8bqething else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the o-8q-rm1+hl7 ksn0;dclv 5gc)laq qhshape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dglql- q)ldm 75+sac0hr1kv;h8oq -c n ashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between3vg9bxq6 l h7thyj xdfn,(4 i2 the conductors of a coax4 6dbh2tx 3j7 h ixlqy,9gnvf(ial 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* +kvl3ee oknh,w 06qol to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on itev ohkn+l oke*3w60q, is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle dn*8 l 0aiprzv+eflects 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 yearsgq1+.jznhh12 v w l5sw, what curren.h+zsngw 52hqljvw1 1t will give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torque54-kedqn;ey-q mo eg - changeegdk- 4 o-em-ey; 5nqq?

Show that the magnetic *3olq9/aizl9krc9r-d bxcqryud :u- :* p2lqdipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of/*r9k ua xl9: bq9 c 2pcrq*:rd3-udl-zqoy li the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and cz/un ama-tb1e ims4 03ontaining nine loops lies flat on the ground. The Earth’s magnetic field at t-zmba/i1s mentua 40 3his location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic fiel n.n+u *zsuye1d. What value of electric field could make their paths straight? In wy1un*.snu ez+ hat direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvaturek5dp9w + r5 avk;,o +pup0jabk 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+ kk pk5a;uba,rd5p+j0wvp o9 masses of the other isotopes?

  Suppose the electric field between the electric platese9 zc7sv,jmqeozt . qm76 *6je in the mass spectrometer of (Fiq o7j c7z.z,t66*mesqv ej9emg. 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 yd 2;se5fvf 1tbeing used to monitor air pollutants. It is difficult, however, to separate molecules with 5f2;se ytv f1dnearly 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 0 kexvp6n6.zsV before they enter a magnetic field B. The ions are assumed to start fros zxv6.e6kpn0 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 loops of wire per meter, and a 25-A current flows9ouowdd(,n 5 0varx-s t0-oxd sn5v,9 ru(oad whrough the wire. If the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm cl)c)acrre1 v/(qol9(o t3njin diameter, and has 640 turns of wire. The magnetic field inside the jvco)n (rl/lco3e( r1ct qa 9)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 momentu;nci-xb 7-ebsm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upr04vasbkv:ym+ 0e 0 gnon entering a region of constant magnetic field. What is the ratio of the radii of their 4ry:v v 0msbn0e+ ag0kcircular paths?   

  The power cable for an electric trolley (Fig. Below) cayppf.fpzyo og-( * *-*,ctqporries a horizontal current of 330 A toward the east. The Earth’s mz,o*.f* f(-g yqp*opppc y-toagnetic 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 airpl0o7 l; *jipwubane 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 Eaqf8uxn7lq+n :flnd(/.s+xu w rth’s magnetic field points almost horizontally to the nor8uqff.+nx 7w du l:n+l/(snqxth 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 helium abx*5i p* o1exitom, whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A large current moyzf i j0, qk3dqilfk*(07rk+wves 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 thei,qk+f 7wkdz0kyq3 r0* l(i fj 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 t pqxyo x;n1:ogi26xo 6op wire is 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forxix6:2p oxqy1n;6goo ces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plan ird f,yo6kuqh 3xv01c 8(zzx/)er7ree act as rails to support a light mety 376/eixzkruzxo ceq r0h( 8dvf1r),al 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 approximate maximum deflection of the electron beam near the cen.90dx3 unfcfmpyn *l *ter of a TV scpxyflnm*90n*fd3uc . reen 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 d)3/h,je.xfzlp 9z2g+iqtv p vevice used to accelerate elementary particles such as protons to high speeds. Particles starting a /v xvp2pteg9iqf+jzh .,)z3l t 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 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 square of slmb aay*fy0a;6o c0un1ll,*k xsk. x0ide c axy0kla lymxo 6s,*0.k 0*f1n ba;ull, 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 s1 w1g s-akt/kuseful in particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s dire k/t1a1ssk-g wction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wir5y b7w:xyzfh7bmtnd5a1 z6 h0c 3 ojs8e carrying a current I (as in71z0y h yjnmozf5wc3d 6x7s:abthb85 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 magnetic field is about 1m ycur47.9wrozb+n fb1+es;z G($ 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 prodbz 37(hej3mf3 ks 2y.by4afpo uced by overhead power lines. You estimate thatzfsyh 3f27 (.ebm3kb jpa y43o the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field wo92mpdggp6yj; 3p1 ize uld make a beam of electrons, traveling to the rigg6ppg3 e1j; m9ydz2ipht 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 0.0;lakc7x- sn3w( lbwnx s6j:6l10 T, perpendicular to the pxwk3lba-c sn (s6xn;jwl6l: 7lane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in dic7)/ /- ; t1bqr vcmgkz)ayaogameter, is to produce a 0.30-T magnetic field at its center. If the maximum currg)q z tag;c/y7 -/)cvakor bm1ent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminpekr;u elnjs x)*1*:xum wires, each of diameter 0.50 mm, carry the same current but in opposite directions. They are j*)kn;pe 1slu:exr*x 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 uqo0o(+ ppias.vz ,l, vniform magnetic 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$