A compass needle is not always balanced parallel to j6c/fk an6g/u the Earth’s surface, but one endgfa6/ k6 jcn/u may dip downward. Explain.

Draw the magnetic field lines afk0w4 wymnt3i/ z /pf2round a straight section of wire carrying a current horizontally to4fip m3f 20nw/t/ykwz the left.

In what direction are the magnetid5q v5 rmf/sn vg 10akl*9df;pc field lines surrounding a straight wire carrying a/ 5df59qsm an*rvvfg 1k0 l;pd current that is moving directly away from you?

A horseshoe magnet is held vertically with thudkpsl dqqd;x o; : 93a n(-e 3(ed+ev8)ftosae north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the a v9qq3k(esaex luft+;-d (d:odn)p;3so 8d e force on the wire?

Will a magnet attract a:v8pwr:v l0m -kggw2o 1m) evtny metallic object, or only those made of iron? (Try it and see.) Why i t-ovmv wl0)prkv1::g 2wm 8egs this so?

Two iron bars attract each other no matter c xq 55/y1gv62kls tgpwhich ends are placed close together. 1gspyxl 2 vgt kc5q6/5Are both magnets? Explain.

The magnetic field due teo2jnnr*tj5 a0c h7 ,ko current in wires in your home can affect a compass. Discuss the effect in terms of currents, including if they 27an5, *ekhrjc0njo tare ac or dc.

If a negatively charged particle enters a regi*zz) /wt oh ljkp(4q 5dphiv+ kmxo:vp3+v1u*on 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. (Neglec4(lzpp5uwhvqd1 x /z :+vok*t +jv 3mokip) h*t gravity and assume there is no electric field.)

In(Fig. Below), charged particles move ipdkz l3 k::vjl 7u 1gwgp8+y5in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic fiewppkg5l3:i+g8kd vy: u l7z j1ld produced by the wire.

Three particles, a, b, and c, enter a magnetic fi:tzy rz gjxlm713fhizq d-dbu,+8p ,vq9 e4-reld as shown in Fig. 20–46. What ,l rd3-z q dhq ,mei+utfrz-9 xvby84j:g71zpcan you say about the charge on each particle?

A positively charged particle in a nonuniform magnetic field follows (ghogembb3h0.qa4*k the trajectory show3a4bh m .ge*bk0 (qohgn in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a m t w cfgo(nd)6r*-y1jo4d r;jhagnet attract an iron rod? What must you consider to answer these qrfyh1cod*n6 jd4wo;t- grj( )uestions?

Explain why a strong m+n2lfjyd e1m*j0 ow8g agnet 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 the strongest. [But don’t risk damage to your TV by trying this.][/But d+mfygdjw *2 jeo0 n18lon’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized burb kuq o mw9f9l c7/eas9qe+80t the third is not. How would you determine which two are the magnets wu9 89 le+fmbeqsr7/9 qao cw0kithout using any additional objects?

Can you set a resting electron into motion with a magnetic field? Wije oe78/52tpx, hgfg,1c jmecth an electric1ofxct 25,gc/p8, jegme 7hj e field? Explain.

A charged particle is moving in a circle under the influencex1lbmxml+ , c+6aj,k r of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, d1b +xm6j cxmkr,l ,la+escribe the path the charged particle will take.

The force on a particle in a magnetic field is the ide xvgi1 4k4td;ca 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(F1tgckx d4i;v 4ig. 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 towaf8d amea8z+ dm*e.9n1zsit 6 yrd a horizontal wire carrying a current from left+*9 ztds8.m ya6m niaze 1edf8 to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magneti(zqa u7 ef(ixw 0;qtdapr95+sc fields that surround a moving electric charge.0(axda9z;iufte qw5 7r(q sp+

A charged particle moves in a straight line through a particular regio6+4fd .nvrx5wnlt m3 tn of space. Could there be a nonzero magnetic field in this regio t ndtmx w+r6nv43fl.5n? If so, give two possible situations.

If a moving charged particle is deflected sideways in some regionuug(,3fk f24 7bidigw of space, can wediwf(i fgk 3u7,2g4 ub conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magub(c0 -qn)*zbm sg7z ,t:u cubnetic 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 e;8 spa(9:zgdtn jhr 9qlectrons in a certain region of space are being deflected by an electric fiez89( gsthn;p ad:qjr9 ld or by a magnetic field (or by both)?

How can you make a compass without using iron or othkd;s5n+2uv ;hd + tqz9qe0 xpner ferromagnetic material?

Two long wires carrying equal currents I are at rigei,o 7og k0ei+15mxwhht angles to each other, but don’t quite touch. Descri 1gmxe,i5+k07h oieowbe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational fields9 eorqptqn1 2+0 dx5d, is suqs5x0o+ 1pdtq 2 ndr9espended directly above a 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 ofi d igqm4hs:+8 a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an ;k5xzlc/5f*viqsh6; hov6f q vyp j9qot,q1 )unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the /k5)5yt ;qv1os6hp ; cv*qhzfvi69qqjol ,fx other end will attract a paper clip. Explain.

Two ions have the same mas,ejo(7s prhvaz+4o2o s, but one is singly ionized and the other is doubly ionized. How will their positions on the film of a mas7s2(oeh4z,o+a r vjop s spectrometer (Fig. Below) differ?

What would be the effect on B inside h 4ykbd4zq;t. te5v:rna3x,9pjxzf.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 r3ywveamug4tw(3em8, elay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very lagw8evy4u a(3 t ewm3m,rge current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of lengtbc 1qa3i*cm3pmaf t2 /h on a straight wire carrying an 8.40-A current when /3c q2bcp3 ai1mtfm a*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 o.ic ky+,fx 3cbjz:slu mt 418hn a 160-m length of straight wire stretched between two towers carrying fc:jh tb3z mx1 +k4 ulisc8.,ya 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of st6szr2y gkxz37 5 prl*cvy/*,h+kdavc raight wire stretched be +y,r5l*y*/c g hp2 vzck3d7 vkras6zxtween 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 wire 4.80 m long if the maximum fo sq99wdz 4v.5mluf w,ury5ma1d9rmt-rce on it is 0.750 N when placed it549ma5 1ry. uv mmz ds9-quwdf9rw,ln a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is orieg- j1h89zmw5q .;gxlq hgw vo-nted horizontally. At that point on the Ear-lqm8;j 9 hwwgxvg z- 1qh5go.th’s surface, the dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when place6nlu: wf 34a 3eqj 6oelxei:o(d between the pole:4:wfao33 jo ulen(6xqelei6 faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of its maximu me b-d;a.i shxx60sk3m 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, calcxxb3ismh0k-d;6se .a ulating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximumq4,c:emf(x5px d 2ew r 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-diametkw8bh;1v*e-t3gttsg 1g k w ;uer copper wire could just “float” horizontally in air because of the forg1 tw1btt* k8 wku;heg3g;-svce 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 charh,x -huzk1y w -4avq37tn dcq8ge $q\,=\,+2e$ 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 forceg ;ws4j1impiin3q6k3 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 oq*o:. hf z/qoxlw5b;k n a negative charge for each diagram shown in (Filk hwz5*f:q q/;. oxobg. Below), 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 direction t knk 9ikb9t75w erk/,q76ohoof $\vec{B}$ 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 acwi ygf-0 + w6pzetx,4 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) protyry:+7q5irm3xxy93sdm yv 4won enters a 0.20-T field, in a plane perpendicular to the fi wq79sxy4:yv33r i +m yrx5mdyeld. What is the radius of its path?    m

  An electron experiences thcyn7f2fh7 lm u 30aq+oe 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 undpco:5) / wpvihlf qz/8eflected when passing througfvwp/i5o8)z/l p q:chh perpendicular electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium wy.0i5i3wt+ e rfeh4q atom whose 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 Tgt 5h-yc4gc s( required for a particle of charge q moving with constant speed v y4c5 hscg(-tgto 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 dy-/ ay qn3)/0 .gavzldu*adbwu3/ jt of radius r in a uniform magnetic field B. Show 0n/u l)v z / g3dud-aj.yw*abtyd3 qa/that its momentum is p = qBr .

A particle of mass m andk41ylm f5 oxt0*ucx-p charge q moves in a circular path in a magnetic field B. Show that its tfcmxl-4 0p*5kyx1oukinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momedncrk n)(hm.+ ntum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s maq /:q o;h7yx9xfl dmc9gnetixc7 q9l/: oqd xhy9f;mc field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equator has zf+,) hxl q q*)igkt0dmagnitude $0.40\times10^{-4}\mathrm{~Т}$ 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 z54isqlj t 4,kh:uq0b 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 to6 i 4zu+:sp*g0zu(j/deos9d+fj axlx start a stalled vehicle carries a 65-A current. How strong is tso(:0zfuj9*/ x +e duzs4xagd6+lipj he magnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no larger than that noz5mlv h9ifil,o3hmnv8,fy*iz7b0l/ :t7rof the Eart,hvf5vznn0ot m b ,hm8zfl o y7i/37r9l*il:ih $(0.55\times10^{-4}\mathrm{~Т})$ 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(y., zb7j upia3wq( q )6emonm*,i mmk of the page toward you. Indicate, with appropokqa,m).ib,* n(u (3j mp6 iem 7qyzmwriate 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 exerts an attractiveb8l, dd,c;nuv3:j .ed cv udk6u .paq0 force per k80 ;ujdc. b,n:6p3 ,dvl. uqaedvducunit 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 dikl ub(dcjwj4 4q. n*,yrection of the force between two parallel wires 35 m long and 6.0 cm apart, ea lq k4wc.j,jbd* nyu4(ch carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s ma+mr3 gr;5(lmija w,iqgnetic 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 t(m+l3am5i rg;wiq jr,o be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high poles. Wha eorjq9lc6tc4uvh (s6 8h5fuo 3:nf/bt is the magnitude of the magnetic field produced by this wire at the ground? How doe oqh69tc6r3:cujsnlu vobf/ 5fh(8e 4s 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/, cmptqbwx 1et5e i//sal (p, carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm tsixp mbl/e 1p(t e/5w,,a/cqfrom the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south zmhp.un;wo7 0i a 65cvalv/v 6xa4 qo)from a straight vertical wire carrying a 35w0h7o nac/qaza;6xu vlm 4ov .6v5) ip-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. What is theyskh4e5hh;- qvr *2 ds net magnetic field 20.0 cm due west of the wire if the Earth’s field there poin; d25ky hq*sehhs4-v rts north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a rate o,b 9e*eg1 l0zrgrl7jb f $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic fim g81 1nloaeid*r7 0ngeld midway between two long straight wires 2.0 cm apart in terms of the current I in one when the other1nelr7g108n*mdgio a carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to,9)97oypv bm n3fp2pg,3akb sg and from, an instrument. If the insulated wires are of negligible diametyopp 3k vbgns39g27b )a9p m,fer 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 pw 5msmev(2 udm1l tt++lane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force sd(t++et1mu l5wm2m v 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 points 2tv;3 hbddsiz r(c o;*+3$^{\circ}\,$ 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 wire0x,pvuv wn 7 :+2tq3zes:z +pjx6af sy lies in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determinzp+ 6e2+w fyx7 sqxj:03:uatv spzv ,ne 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 ofoc8 8mr b e2 qysfls0lkto56l0;; x(kn 48 A. A second wire, made of 2.5-mm-diameter coc;0k (r82qtlo n fl0xbssom6kyel58;pper 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 perpendic x(s)f60wspiqkux/+ sular 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 midipxwq f6xk+s0/(s) suway 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 apk h cz6cw)o8vd; qx3)hart. Wire A carries 2.0 A current. Wire B’s current is 4.0x3;cq8)zhkh dc vw6o) 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 qnb bu6mw5 )5uy98 bcsone another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each9cw)nmy 6 b ubq55us8b wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the magnetic fie.mta 3 d7mepf kq7a6ke5a-o9rh02i zkld at the mid7 dk tr p7k0fkmq a32.i9a 6eo5hzm-aepoint of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallelujw iddc(brdids4:rv b:(rj8 z) 7,3c wires, a distance d apart, carry equal currents I in the same direction. One wire is at xd87z)dbjibc:rid,: wd u jsr4 c ((3rv = 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 carri6jpp5l. yg he/ czhb55es a curren5 bp .h56hcl5ez/gjypt of 2.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to pro2xk qn ,cnfis t9s2im+x8i/( hduce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turn9mts,8fn kshn+/(x 2 ciixi2qs of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it zxgh5 y2jcyv4 v7hj3j,x.j d9is 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 xj2h79hyvjcvy jx3g j5dz4. ,the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to mak09: (gofwdlz7 zfs2 s p5lt5jle a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, shorlsl d5f7o5z2 ztfgpl0j:s 9(w t 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. Beleg- 0,hnwklo(xsst 5xy(o iy cu 8h-:/ow). Use Ampère’s law alons(,:ox/ h t(kuyc-lxh8e 5-wnygs i o0g the circular 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 law to show that the magnetic field between the conductors of4fm3 8 fl1k4zrk ozy*w a coaxial cable (Fig. Belr3844lzo y1*f k zwfkmow) 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 onn3 h 2nlm0qv mdy4evu/1o+, ud a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows d d ehv+ n,4y/0muvq21lmu3no in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needleae-qzx v be e6 w44)jjm2ec,6w deflects full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% ovi39 fjbp7 -vz+qk1ltuer the years, what current will give full-scale deflection if it origvz kb793 -ltqj1f+pu iinally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output ti 1q7ff t3k8 bhb5(steorque changh8i 5kf(tbteq1f3 7bse?

Show that the magnetic dipole moment M of an electron orbiting 6sc* .nd x-wk1ni9i54prdoqtthe proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the electronwc it1r pnds.9o6i5qxnkd*4- by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loopmej *2 206emjfwxwi (us lies flat on the ground. The Earth’s magnetic field at this loi(e26 f jwmx0wm*2u jecation 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 field. Whata8;evwnke2nl) d ;h. k value of electric field could make their en;2 dl.ane8 wvkk; h)paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, gerb dnf:xuxd/.1z v5 3mpmanium 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 massx.fdvmdn /b:p 3z5 1xues of the other isotopes?

  Suppose the electric field between the electric pla::flr gadmq,ht 2iv (sk;je36tes in the mass spectrometer of (Fig. Below) is k6 qi vmr3j(hsd g: f,lat2:;e$2.48\times10^4\mathrm{~V/m}$ 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 4fh4ap1;lw+0kz -cm9 zdqfra is being used to monitor air pollutants. It is difficult, however, to s4rkc;ld az q-m4z1hawp+f9f0eparate 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 io- :)q y+u;vgn pww2voens by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show thaty:2n;)uww+g ovpe v q- 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 trb*9h)-zi-f 0) ca0yuasgejmeter, and a 25-A current flows through the wire. If the permeability ofb)hyafs 0z t- a9c*ij)0-ureg 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 diaw4z5-c.au3fooq ia6 lfrh+/ p meter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A fl4ho r.pfil5q3/c uo -wf+6za aows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu q6bm-zhry*o6 m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kinetizf3opet1k)h*k o9uc /* 6kva ec energy upon entering a region of constant magnetic field. What is the ratio of the radii cktkvk1z6f* *p9e/ o3haeuo)of their circular paths?   

  The power cable for an electric trolley (Fig. Bedhf6v,mexkh) ;w1l m3 low) carries a horizontal current of 330 A toward the east. The );1ew hl,v m6 kmxfdh3Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a net charge ofin83vv-qt l /k: v7ukq $1550\mu C$ 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 Ef w3bsjy k 1(g):zut0sarth’s magnetic field points almost horizontally to the north and has magnitud1b sk:30u ) t(jwfzsyge $B=0.50\times10^{-4}\mathrm{~T.}$ 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, whose mass isw97hl3- o o70ghlaqijbpz*f + $6.6\times10^{-27}\mathrm{~kg},$ 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 s0i;a41 ywi kamhown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, al40iiyma;w 1akmost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and isazp,d r-c:vh ( suspended in air due to the two magne-v,rhzpa d:c(tic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l aparf* 7d dpw3zt)*5i3i.bhdhis gg9it, o t in a horizontal plane act as rails to support a light mets f *bi,).*z3gpdh9di75 hw3gto it idal 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 l vf. 02: uu0xgqfne*+no8tv ;juzsv+deflection of the electron beam near the center of a TV scr2s lj oz+vv+g:*u.;f0uextvn 8fnqu0 een 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 m :d:-zoxh34 dq+i9v tmxkc 2delementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the ma xh924qxdv t kmc:3mdzo:d-i+gnetic 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 a jy k+j2gn/mrf xt7fx0uj k693t the corners of a square of side l, carry equal currentm/jn6x kgyxjfr9 0t+3f27u kjs $I_0$ 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 for “beam plj5uz42 rougn oq6(1 a1*vhe steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fizn4o (aljue *2q u1r h1ovg65pg. 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 cofxeo7;q me49 ircular coil of wire carrying a current I (as in Fig. Belowem x7f o4;9oeq) 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 0sd3zu; nd.aive)z;s hdd9i 9; vblzm+j+dm+field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produced by ovexa-ef go2mvbm x;h,96y;jgzr aka,1:rhead 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 ,a6f29: xr;avo b,egm ; 1y-h kajmgzxyou 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 fier0*ibsqxo78 l 5;dthu8jz m4 ald would make a beam of electrons, traveling to the right at a speed obzmut;oi4d 7xqhs*85a8l 0jrf $4.8 \times10^{ 6}\;m/s$ 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 mag*8xqhp8hr:9z fmx- 5coe9 pc/sp m.pc netic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at o mcp*q-8 phe5 9/.cm8cxx 9 rppfzsh: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 dian c2. diao c.r0:in xgw3+dzu0ynf,a.f)n* x ometer, is to produce a 0.30-T magnetic field at its center. If tdao.0r+3 )xn y nxnz:i,u0 gcnwfd aco.*i.2fhe maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the same cuw7c6 *3wa1lbzj q*d2kaii )hyrrent but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle zj6w i3q h7ba* *yw1c 2ak)dliof 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetivjr7qh p ,ocf3 n0(/mhc; .ml7j pu7ss)a tzj-c 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$