A compass needle is not always balanced parallel to the Earth’s surface,pwst j 70/3yy3s,yrge;ue6vp but one ende7g seypv;yrpuw3/ , 036jyts may dip downward. Explain.

Draw the magnetic field lines around a straight section of wire carryingb+1xz7 6wa4adqatq + (zby km7 a current horizontally to the left.xm4kbqa1 (+7db7qa+ a z6twzy

In what direction are the magnetic field lin9sd uevne*.zb.m)rb ;es surrounding a straight wire carrying a current that is mo)nzeb9rb. vu;m d es.*ving directly away from you?

A horseshoe magnet is held vertically( uu/ sq3iucj95.ik le with the 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 froj3si(k/5q ul 9i .ucuem you. In what direction is the force on the wire?

Will a magnet attract any metallic object, orb,.8. ugspmrt piwrsn* t0rj43g 6e/q only those made of iron? (Try it and see.) Why is thm4 /3jsi0 p.rs*tbrnr6qw egp8t .gu, is so?

Two iron bars attract each other no matter which ends are placed close t- 7n8ej)espf2osd o/ql d+)i*yt0 pquogether. Are both mq7e) p+8tiqn -*dd 0flyj) uosepso 2/agnets? Explain.

The magnetic field due to current in wires in your home can affect a combv7xzgy9)4o 6 8 ht4uv)jqwrmpass. Discuss the effect in terms of currents, including if t gv7zoxm)rwhqb 4j 9vy6) 8u4they are ac or dc.

If a negatively charged particle enters a region of uniform mh:sbj2er 5w h5+ fbpu5agnetic 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. (:2w furbj5peh5 + 5hbsNeglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move .j3 -zy6dypr-jxv7/1am oajd in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the chargeoz 3. 7x6da jvdr m/1jj-yyp-a. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter ae v2: awphm6+uz:lq1vj6 e;tq magnetic field as shown in Fig. 20–46. What can you say about the charge on each q6we+;uv :1a m6zp :lq 2hejvtparticle?

A positively charged particle in a nonuniform magnetic fieldncmkhs3 pjmdn:10 2l4 follows the trajectory sho 1lm:2mhjck04dnpn3s wn 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 txx8*e p okl,e;x(n5m+ n hvm8magnet attract an iron rod? What must you consider to answer these qu ;m+mplkxe e 8(n* ,h5txn8xvoestions?

Explain why a strong magnet held near a CRT television scrtkn-p5fv(w t5o8j+ wueen (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 don’t risk damage to your TV by tryifj(o58-+ vp ku tw5wntng this.]

Suppose you have three ic-vmdz 4oot m9e-e5s. ron rods, two of which are magnetized but the third is not. How would you determ. e4 -sd5zo-mmt9ov ceine which two are the magnets without using any additional objects?

Can you set a resting electron into motio)gr d,7zh ced0n with a magnetic field? With an electric field? Expczg rdh 0,e)d7lain.

A charged particle is moving in a circle under the ;-yco4larnxmj8. /tb.xwpv g7f, 9n b 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 particle will take. . ca79tw8y4;ob,.b glxm-nfj xp/rvn

The force on a particle in a magnetiqen z;f3e 4to*-nl.inc field 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 ;eqel3. i -ft4on *nnzin(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directe 0jc: /c* b +nj*fku,mxoti. kk.lffr:d toward a horizontal wire carrying a current from left to righ.+m:n*ikcko xbj j,f:*u /rflf0t. ckt
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fiev ny wv57vp* dw,pn)l9lds that surround a moving electric charge.7dn, 5w9vvpvyw l*np)

A charged particle moves in a straight line through a part)lol-cm hto+, icular region of space. Could there -)l cmoho+lt,be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of b-xkc2 r +)m+2nmoima space, can we ioa+ )b2 +r-mmk2cxmnconclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there 7x7d-q *eqib6v m8gyd91d/zlrpjmv9 is a 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 certainklj dz5b1b4c5z d1-il region of space are being deflected by 4 b1i-dbzz1jk5c d5ll an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic materibr:s6f q itz0pk k5qp+):1u rtal?

Two long wires carrying equal currents I are at right angles to each ot0mp svo -(zhob1;r*zqher, but don’t quite qz o*r;1o- zmsv( b0hptouch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth+wn+lqe6n,ig ’s gravitational field, is suspended directing +e+ lq6,wnly 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 of a magnet attract an unmagnetized piecm h2a 8ns+: po2 myj3xp6kga2ce of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. m3o0rjmjmq -: * -2 m)xich-8iuvqqtyHowever, if one end of the nail is in contact with a magnet, the rioth 8ummcymmqiq)xv 32 *jqj:0- - -other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubl/igh arry:8mu w 3lj;,y ionyi,3 hwl r8muj ga;/r:ized. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B f c89.w8h /gn5uodh.x s,tsfjinside 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 similashrx:g-* fk n 8s9yh.it9 usi6r to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivix-n8h. sh*g69ki rsu:yf 9st ot. 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 th5wle ff9( q02xy 6vjk jn9h/dle force per meter of length on a straight wire carrying an 8.40-A current when perpendiculare (fljd29ly9 h 06fxn/ 5jqvkw 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 b b.hbvs1g9d8 oi2en)force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field of g9 v2hsd.8 enbiob)1b $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 1j58z o1clfhn u;32ltb60-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magne;lul8obcn3j ht 125z ftic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wiz0.w d omr0lh(yb ohz;5 evt)2as wpb844z) hqre 4.80 m long if the maximum force on it is 0.750 N when placed inw (mzq e4;.vza0hwytpr 5) bbho0l h8zs4o)2 d a uniform 0.0800-T field?    A

  A 1.5-m length of wire nvdu p374ul2e carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s su3d2enu7u4v lp rface, 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. 4)j6zxva+g spsf7 (kn75 A is a maximum of 1.28 N when placed between the pole faces of a 7xs+szangfj 6v ()k p4magnet. 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 genw jpqt4z*36 ie6-jn49 sqgmaximum possible value. Sketch the relationship of the t qe43in* j-jwn6p64 gegs9zqwire 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 field.    $^{\circ}\,$

  The force on a wire is a maximum5.w+t ho )cmpl 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 0gif0 g) u c rh47u6rrii.ff-k“float” horizontally in air because of the force due to the Earth’s magkg- frguu0i46r.)0 f fi7hcirnetic 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 chaj: 6 tah2-sm.e5s ngtfrge $q\,=\,+2e$ 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 elect1)hp7u a9,ya2x1wefn crf ew1ron 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 foevq (sv-l7 z5xr each diagram shown in (Fizxqse5 (v l7v-g. 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 direct5bb6 x,kf zfw9ion 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 vednnt+j p 5b723y.iikn x5c*ndp.ll wb,7tj8n rtically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plane perpendicula+ xulh7phf b,( 6po3no ss.ot0r to the field. n,7 6 o0u.p+(olo h hxspt3bsfWhat is the radius of its path?    m

  An electron experiences the greatest fq dm37xbod47 corce 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)dp sf7cp)cp-s jcz02 beam of electrons that go undeflected when passing through perpendicular electric and magnetic fields o)c f j07p z)sp2c-scdpf 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 whosece8,y bbnoitd*jte: j/5 3c2h mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a pa( h*g z g9o(x;mhisqt/rticle of charge q moving with constant speed v to make one cirozx9mgq ;(/hh(*s tg icular 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 p xlv+*f)sb i:wath of radius r in a uniform magnetic field B. Show that its mo*:vxl b)wf+s imentum is p = qBr .

A particle of mass m and charge q move/qi/xa1eq2h1 o ivyyydw4l(7s jb 5i+s in a circular path in a magnetic field B. Show that its kinetq1yods4b ej1 w 27hyq5av y+/iix/i(lic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in - -qb /: uhvu(kphq56 zwiz,dtProblem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a sprlc 7- tgoh3 t;xwmzumi 1p9;;eed of 160 m/s perpendicular to the Earth’s magnetic field ;o9-3w1mz ht gir7pxl t;;ucmof $5.00\times10^{-5}\mathrm{~T}$, 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 magr-. 2mr zmw rr0*j g0jy0rhw.ds1i.8jhv7xr r netic 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 slc/47aldoa /v peed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 j8fr3+ j r n-7/xeviaya stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Eav8a f-en/ jj +r7iy3rxrth’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 tb) bmqr,t q36oo produce a magnetic field no larger than that ofb,t )r3m6bqo q the 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 hn5qc5o giy.1e g 00vkstraight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction ofone iq g1h5g 00cyv.k5 $\vec{\mathbf{B}}$ 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 attractive f vs-ya26ro1 r9iv o1c4x rj qfg+v:p*koy+ax 4p12kq of1 ijr o-vcgv r:6s*9vrrce per unit length of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of t i6eotk+8 k t1ck:9eavhe force between two parallel wires 35 m long and 6.0 cm apart, each car8t ti16koae + ce9kk:vrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 t g9p1. 2;njcr b jetoojaxs6-yzn.;7m from an electric cable. What is the maximum allowable current in the7jsoj 9t1 j6eanc;p btgyn2x.;-ro .z cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.b ;bnow me9q3-5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with-m3;e9q bonwb the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents in the sam/un7 9oipwmr.i8s; ume direction. Determine the magnetin/m7rmsuo i9ip;w8 u. c field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south fros0: ub jq s+h l7 is/jg8.a*sbo.-xvxbm a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point abvxa.-xsib7s.80+gj :bhous*sl q /jt 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 northlqr)rm4 7jku1kpzld qni/.iz -* t9 7q. What is the net magnetic field 20.0 cm due west of tr79il17qqp4.qnjm z)itk r*d/ -kulzhe wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in sfs0cwrf5jy6+8+j) z zecu-zspace 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 lonb)ha n1, ,mafeg straight wires 2.0 cm apart in terms of the currenm),enb ,hf1aat I in one when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires cor(ox)b9)m2j; f gi xklnducts 25.0 A of dc current to, and from, an instrument. If the insulated wires are of nex9mkx jr; 2gif)o(bl)gligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. Boxv ek) j7vhfy5+w: p1elow), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on eacfevxh yv5:wpk 1 )7oj+h 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 2t hh42,l e f7*8pmnjy.av5v zv3$^{\circ}\,$ 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 i2k(leh0,g ak33;yhs+ ahm f8 czvu kp/n the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of tcg/ h kl8sh +vmu0kpa2h3 fz ;3ye(,kahe 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, ma2qr4dm9 t 0kvtde of 2.5-mm-diameter copper wire and parallel to the first,q29 mt k0vdt4r is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicular to each other. At /tw6 kbjwkbw yr .2vh1z8:mu,their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if ,k1bwr z w:jmv8wthb u 2ky6/.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. i;4:xu9v*d*yli t ioiWire A carries 2.0 A current. Wire B’s current is 4.0 A in the same direction. *;vudi *x: iyotii4l9
(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 3aimk 6c x0l sd18bo:afrom 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 opi13cl dab s8xa:km6 0oposite 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 magnitu0rf sno;1x1 z;sgm* ozde and direction of the magnetic field at the midp10 zofn *zosgm1 ;;sxroint of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wii+ jw bob+h+ax1, i*e0nof e23hab wf.res, a distance d apart, carry equal currents I in the same direction. One wira*fwhi+e bab+x h,01o+3w j nib2 .foee is at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 4/v ot 4cvywf6320 turns of wire and carries a current of 2.0 A. Calculate the field inside near the center3v6/o4 ytcw fv.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cmmama,f 28 6vvl in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wire?vla8vm fam 2,6    A

  A 550-turn solenoid is 15 cm long. Thdlg3c1h 98j eme current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the fojmleh3 8 9g1cdrce on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make ag-ca dxrgo .u2lk.7t) practical solenoid that produces the greatest possiblc-g ..xrk2)dulg7ao t e 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. Below). Use Ampèr52 w rqsi2vmfz*l y0g/ib3/ bne’s law along the circular path, shown lwyfs / 2gm qi*25bb0vzr3/indashed 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 conduqr mi2. kye;ojy-vs4 4ctors of a coaxial cabl e-ov2q;4 ksyry.ij 4me (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 wiradzw7t44)opfmc*y4. py:l b he 22.0 cm on a side is placed with its face parallel to the magneticza 4 byhyc l*d7.topf: w)m44p 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 defl i*62gu8tabrrd n0 pe*ects 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 weak;le8 u -uj tm+8wr2kmcens by 25% over the years, what current will give full-scale deflection if it originally requij-8 eulck;wrmu28t+ mred $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torqh04 -i)+mm9d hl0x.lwvc i hygue cha.90-lhvlghi mcxy)0wim d4h+ nge?

Show that the magnetic dipole moment M of an electron orbiting bk3ng 5l6 -rtpl5 peg,k 29xnal-hl4sthe proton nucleus of a hydrogen atom is related to the orbitx5l ,ngth 49 eapsg-ll5n 2bkkpl- r36al angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flat on the 8hape/y/vu2w*)c cbq ground. The Earth’s magneq)yue2/c/p8ahc*vb w tic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle ofr-f;gu 1.yhoqt))hlwwm5.d b radius 5.10 cm in a 0.566-T magnetic field. What value of eg1)l)wy; bh .fw-mh.tqd ou5rlectric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvatur,)c23 b tvjx2*puyrle e equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest ra3,2 l b2urjecvty x*)pdius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the ea h0xvyv+q692tr y:e .zc9pw rlectric plates in the mass spectrometer of (Fig. Below) is9xp+2wvc rtz e : hy6v0a9.yrq $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pollutants. It is 1nb3d(r4t 9fej 3jzoqdifficult, however, to sepj1 fzrb 3j3(nd49 etoqarate molecules with nearly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V before they enter bi4pe : 4niv(8x1hen8u0aq oa a magnetic field B. The ions are assumed to starti8 h( nbae: evi1048xpuaq4 on from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A current flinmxo:.m8gop9 dpbnwg3 h /43ows through the wire. If the p mio:wxhb .po33/dnn8g9 m4gpermeability 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 1.8psgvmg:/uha 81-j ,y(w p0w py cm in diameter, and has 640 turns of wire. The magnetic field insid pgjmy(g v:w8 1/ py,-s0huwpae 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 momentu)a q2 jukhlfbk) j/t a56,* wfe7buhx/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 kinetic energy jal v (l9*e7g2v o-skkupon entering a region of constant magnetic field. What 2jk9a7(lvgs*v k e-lo is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fivbkgx 0m/r.:q g. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic fielq k0/:vb m.grxd 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 charg+bo yukwt9so*v)j16 s7s )qqne 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 8uszl3h g ap1o )7k:wdto the north and has magnitude) o 8gkwsp:ldz7 u31ah $B=0.50\times10^{-4}\mathrm{~T.}$ 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, :))viv leomr7 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. te1b94 kw.uop9 ihjn, vl;4bu Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almokve;wtbu9 .4 bi ,onhu4j19lp st frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and is susp7 euc4p qac1 i89grs2oended in air due to the two magnetic forces from the bottom two wires. The current flow through the two r 8ocequ1sic72 g4pa 9bottom 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 plane act as rai4n*k-+;4 vz mpbzjj ynrg)9dvls to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnep4mz y4j -vdk9z+vb*;) rgnjntic 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 deflectiomi8y 85xpu. h8d lb9zjn of the electron beam near the center of a TV scrh98pxdbi8. ljzm5yu8een 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 elementary particlpsrgf*r9j*, 9t fiod3 es 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 be fspg93r9 d*oj tri,*ftween 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 s vs2b*p flh5df tr-991u qvl3sqon j9)ide l, caon9fl f uqs-*5)2 3 slv 1vt99dbqrphjrry equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators forkqvsg**qk 5wv56t v*l “beam steering”; that is, the magnetic fields can be used to changgq*vq5 ls wk6 tk5vv**e the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire cl; fph39n/- ng7bb ,o0bwpfe farrying a current-wn, pbg7plbffn / 309; fhobe I (as in Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the mag 9akx2-gko.bxnk6be9 netic 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 magnezju-b:xgb 1 ae;+c+zx tic fields produced by overhead power lines. You estim e+bx1x:-+bjg ;azczuate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might 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 /i(ne4z3ac- ja0p b+y b,cgypwould make a beam of electrons, traveling to the right at/z,-yinaegb c( jb34+ ypca0p 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 thro(f 2 gof9;fjhf5z0iewugh a 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 radii0;e wgf fhj(z9 fof5i2 are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in d.hp 7g z)g(5japvroz5iameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how man j.gopzrz7)g(55 v aphy turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, eace xo5b/(p lt. jpe477 cdjtz5kh of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as ske x4l7zd(/ t7p.ectbjp oj 55hown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T at a (qfh724we pg jq(89l xu kdbh/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$