A compass needle is not jnhr1p5y 8)wyr6el/q9xm h ymel/) 6e always balanced parallel to the Earth’s surface, but one end may dip downward. Explaxhy6/81n9re ymm epr 6lw/y e5qjl)h)in.

Draw the magnetic field lines around a straight section oiz4o cl(c d71opp) 8 vir-xqkpld*o) *.zn 4pef wire carrying a current horic(* k7 l1q8. cdz4lropp))-pxzi oieo*vnd4pzontally to the left.

In what direction are the magnetic fa0/o rbmbl ; s- 4mkf.3gl;ldep4klk6fb(h4mield lines surrounding a straight wire carrying a current that is as4; m l/l.0lmo 3mhkfgb; dp6-lbkbfekr(4 4moving directly away from you?

A horseshoe magnet is held vertic w *wbj5d+(v.f3a csg5t uqoj3ally with the north pole on the left and south pole on the right. A wire passing between thebfvoj.d aq3jw u3t*(s+ w gc55 poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic objecty8+-yi,ecqyax ,2 q 0xryv9hv , or only those made of iron? (Try it and se,qy ,xaq yc8 vy+yi0 h9e-r2xve.) Why is this so?

Two iron bars attract each other no matter which endsl 6ni4/e sl ak(0/wfgm are placed close together. Are both magnets? Exwfmk4in//(6 l lsg0e aplain.

The magnetic field due to current in wires in your home can affect a compass.qq ,9uvut9ol0asp okiu 05d2eko f , 43kn(no7 Discuss the effect in terms of currents, incl koukt4dooivfa7,,( eok9 5us9pn23nqul q0 0uding if they are ac or dc.

If a negatively charged particl(qom73w/ lsql /.f hzxe enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay t/ s7lxhmfz/q (3.qolwhe same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), chargej p)azt5-m:ijd particles move 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 charge. For eachij)5jtz m -p:a of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and cy /af +kfkaaqx gv71jdmy73 0x4tq nvj):he31, enter a magnetic field as shown in Fig. 20–46. What can you say about the charge on eacjt :13k f)j07gy3vqq1 n yav+h/a4 m kaxe7dxfh particle?

A positively charged particle in a nonuniform magneti8pj itanqs1ns9)cp;1k0 vb :w c field follows the trajectory shown in snn; 1i9kas0t 8):ppvj b1cqw
(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 magenr )+kk4(7xhcr zr3 enet? Can a magnet attract an iron rod? What must you consider t4ez (x)rre 3rhnk7c+ko answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10 cq dgn1abm-)fz13w.q) 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 ta1- nf3 .)q bczqdgm1wrying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three i 4no+ /-s yo 8tahfpjx2g4c1u-4gfis hron rods, two of which are magnetized but the third is not. How would you determine which two are 281 4h -fsjtngif +s pcahy4g4o/-xu othe magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic 06gv; ; ttfiz+fbyrkv 7vxv*.field? With an electric field? E0rt.vf v bvkx7;6gi v;f yzt+*xplain.

A charged particle is moving in a circle under the influence of qy n09g- 8 m/7khwyp.l wpf7dva uniform magnetic field. If an electric field th fn hw0m/p7-pl. q 9wygv7k8dyat points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magn8 90;qrit+ xg:tq nlav4k mz1oetic 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 in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positxigk+nr t;4ml10zv9 t8 aqo q:ive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a curr8832 ggkz9aczkd1qi l ent fromg8ikq9c 8az2 lkzd13g left to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or ma zl-1xz7mz8mb uiu9g.gnetic fields that surround a moving electric charge.7 mz 8ux m9ulzz-.i1bg

A charged particle moves in a straight kvk)sn4 +mficy* zmsehfd:5 4ti.y50 line through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situations.fsi kh5y cef)d. mm i+vzt04nsk5*:4y

If a moving charged particle is deflected sideways in some region of space, 2*gw.t7rauc9wn ity ev1(en, can we conclude, for cerit9 e2g,yvt( eaw.c1w7un *nr tain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space therecmlyua-9uxr 4 5,r 8cr 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 whethg;py +w-ng5gqer moving electrons in a certain region of space are being deflected by an electric field or bgqp5wn-g;gy+ y a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic materia(jhpw ou 7c2w/l0,gral?

Two long wires carrying equal currents I are at righzt0vbyu/j6 q 4 x4exbsa:m1/lt angles to each other, but don’t quite touch. yeb44zx/16s alj0 xv/m :qutbDescribe the magnetic force one exerts on the other.

A horizontal current-carrying wirepd/e+0s yeg;z* 3ourwdlk*4o, free to move in Earth’s gravitational field, is susy/gwlo 0pod +usr;3 4ed zk**epended 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 of a magnet attract an unmah,57i(gea1yw2v kq oq w*fvu1gnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if onp 7z*bzeqy3e yb;9vs ,e end of the nail is in contact with a magnet, tbve9zq yp7zy*;es, b3he other end will attract a paper clip. Explain.

Two ions have the same manzy pck7(n92uss, but one is singly ionized and the other is doubly ionized. How wilkpn 7n2( 9uyczl their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside q-:chla/w *zn)p pfj: 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 is an elecbma 7kao*g;7in;h. v ltromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for th la7 *;g;m kvib.hano7e starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of ht6/mplb6n ,ur;xb60yduz ) kthe force per meter of length on a straight wire carrying an 8.40-A current wh t/ ku6nr0pl,m66 xybubh; dz)en perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m lens +d:gd*3itzz pur3*d gth of straight wire stretched between two towers cg*u:pdz 3r3+tsdi* dz arrying 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

  Calculate the magnitude of the magnetic force on a 160-m length of straight w, 2 nhhf z(ndi-f 5 i019tqkxmgjv(p(pj/(rmwire stretc 0g ,i/hpm1f (m f nntjk9((2hizrqxpdv w5-j(hed between 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 on;nse ,n- wgx1)ccs 3a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a unwcss-xc) nn3o ng ,e;1iform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented b4ge 58mf g1h8+lboo7hj n 3txhorizontally. At that point on the E1t nj 4bfomxb ge5hol3g7h88+arth’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 isogdmghau4 yglitv. 9 ;40;n(o a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 5 ggg ;v9h0lud t.oam4yn4o(i ;5.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per me pnsj ;*gb/cl/ter on a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of tp*ncs/gb/; jl he wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum ofzlz(62/ 6kgof rr;thn $ 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 “h7cko zuw7/n)r,o km 7float” horizontally in air because of the force due to the Ekh )koo7nu,zwc r7 7m/arth’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 charge qecy (om* -jq3$q\,=\,+2e$ 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 directiorec*(ms 5 zlv7cfk5b*m 6dg 9kqe4nx3n of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for eachq 0-g zbf39ssj diagram shown in (zfb s39j s-g0qFig. 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 directid (c*h mi :87oc/xk5ltl4mpnhps: v wzm681 kion of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward with a nhzak 2 +/2 brfjp u89qx;)2jlaay3ncspeed 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 perpendim37vh uw,aq flk w4t8hi4n5 /xcular to the field. What is the radius of its pathhv t / ,k74iu58wxlwfnm3h4 aq?    m

  An electron experiences the greatest force as jb0u:n+*;al9v oc 4xsh9n p w4d ktz)sit 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 undef3mrahg2u s /n1lected when passing through perpendicular electric and magnetic fields of magnia1rs 3hn/gmu2 tude $8.8 \times10^{3 }\;V/m$ 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 mass iss:iduuc , x;)(lo zl2gqi e,o/ $6.6 \times10^{-27 }\;kg$ 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 wk4-ya2m(ft( 9jabcyub mf:1 rith constant sptfyyua(m- rb:j 1f 4c9ak(m b2eed v to make one circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r io (xo2svstfn5083a es n a uniform magnetic field B. Show that its momentum is p = qotx 5(2v0ssen3so fa8 Br .

A particle of mass m and charge q moves in a circular path in a magnetic fielvm oss7m,*r rr1;pzs6d B. Show that its kinetic energy is proportional,s1p r sr7svmo6 ;z*mr to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem 21 i ca)5btq(si t5s $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s p,a*t03: ytm+lzozmu perpendicular to the Earth’s magnezt 0p3atm ml :uzo,y*+tic 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 magne 7cudj0j2m (vdtic 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 withd)e,3onis ryn/h 0f:u speed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a uw1(o,do ;,ut xc5gwi stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 ix1g uw;w oo,dtc5,u(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 dyws9 w2qv+, s4/p rvidocr96*njs-kproduce a magnetic field no larger than that of ts4v/9 s y9+c*,nd6opwk jv2siwdr- qrhe Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I ou(ruavox19tyy6 k t*8x) kqd:0tsz(ts t of the page toward you. Indicate, with appropriate arrows, the directt9t6(q kr yz8):sx*xy k(vo 0t1dt asuion 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 atti +x egj+foz;bvw,( y1 m*ygclco842fractive force per unit e4 lfix,+(2ocjgfz+ g*c1bwo;v ymy8 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 ;-; yhzseq)hs of the force between two parallel wires 35 m l ;;shs yzh)-eqong and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic f d m:; zgghu5svel(7 +96jeewkield is being carried out 1.00 m from an e;zgsudel + e67m hg(9w jke5v:lectric cable. What is the maximum allowable current in the 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 8.5-m-hig9:c8phg:ed 7pfrt yn eirnm,) 2 a(qu,h poles. What is the magnitude of tidte r,:m :yn7 r, qu8hef9anp )2(cpghe 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 -m ,gnmg1f/ar 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fra ,ngmf1-/ mgig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical y5chp 7:i,r: wtxo:euh i/g.f wire carrying a 35-Ah7o:rgw y. it:x5e,/up:hcfi 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 the ne2hp6a*ngnj cfm/k8c. t magnetic field 20.0 cm due west of the wire/acm*n2nc6hj gpk. f8 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 protonsvit ic1c3 f2 5 abo-+yr*;zhec2q8ks d passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field mid 6haa m njrk;aqh9:2df6orq1ndv5 - 7tway between two long straight wires 2.0 cm apart in ter:ddmh7arj6fva 91q; anh2-q r k6not5ms of the current 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 conducts 25.0 A of dc current to, and from, an i f7hsq f0-q11xcjonk- -s 2xqhnstrument. If the ck-qf0 q2hx sn1-xs7fq1o -jh insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. Belof*xyieppda v+;,taxan (;qkm fjz./y .w1 8/fw), parallel and just to the right. If it carries 25.0 A upward,. papt y /z ;x1*ax avqffn, .k/ydej8+(ifmw; what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle point73 t *quwlo3zb2tn (ses 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 wi6 jpdb4iwi3.p re, as shown in (Fig. Below). Ther 6wipi4. bd3jpe is a 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 currentoj i ql 5bbb2h.:uf 24pe;:nbt of 48 A. A second wire, made of 2.5-mm-diameter copper wire and patbi fejq :obp 2n4u:2b ;blh5.rallel 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 perpendicu 91vo*ypwjj. ovz)kb,lar to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetij*1wpjv ov o9)zyb .,kc field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carr2qq rg84;l y3ob7+lpcc qy1yzies 2.0 A current. Wire B’s current is 4+7;81qc lobgryyc32yqq z4 pl.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(fx)1)ovb g /) bie-2kmoughfg 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)1/)(okxufovhme)2ibg gf )b -. 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 dizitjaak,t70* on l 8nf7 41azxrection of the magnetic field at the midpoint of the side of the triangle between o7aktfz80i1t7x lna* j ,zn4awire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents)nr9dv q-9eovsv6.h z5 6ozyk I in the same diz6v9 oe.-nq9v5r d6 z) hyskovrection. One wire is at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carrie3gj-p-a e qhzcx,fcj(a1vg rlqcl)r2/w;;f 3s a current of 2.0 A. Calculate the field ins/jhw1q(x,-r2a ;a jlz gc3c) gl-cpqf vf;3reide near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to prodx h sr0j)5zd4wuce a field of 0.385 T at its center. How much current should the soleno)z djwh x450srid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long strant*xhzdtr.6qwtlq : *(.7 c uxight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A currex.:z r 6wtqnu.c**d l(tth xq7nt downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid tha, esrb/yq*6f.yu6fxn t produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short anf, *s/eyyqnub 6x6. frd 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.dhrdm,zkx(6o2v9difa1y5i 5h 5(t vr Below). Use Ampère’s law alona56t15i5ihykddforxdhv r ((zmv92,g 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 betweegcg-ej3 j7odyuj5 j0:n the conductors of a coaxuo:jdc7j-eg3jy 50jg 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 placees0 e8k 92cwacd with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the c208ckwc sae9eoil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale for at1,oym rdbp80 $53.0 -\mu A$ 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 spr:of.h*b;3onx f mw+0uy 6srka ing of a galvanometer weakens by 25% over the years, what current will give full-scale deflectio+6 ys 3* on;oa0.rh :ffxbmwkun if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does tjfwf,m5 r cqmvl/q1)(he output torque changerqw(mf fv/cj1 ,5mlq)?

Show that the magnetic dipole m1 *ilg 8bood,moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to th* 1,dm8oo bilge orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter a )sdbb 7a;:r 5 pl*zubz.7wvhund containing nine loops lies flat on the ground. The Earth’s magnetic field 5h bz.b :ublw;pd az*7vr7) suat this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic fie met-g jie7k;0ld. What value of electric field could make t7tkj e mg;i0-eheir paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radiiyuj 18q iqfj3. of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius correspqq.u8 j3f1jiy onds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spect0l lrqf). 7gkerometer of (Fig. Below) gekllrf).0 7qis $2.48\times10^4\mathrm{~V/m}$ 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 difficult, ywd(b0ja u58 :vl.uyohowever, to separate molecules with nearly equal mass such as CO y8 ( du.l:vjw0ya5u bo(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 (p c/-ri g;ay 1y0lz s0nd,6w5rpj vnta voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show 0ndyc/-arpg y0j 6zwrs5p 1n,tl i;(v 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 k - *rut.uzv9n n5d0puloops of wire per meter, and a 25-A current flows through the wire. If the permeability of the iron ist9u.*kz nd0npu r5 -uv $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm lotz0y,nc k-;ov ng and 1.8 cm in diameter, and has 640 turns of wire. The magnetic k0 ,tv;o-czynfield inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum vitv2 -q pjd70*:srwqd98zv z$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 4o -ev42rvl+mii7fb m the same kinetic energy upon entering a region of conbom4 m7 il2 vrivf+e-4stant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Belowip qxzz+ b9+8l) carries a horizontal current of 330 A toward the east. The Earth’sqpz+l9x i8bz+ 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 which7chq/sjp4e 6 vsdxe: rwy 60t* has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points al j +8jqgmz(p,pmost horizontally to the north and has magnit g,zq8p p+j(jmude $B=0.50\times10^{-4}\mathrm{~T.}$ 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)s pt1i;)cdjn il3y/4 x y2agt 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” iy izj+rn os63i1hq0nn +mp:/cs shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendin+nmy o j+:0nhipzsq361/rcicular 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 anyvzp0.o1i u +td is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through tzu.to+y 0vp 1ihe 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 plane act as raw/x;x,iz:fv0 saujkzt(d ; x:ils to support a light metal rod of mass m (perpendicular to each ra(:xuvwx,iz/k; x :taf;j d0z sil), (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/b* qab67t kuj beam near the center of a TV screen due to t j*qkba/ ut76bhe 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 particl3e if(dqf1 1d)4ahqj oes 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 fqf ej ddio(13q1a4)hparticles 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 wir -ikj3d7::tnqi 3wnph es, located at the corners of a square of side l, carry equal currenw 7p-i3n::dkih 3qj ntts $I_0$ 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 in62o kh a(fdc/pded;6p particle accelerators for “beam steering”; that is, the magnetic fe6c/;o6pp2d( dkhdafields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B o,6sljr+*a a9l2tut sat the center of a circular coil of wire carrying a current I j*l +t,2at6oasrsl9 u(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 thf- w w9zgf/4mge magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnet57zr0i zxyl6qpgiebx 21x h7t h j-72eic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic fielqzhz5t7e6x1j7g b0 riy xx eip2h7l-2 d you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would ml7d5xv k-yl+ 8k,kdw/m+n og jake a beam of electrons, traveling to the right at a speenj kd /8kylg7xm 5,++vdlk -wod 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 fielhq td: 5ggt cp-5m0jjz(usvfd +8*to*d of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two s tjg(u+ozj0vm8cfs -thdd5 q 5t g*:p*uccessive 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.kgp.a q ro8-f cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must g 8r-p..a ofqkthe solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires,+ f km1w04rnet each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make a4tne wf +1r0kmn 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.yqq 8cf,mj;,g2dz iz- 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$