A compass needle is not always balanced parallel t*, 2)r io ydmb.uotluk. x/h+3n(0x glpykvn4o the Earth’s surface, but one end maym.2gp03uky, .ubx(on nlyvl 4it*k/hr x )d+o dip downward. Explain.

Draw the magnetic field lines around a s;7lhjbfd,/80 p;o rs4 ;dedom zymh0iah b06jtraight section of wire carrying a currentf 080 o;smhb,m4yhri /dh d;z6l7o bja0pd ej; horizontally to the left.

In what direction are the magnetic field lines sur-rk ni97g/ky, e5ej nhrounding a straight wire carrying a current that is moving directly away from j5i ,kn-e/k ne9hgy7r you?

A horseshoe magnet is held verticall,kkx bc 5se8 : g0olqoa(m81zay 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 from you. In what directiak,5 m: bkq0a8(g oz1sloxe8con is the force on the wire?

Will a magnet attract any mexc4y;y9*d v oztallic object, or only those made of iron? (Try it and see.) Why x4d 9yvyoc z;*is this so?

Two iron bars attract each other no matter which ends ar304o85sgebfsy x j c*te placed close together. Are bot4 esftxs*5b co0yg83jh magnets? Explain.

The magnetic field due to current in ;;j(jbyzrh6qz/ /y jnwires in your home can affect a compass. Di( yr;yh;/jj6 j/znbz qscuss the effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform mafh2p 1j0(tu: 3;qq ipstztjfne.wg0li .c 3d: gnetic 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. (Neglect gravity and assume there is no electric fiez u: eqit f. 3n1gl(jt0 ;phj t0csp:q.3fdwi2ld.)

In(Fig. Below), charged particles move in the vicinity ofejq05*+ht7 wppd- pry a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - yqj-te 5pr 07+dpwph* indicates the sign of the charge. 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 a magnetic field lk+ owjku62,5f-z mwyjf tp+1as shown in Fig. 20–46. What w k2,k6jmf 5+o1zyt+lj wpf-ucan you say about the charge on each particle?

A positively charged particle in a nonunifxs6n i8oka)4 a,wksx 4orm magnetic field follows the trajectory shown in x4 o a8), k6iaxswnsk4
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attrv(gg:z5 b9e ip.i/0m+ bee4ctjro wt1act an iron rod? What must you consider to answer thesevi1 btoj0ew+(/c g 9gp.t:mre5bi z4e questions?

Explain why a strong magnet held near a CRT television screen (Sectidvw1,jaa*,2j(c ecpbon 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 ba vbccje (a w21,dpj,*y trying this.]

Suppose you have three iron rods, two of which are magnet/w1 m(l;zj v-v ac*dvsized but the third is not. How would you determine which two are the wlv-*szdv;c(mja1 /vmagnets without using any additional objects?

Can you set a resting electron into mo9eou4w4gc)-ify ut( s9 /tcfb0hx6e dtion with a magnetic field? With an electric fiel 0/469ic4e 9ecyou-f ) ts(dtb hwfuxgd? Explain.

A charged particle is m 8 tyh v/*,jbqdn0+/ikp,o-qetkm5zioving in a circle under the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic fie iq+ ,h*bvkdoj8/pttnqiy0-k ,/e5zmld is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind elecb /u nw7tnf p z2h74pmu/u,zy*tromagnetic 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. /pw7tp u n*yh/u,nmf 72zz4buDo positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a curroel,if n; o muewv;),.ent from left to rf. ee i,now)vuo;m, ;light
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround g.-wkh v9w/l0rv+lc ja moving electric charge.h-w.l/9g0 cvw vrjk+ l

A charged particle moves in a straight line through a particpasxi f+g8h oph+ 2j 3-rvhf18ular region of space. Could there be a nonzero magnetic field in a8hhx8 o1rh+ivfp gs3 pj- 2+fthis region? If so, give two possible situations.

If a moving charged pnz,p y+k7k (le; uwpg865fkifarticle is deflected sideways in some region of space, can we conclude, for certa(w7+l6fy ,p if;5kk ukpe gz8nin, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a8p(:s8pdg l*hrdv hm , 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 whethernf41x 3vivlj2 moving electrons in a certain region of space are being v24xvf1ijn 3l deflected by an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagneti-- v1gtpysr z jur0t)q (wl1m)mth-*qc material?

Two long wires carrying equal currents I are at ri(;lp*djt )o6ed)fyf l ght angles to each other, but don’t quite touch. Describe the magnetic force o;jdf)d y*p l o6(ftl)ene exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitationv0f.6qm*brzwarv*u0 5vo3 .tbhr o/ cal field, is suspended directly above a seconv r ocm*.b0v .r3q zo bhvtuw6f5*0a/rd, 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 piece of irondh :x*+aff e:2bnawx6?

An unmagnetized nail will not attract an unmagnetized paper clip. Howevetzsqr17 f+m6 yr, if one end of the nail is in contact with a m7my+rt z16qsfagnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionnwr z m6km.l3l3w6x)d ized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Below) diffk 3 )w6x3lmdzrlmw n6.er?

What would be the effect on B inside a longbdr.cj vi,r) /s08kpv 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 .c 8ki-0wfgh/r+u3 ih s 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 large current but you do not wanfg i3 8wsu/h-hir+0kc t 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 magnh. g6fs)u,s./ xw e3hx v,vby1 zely)mitude of the force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic fieu)whx,byyfh . /)s z.6x1m evesl,3gvld?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of t wmrn6kb63(8*f(fk(upmtwy straight wire stretched between two 6*umbm pktw3 fw((ft8kny 6 r(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

  Calculate the magnitude of the xi) pom)jt(n ngj;jqx4e k0/)magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fie 0j o;i )/jjpk)4gnemtn)(xqxld of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a fpxijd 228isi- fs(0dwire 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fielif s(- is0xi8pdf2j d2d?    A

  A 1.5-m length of wire carrying 4.5 A of czhv4xbw 7p:) sev.dtv3u3s )surrent is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes3 bhs7v4) ).zsxst wveu3:dpv 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 owte. 1ahj9vn1f 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is t.e 9hna1t 1wvjhe approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be ogv,t h0qixwy5w6si(( nly 35% of its maximum possible value. Sketch the relationship of the wire and the fietws,65h0 x(yi q(vg iwld 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 maximdc n/ jernxk49 rz,w* cg65w/ium 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 1.04wh ba)8n ys xpr .e+q48s9kdk0-mm-diameter copper wire could just “float” horizontally in air because of the force due to the Earth’.+n4 8ske kawp yx4qdb9r8s)hs 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 char ss9yzgl-rd3c5qy 15t ge $q\,=\,+2e$ 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 directioum*;ipbp gfwh/ue h l1,0 .ml*n 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 each di 7i/zl*nmzh, wagram shown in (Fig. Below), whern z/7*mlw,izh e $\vec{v}$ (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 directio4p (yw 1d(0/v/wmvip-oyu jpvn of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected ver/kgp,w-f)s 0qq qbjnj ,(ves+tically 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 z ;tzs*tr,m-tw(i 0q qplane perpendicular to the field. What is the radius of qtmsrt0(-zt*,q;wi zits path?    m

  An electron experiences the;0zmjlnzib0 2,0i vi t*id7af 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 undeflet 56u8az75y p lcyhll69zfqsm z97vm7f( x0eucted when passing through perpendie zy9m pzqcvl7zt5(750h 9 ff7auy6xu lm6ls8cular 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 heli 7 gghhbelp2wf )h -neeo oy4o+2-;ws3um 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 T requir + 0tu;ectio4e0i lrnplv0lr*14dx.vo g +x:xed for a particle of charge q moving with constant speed v to 1o0+l4t 4 *dg iu or.pirx:xn+xev0lte 0lcv;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 xn.yw3(kn or2moves in a circular path of radius r in a uniform magnetic fie kny2o(xrn.w3 ld B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetitrmr0 h1:ag jib7 -qfflc/ 2gkak1)k+c field B. Show that its kinetic energ)t: lrga m ak0 2jk1bg/-h+kqrfif7c1y is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular mombkqav82 )d; esentum 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 magn)bf :ran)6(zk 1sh*v trp *otyetfv)* :*arb) rto 1nshkp(6yztic 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 magnvrvo4u5 ajg1 4itude $0.40\times10^{-4}\mathrm{~Т}$ 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 speed npa4ixp/1 2r 0mogy5i$\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A currdtdh5s*g02 hg k4xf5n7f0 nl hent. How stron gxfkn4 5g 2*7s5l f0dh0ndthhg is the 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 allow8aj rqd wqrc3i3uc) qm:2z;kun5 uu 99ed to produce a magnetic field no larger than that of the Ekcn qu8wcu2 ;)i uzr3aq53mjrd 99u:qarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of the page 2yitw/myq*4y 0b6dpc a,i15 zfn8bw htoward you. Inp24 5i81 qwwyfibdz,06bmh ay*n c/yt dicate, with appropriate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A current exerttjk3 z3zxh+ v7wpow m)/6 c.dzs an attractive force per u)ctz .zdwvz3po6 7hmwk/+3j xnit 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 the force between a4-3vmfc p mv6/r6rnt two parallel wires 35 m long and 6.0 cm t6vmp/v f4nr a3 mc-r6apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is b zn3tyq:fp.7 seing carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experimz.t 3pqfny:7 sent is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high poles. q eg+on 8kpc((What is the magnitude of the magnetic field produced by this wire at the ground? How e cqp8ok+(ng(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 ( /y+k2; vigf4 r7p3d estoe 79bibv+ywc,hwpcarry 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 othebk2os w +py/w,77ty9i gi phrdb;+e(4vc3evfr(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vert bl32nn9dcrw46.b,qj 1nywiw ical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s fie2jcwwnl19yn .n3 brw bi6,q4dld 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 isdp88 svv w1sb2i+ 5urs the net magnetic field 20.0 cm due we+udr1b8wi svvss p285 st of the 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 proto4e/ gcdh )n-pbns 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 midwaysjlq x xof)hvba:o1)3 i2-ay)bv:rp 4en*(vo between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume t4h v s)f-iy bep)x oxa( lovjq2vn*ra1b: o3:)hese currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current tu li(llrx(o9cku6 ;bs4 1t)+xevqk+ to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic fieldlueb;t+ 64v scl1(o k 9r(+lxqtui)kx 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. Be0h+ )kirljg 7e8h.z7 6ymrnns dz8pv i.n-pj 1low), parallel and just to the right. If it crep8phk7- 0dl y6mjvzi7h..z+ 8)nngsn1jirarries 25.0 A upward, 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 points 291pk eoy ;*woqmc/ xiv6 jm9n23$^{\circ}\,$ 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 lvbahp j g3if;3d;:0scies in 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 magni3 s03gcjad; h;v f:ipbtude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire, made of 2.5--(jhgaokw5ztp , x81e q- tpy8mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below 1 (ox-5gk,-ptwhe t 8j py8zaq(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. in)p5l wtt qt4 p(i05fip ;u a0uu4 nonbgn;55At 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 the top one carries a current of 20.0 A and t(ppnu u 5in q5;4pbntoi; 5t0)ia4fwt0 5nulghe bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A ca*vt vutk.v.6 x+a(kb drries 2.0 A current. Wire B’s current is 4.0 A in the same tvt6da+k (v.*k .ubvxdirection.
(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 hy:m8.y.y0mpilao81ynk 4 wh another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length owy18:80a4h.y.l m kyp hyim non 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 fief2oit- *ho 5njy sph7(ld at the midpoint of tf( ot 7i2*nhyho-js5 phe side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents .y yxk l846qi 52kgvq/zjnzs 9I in the same direction. One wire is at x y5zxy296gn4v8k.z/i qqls j k = 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 carries a currpxcl7 eh(n;a+p 37phcsu2 nq2ent of 2.0 A. C2u ;plx3qc7 +hncha n( pe7sp2alculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce / 0ukh7lsh*vq)iey/ha field of 0.385 T at its center. How much current should the solenoid carry ifv//y07l hhuqhi*) eks 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 stg2tf8mq1 r* aa*wc/tc u/vi r54rq.n wraight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A/r cc5.t2g iquta/fvw r14w*a8 rq*nm current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of cod1 9e(mbj6rn etp7-xdk.0co wpper and want to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, 9 cw.k eemr7(nxbt 0d6jop1-dsuch as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use p 7j);1o;k*duzx f jmjAmpère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic fied pfx *jjjzk1om)7u;;ld
(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 condu4ra; jxz1gc5lcn5fn2 ctors of a c;aj 4ncnr2fxz 15g5lcoaxial 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 7-;;o 51fipiuuoonq7o rwh ,ton a side is placed with its face parallel to the magnetic field between tuif5roqpoh wn1 io-7,;7 ;out he 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 deflectl tn :8i raw3pr(ar*blw+i4m4a ft -y)s 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 galu ) +he.kd5:duzgdpj6vanometer weakens by 25% over the years, what current will giv du:djk5e6d pugh.)z+e full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by whveb + x*4z)jk a9/hbckat factor does the output torque changake)/bh x 9bzkv*4+ cje?

Show that the magnetic dipole moment M of a7v+9v,zclx35kowc q z-, kngln electron orbiting the proton nucleus of a hydrogen atom is related to tzlw-,k k7+5vz9l,q xnvcg3 cohe orbital 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 ont/om 1x:s4bbp the ground. The Earth’s magnetic field at this locatio/ b14mpbs: txon 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. ku8* ja ciww5p / c5pz6)c8zylWhat value of electric field could make their paths straight? Inp cu8 a c)8klw6jipy/5zz c*5w what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have rad4x27vs lcmn w a;kaz77ii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius correskzs l742xc7 va7;m wnaponds 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 spec xl6tif7f n95ztrometer of (Fig 57nlz6fx if9t. Below) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pollutantsd eg05;1h lq;4i 16wmffdl xwn. It is difficult, howe1 6 5hlnxd 1w e;iqdw0fgm4l;fver, to separate 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 accelerj9n kv6q:jr8w0xat :rates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that thevw09:: j8k6rtq xjr na 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 solenoiddu00 h w6c 9usjs6by1h has 430 loops of wire per meter, and a 25-A current flows through the wire. If h606j1cbuy hd9uw s0sthe permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid isa1m9e4mniky8n f(:z cve4t trx( 5a0b 38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability (1r85t c:0(9a f nvat yx4embei4kznm$\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumbfbaz .h vaeh1uxye 7331f9 v65vufr- $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 k0)j 4j.kwlq m8rrpl c*inetic energy upon entering a region of constant magprc)lk 0*8m4.r qjljwnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. g:t p i a*9zdv;1lw2 js(i8vusBelow) carries a horizontal current of 330 A towargpij sv 1vit2luza*s9 ;:w(d8d the east. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which ha:5qsh qdmv-vmlu4g33 c.evq;s acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almost horizontallyda7o:g4n2c6qz )o pwp to the north and has magnitu)wc67 :2oo zpga4dn pqde $B=0.50\times10^{-4}\mathrm{~T.}$ 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 mam- ul- lidb)h,ss 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*acgc9j:oj*k (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supjcko* cj*: 9agply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a 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 g1/ 7 ekln,cfi1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current f1f eglnk7,/cilow in the suspended wire.    A

Two stiff parallel wiv6+4wzp) k iq +(msqnrres a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic fielkqv6q+ mi)r+ spzw(4n d $\vec{B}$, 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 electrona-ukd +kf5dr: vu;ni , beam near the center of a TVavdku: ru-5; nkfd i,+ screen 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 acceler q7 o/av/9 96dy9kkbwng s0h usn:e)8 *lrucdpate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are acceler9s09 n:eag/yo9 67sd /u) lrdhc8kkup nbqwv*ated 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 straigh*v f 3w f :p3b(0hcfs.s4gpourt parallel wires, located at the corners of a square of side l, carry equal:svh wf4 0sb 3up *fgf.c3(rpo 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 for “s n9c9gv;1 zvsb8y: vvf +iad3beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angcg3ad8s9:91if y sn+;vz vv bvle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of avjcbd9 +y1o hagr+q1+d*n ;t s circular coil of wire carrying a current I (as in Fig. Belo1 v+q1 og;t+y9h dsj+cndr* abw) 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 fiemk* oi-o tuv)/u,rbif6f wv3a1 f5fh-r. ;dwhld 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 idw8up- q)iate7ea of the magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company 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 thet-ap8i7 ) wuqe Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of elect pwn7t4d-avav e+zci6n-u1 9grons, traveling to the right at a speen9164cu7vn+pg d- zvaitea- wd of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field fuwy79p q1p a,of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from Ppw1pq a ,7yf9u to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T ce+d9rv d5-wkmagnetic field at its center. If the maximum currend5vwe kc-d +r9t 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 sam/-vc2swguke/ y2ak7c e current but ie7/ -k vc c2y/2kawugsn opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T9 ofqoi2 . jr65lx/x :dqkvlp0 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$