A compass needle is not always balanced parallel to the c7-a -nb ;6gai 9ri yilfnr4,kEarth’s surface, but one end may dip downward. E9 nf46ki cagi-,-inyral ;b7 rxplain.

Draw the magnetic field lines around a straight section of wire carrym *svs5/.x8istttv-feg2e e;v6c qw o.v:i6e ing a current horizontally to t.m;.tt6f qcs/2*sve6ov 5 se:gxw-eitev 8ivhe left.

In what direction are the magnetic field lines surrounding a straight wire ev0bsx(pucpg/ *qwih ;rf 6,;. .k skfcarrying a current that is movinc .k/hw;pf,0 (erp. i*bfsq;ugkv6 xsg directly away from you?

A horseshoe magnet is held vertically with l7tii78- v,x.u-d +cu1jqdpyl1yp*f) j uryp 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 direction is the force on the wir cv , 1xi-ui .)1t*ddjul7py+j f 78ypup-qylre?

Will a magnet attract any metaf7a2cdob3 .q,9o yeakllic object, or only those made of iron? (Try it and see.) Why is thi kyfaooc7deaq3b 9, 2.s so?

Two iron bars attract each other no mat(0x. 1pxeh qblter which ends are placed close together. Are both magnets? Exb.x(le xqp 1h0plain.

The magnetic field due to current in wires in your home can affect a compaszybtx2:z8 l4rs. Discuss the effect in terms of currents, including if4r8l 2:tyzx zb they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field mrt gml, r3+y.*lvmw, which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Negle *,,y mmm.l+vlrgrwt 3ct gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current- + eu4w0 emufgi(gkv:)carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produce:vggu( 4miwek )e+0ufd by the wire.

Three particles, a, b, and c, enter a magnetic field as s )kh()lu qq4z+.hveq8kg (2r3 jbzaskhown in Fig. 20–46. What can you say abou3levsq (4 j( kkz8hah2zr+ubq. q)g)kt the charge on each particle?

A positively charged particle in a nonuniform magneticvicvtm k3w17v v/ i.7y field follows the trajectory s7wk.3/yc1 tvv ivi vm7hown 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 q y.sg;*/gu:v f/m solmagnet? Can a magnet attract an iron rod? What must you convgg*/u:/ f; ossly .mqsider to answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10) cal42ucwe h-eoay9fe2on .uo 72 uses the picture to become distorted. Also, explainee2ao n-292uf4u7hoco.w ely 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 trying this.]

Suppose you have threwo/*,e osix ) *k.rrfpe iron rods, two of which are magnetized but the third is not. How would you determine which two are the magnets without using anyw)fxeo kso*rr.*p/ , i additional objects?

Can you set a resting electron into motion with a magnetic rv3jm7ar 4;qb)*8 euwudc k8u field? With an electric field? Explaiwurba uqu kcm483*8;7rdvj)e n.

A charged particle is moving6 f5- xv)med v3vphf4d in a circle under the influence of a uniform magnetic field. If an elecd5ep )3v4vvffm-6 dhxtric field that 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 magnetic field is the idea behind electromi rwiji)(v -3 /xa*twzagnetic 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) -ix a3)iwi rw(*zj/vt. 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 iv g;rj h:oeqnl*+v*-zs directed toward a horizontal wire carrying a current from lefte vh*lozjvq- rg;+*n: to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fielo npiyy+g8:a6u ) -vjlh ckd: vd0;.pads that surround a moving electric charge.pdolvp v; h:iy )cg8ajyukda-.n6:0+

A charged particle moves in a straight line through a particular )so k(trgw87 n(ri5kd region of space. Could there be a)8(s ir w(kotkn5 r7gd nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflectedjv8ml mm oo lt xnq126l4;xn0* sideways in some region of space, can we conclude, for cert 14ln6xl ojln0tmox; m2*8qvmain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a)zaje-rwru id- p z-x*e/j4r8 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 elec-do,0 h o1ihrztrons in a certain region of space are being deflected by an electric field or by a magneth,o rd-0zoi h1ic field (or by both)?

How can you make a compass wijp*rqe o bb*.m+v5 sv6v,k0crthout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to 703p u:h/fgfy+izj0xw4* *pfjn ae ju each other, but don’t quite t*gy7xf0jpz e0nf:4*fwp+i uu3jh ja/ouch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wih*r) n3z snj/mre, free to move in Earth’s gravitational field, is n* )nzr3m /hsjsuspended 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 unmagnetized piece of ir (i nnoyd(b052tx )mlfon?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if x 9e k n55ushh0j;b:ulone end of the nail is in contact with a magnet, the other end will attract a p;s9 5 kb0:hx jlnuue5haper clip. Explain.

Two ions have the same mass, but one is singly ionize.s( /l0inx,nyl uxfb5d and the other is doubly ionized. How will theif l,iny(0/ nxl.5usbxr positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside 3ffm5-n 7y-uf:tla(wwb 3 a- *qm5 ucfhmx 3ffa 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 sa3n jpj-t:/ oywitch similar 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 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, thejt:p/ on -3ajy starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a.poe( (birk/ f straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform mago .bekpf r((i/netic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetib8vtjtocim a2tj 1o5 9 vg9q1o8f9g (gc force on a 160-m length of straight wire stretched b899 a1fv1 8gcbgogov tm i5 tjqj2to(9etween 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

  Calculate the magnitude of the magnetic force on a 160-m length of straiy.bd5cn4: w wemi(qnyhdm97t :xd ;x;ght wire mcwn xxdn d(w:;.4iqy; :tdhe b7ym95stretched 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 a wire 4.80 m long if the maximum force on it ii,srx y*zh(x3) ru6p eu(u(gk s 0.750 N when placed in a uniformzu3p)y uirhk,us*ex 6 (((x rg 0.0800-T field?    A

  A 1.5-m length of wic*z/5)lw t eiqre carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field maklw c)5qz */teies 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 carr6mb/w1x 7 6 xabvq;ndjying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameterb7m6 b wq1/;6daxnxjv, what is the approximate strength of the magnetic field?    T

  The magnetic force per me8s3hiqe7x)j uter on a wire is measured to be only 35% of its maximum possible value. Sketch the rel jise)u7xh83q ationship of the 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 gb8,p:x3 l.d mvcxp(bis a maximum 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-diametere /lywhg.zv10c zj3l3 copper wire could just “float” horizontally in air .j/zcy3l gwh 03 lez1vbecause of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of c+u0) *lzxr1j uxso (c v5gs(jpharge $q\,=\,+2e$ 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 foo dyr/k6fmps6a. )vf 2rce 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 ch3d3v k 88n s(rhw*t)fnmpv 3wnarge for each diagram shown in (F nnp3kmv(w)83 t8hfvdr3*nwsig. 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 directio 5u-ykn0pz)rp5 s mit+n 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 r 62cs4rl o2el2kbsf 9speed 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-1r tt mzn.do,ou-4k4 zu7 omy enters a 0.20-T field, in a plane perpendicular to the field. What is the radius of itstz ktum4 oou -,dz14y-mn.7ro path?    m

  An electron experiences the greatest fn8,aqgv k1i7r. yvex7orce 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 u)fd dn fs0(jm.ndeflected when passing through perpendicular electric a0m.jdsd ff()nnd magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom who 8.jev5kr o4tose 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 pagxq95 q7-k2j qpgz98kquklla -q, o0rrticle of charge q moving with constant speed 9kq5ga q2l9pkoqqj8 rl7 z-g k- 0,xuqv 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 - y0sa /x0ge 3ymz(hlmurilw+3s+ 7wfuo- 2oupath of radius r in a uniform magnetic field B. Show that its momentum 3xu2suf eol7 yy0aou/r+m (z +wsg-w -l0mh3iis p = qBr .

A particle of mass m and charge q moves in a circular path iih9e d( gxg0q;n a magnetic field B. Show that its kinetic energy is propoxi;h0 ( 9gqgedrtional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the parti:j:r s- kcbgm 2sbh+ +bz)y*ieobkr0* cle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a y.4gdbd k .s 4ypu p(-g(85getre.v fyspeed of 160 m/s perpendicular to the Earth’s magnetic field ou g pyfgvdy-sy4 4erpg . t.e(kd5b.8(f $5.00\times10^{-5}\mathrm{~T}$, 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 i.bt1zouk,3br-v 3m0kbgs2 f 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 x3psw98rx91q5 c uyz pspeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 current. Hbn;r-4cm e e q8u(w )uo)a1 owg6d-gloow strong is the magnetic field 6.0 cm away from it? Compare to the - - ber6moad 8gce;uu)ql)1no(o4wgwEarth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field nobfjm7, wkbp):sf 61 7mi zmqj( larger than that ofi(mq76b1)b:mp mk7j fsfz jw, 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 lonbj 9 jofsse:p a(xf/ q(e;kf6,g straight wire carries current I out of the page toward you. Indicate, with appropriate afjskbsx; f9/oj (eq6(fa e,p:rrows, 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 curren- c e8fpt08tpix7*bvn t exerts an attractive force per unit length ob*ntecfp8 v p8 0x7i-tf $8.8\times10^{-4}\mathrm{~N/m}$ 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 two parallel voc(6h gxew6st3wy76/ w r i2.jimib*wires 35 m long v.h2*3c wjs iieb6 wx/ to67w(yg6rim and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magneti 6hk 8tk86vzjor/ut-r c field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in thro jvktk/h8-tur8 z66e 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-high poles. Wha(:g*2gpho , 5ha sfnmwt is the magnitude of the magnetic field pr o *f(hsgp :w,2nmh5agoduced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents in the same dil g5n,it8yb .nrection. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).5gi,n .l n8tby
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due soutvkrqpl pna8kx q0)b:f) 8-.gdh from a straight vertical wire carrying a 35-A current downward. In what dgda8)-08kbnvpq xl fp).rq:kirection 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 isqrm 3 n22 qpf(-cmc)0v:jn uos the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points norn:qc) jsf-m(2uo0 2nq3mcp vrth but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space ate o3ya7 avdq;9glbr,( l-q f-mdo3f8v 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 tpr rj ,m2r rz:1- *objqnc3jp 49ghzx/wo long straight wires 2.0 cm apart rq2r- 3cp o9h*zpjzm b1n4r:/x,rgjj in terms 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, andt f6+6lp kqw1n 0vn 3o4wx+imt from, an instrument. If the 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 pl3m60 qowwxni+v4+tl61fpnkt ane (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 (Flyh1 947k s:yss+kb dqig. Below), parallel and just to the right. Ifskbsdykl:sh+9y q714 it carries 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 point, v 4gsl7ss) 9kdmnax9s 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 f j15bbg6t8*kw3pj 9osdq ix 7in 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 the net forcdp8 7 jo*639bikxg1bsw5 tf jqe 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, madtk4d mfpdh)m( 2k dg-1e of 2.5-mm-diameter copper wire and parallel to the first, is (k h4t )f m2ddm1dkpg-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 +u7jydpd-mgk 6d8vz 4lar to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midwg7dvzm-up4 dy dj6 8k+ay 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 ago *ug j7o+9awires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s curraajog+u 9o7 g*ent is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 ceg.z9gsq+3 kp m from one another. (Looking along them, they are at three ce +k3gqzg p9.sorners 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 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 direct-r bqqp 3gucgw393bk -qo3*joho k-c1 tkw1a-ion of the magnetic field at the midpooc13k3a t3 qb -phckg9qq*u-kbwwr-3jg- 1o oint of the 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 curren5q mri03 h;ag3;rpiwwts I in the same direction. One wirqpwh ;3r i a;3m5ri0gwe 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 to)c0ch:yk f1o2byrn 3 htal of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside near the 2hc1bnfk3y0ohc :y )rcenter.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to prob)uz)k*nocex:fh +a3duce a field of 0.385 T at its ceuo*zhxn )fc) :3ea+kbnter. How much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is jplr qgd26zxl 6: mzg-j5 u,:/fwsy6a15 cm long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter.,dl :zfa6 -rqz6 lpj:x/2mgsw6gy5 uj This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of cog,c jr;dz+ )jqj++ 4getaal*mv:zu0l pper 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,zmg l*rvu:+qj4+l0a )dc, jj;gae +tz 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 Ampère’s *k8fugem0;w on+5sptlaw along the circular path, showne 8p5gkms0own uf;t+ * 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 jby 9a ,7z- iydgo-/qubetween the conductors of a coaxial cabu z yaiq/-og-j9d,by7 le (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 2au 5r- ybo/qs*2.0 cm on a side is placed with its face parallel to the magnetic field between the pole piecb/syr*-ua5 qo es 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 deflectsp x ) .yk7s1b(lmrum0i full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens bni 3ab2gbgkodro. 9zzc5* ( +py 25% over the years, what current will give full-scale deflection if it o i(z.+2 an5o 3dbgogpkcbz* 9rriginally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what :ymu mi-bilh or/ 9;m8e 1:scefactor does the output torque cha-:mi bmyr e eo8c1hmil/9;:usnge?

Show that the magnetic dipole moment M of an electron orbiting the prgiv(4 ; xom(yyc1h2z73ymnz voton nucleus of a2 v;v1(z3yycm( o gm nzh4i7yx hydrogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm i6kv1ke7oh8 ep)k grxo674 z atn diameter and containing nine loops lies flat on the ground. The Earth’s magnetic field at this lah) k4k rpgz7 okv7 t6xoe861eocation 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 fiel3 rtcun2;zx1fd. What value of electric field cou1 fu t2cnxr3z;ld make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, geruarg e .al6x5;x2)zfzmanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotou5ral62z xxg; .)zfaepes?

  Suppose the electric field between the electric plates in the mass spectvj1:*ss nqn qvb:alf+k g)q/1;x :rvb rometer of (Fig. B+:kr x bjqsn1lvqg/:a;)*v v:f1qnsb elow) 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 pollutants. It is difficlt+ 8ap1g qc;qult, howevgq+ca;t1 p q8ler, 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 accelerates ions by a voltage Vt 6e.,mq ohp1e before they enter a magnetic field B. The ions are assumed to start from rest. et hqm1p6e.o,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 currennvjg5 vqruijqf874h 9 z1y9we3ne/ n;t flows through the wire. If the permeabilii8rnn 1e9;4vezuq 57qf/n ywgjj9 h3vty of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is/*hs)e oc*vcuy2ub5k 0rg q-s(8 hv xb 38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field insideq5 s cuyv)8g/s*0h*-cb rkhx2u v(eob 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 momentump:6+gh k1z.* pufyuvw $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 sam1xoz g,ct qn9:e kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii x9:z1tgc n, qoof their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizq5 fc5 -mqdyp)ontal current of 3p55fm-d )cqyq30 A toward 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 has acquired a n/r7uradw5-* n )zhi qjn 7pe-qet 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 horizontal g.qn9 jd2gcs9t u8kr7s:g/trly to the north and has magnitudckt j tg:u29d. sg9gn8/7 sqrre $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mass is z5 jfd(1gd iy(v-d( wjz56 oj2hb*xp n$6.6\times10^{-27}\mathrm{~kg},$ 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 4th(c wh 5: 80otonlywwtu: e+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 perpendicular to the pla4h+ y(c wo:u h0 n8wt5lowt:tene 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 xx3.xf kd(k:pis 1.00-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 w:.k(xf xk3pdx ires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apartjo 8)o(vd ,aysefzhbl b;9km3w6p 4m) in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Bel,dwpo lb39h(ebo ;af) )kj sv8mm64zyow). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron beam near the ce6b-j ypjg:-wh q gingth-)qk2q-5xy: nterk5t:qgjx2ig 6-y:nyqw-- -bh qg)ph j of a TV 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 dev,f2l glkx:dt(c 7hr;j ice used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in thlx7k( jcrf2 h;: ldtg,e magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of a square of nrs h8/r(3mi jynn,wc3nim(, side l, carry equ3rcry/ ijw8nmi(nn, s ,(hmn3 al 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 foie;2tm *q 7oa ,0/se/5cjrbzb.mc gc fr “beam steering”; that is, the magnetic fields can be used to change the beam’ fibe.g s5cqj; otc/recz, m/20m*7abs 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 wis4,su jp6 5b:rkhwzue(3e wm .re carrying a current u( wwjzesks:uh46me .pb3 5r,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 magnetic fieltc6-(y,.hcjo*hco w 1um vh;hd 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 theuulu roo92(1b.phj) fm0z.rn 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 or)ounl. h b0up.1 9u rmz(2fj10 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/bcf(g2pw f 6h would make a beam of electrons, traveling to the right at a sf2wbcf g /(p6hpeed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0.010 T, p if-(0tqf1t9yryu3zt z y6dh 0erpendicular 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 t(ftht3fzrq -iy0uy t01z 9dy6he change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.- nl1 jywd-.we8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A,nw-ed j-. ly1w how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm,:t-z mcn l6z(b 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 an angle ofn(bmzl:c 6 zt- 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform maylv, mv7u 5ud0gnetic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$