A compass needle is not always bali7ec kew : 16pg,ndlh4anced parallel to the Earth’s surface, but one end may inekgw:d7e6l p 14, chdip downward. Explain.

Draw the magnetic field lines ar7g4bf :1+- c zeepect8(kv .+x dlerlsound a straight section of wire carrying a current horizt.+rg-14e: cz b8pee l(fsxl kevd+c7ontally to the left.

In what direction are the ma mj:iw6t9(sq xz*jts8gnetic field lines surrounding a straight wire carrying a current that is moving directly awa mz:j9tq(s*8w6sti xjy from you?

A horseshoe magnet is held vertically with the k8sql4, 8 jjw 6w4hpzbnorth pole on the left and south pole on tb8 sl44jp6k, jw q8whzhe 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 wire?

Will a magnet attract any metallic object, or only those made ohxzbclw :a -a4f38ruur,pud2q ) +o(qf iron? (Try it and see.) Why is to+qhrf8 lxuuda2z3- , 4rw ( qcbp:au)his so?

Two iron bars attract eac+1r91h mwwxkj8 :lzjc h other no matter which ends are placed close together. A9mlr j h cw8zkx1w+j:1re both magnets? Explain.

The magnetic field due to current in wires in your home cannzdhgakcu214 n+)vbxe ) *m sy/qd4q4 affect a compass. Discuss the effect in terms of currents, including if they a4 d+ 4qs 412hm g*y)d /cuz)kbnavxqnere ac or dc.

If a negatively charged particle enters a re+yvn znko:i,9gion of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or +voni 9yk:n,zstay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a cn) 00c *zdmci9mlomf3 urrent-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 pa m)ic m0zcfl30*9nd morticles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c,/vs0;9/um: p ;oyniufs c +fxj enter a magnetic field as shown in Fig. 20–46. What can you+xfuj s; pi 90u;ovym/n /f:cs say about the charge on each particle?

A positively charged particle in a nonuniform ma:. )x*hb nx1e6fn hwuhvg)t6m gnetic field follows the trajectorh)umht6 *xvfwhg 6nx1e). n b:y shown 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 attryz-j rz /xh.p*act a magnet? Can a magnet attract an iron rod? What must you consider pjxhzr* .z-y/to answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10)qru 3 )m09yihx 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 r)9 yh0i3m quxby trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but the pwc h5zuq(u 9:third is not. How would you determine which two are the magnets without using any additional pzqu9u: 5wc (hobjects?

Can you set a resting electron into motion with a magnetic field? With an elect* :in3au,gqi ere*niua: q3ig,ic field? Explain.

A charged particle is moving in a circle ( ;751 powa7tjmdnd tuunder the influence of a uniform magnetic field. If an electricpn; mddtuwt a1jo5( 77 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 n9 .23wijvz 91+o he5bmdestk field is the idea behind electromagnetic pumping. It is used teh 3z.n k99j5s +ob1mvdetwi2 o 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 positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a hoeoh8l, r;k p xcvg5isx /yuuv90;m+(xrizontal wire carrying a current from lecu0x mvx;9h ,r5vuxogi/+ 8lye;s pk (ft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/oe+c8h30lwm u gk4 )(rvkf zf8rr magnetic fields that surround a moving electric charge.)f+ce (mwrvzfh url 48g830 kk

A charged particle mv br;gx q0-5zsoves in a straight line through a particular region of space. Covgz5b-r x0 s;quld there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some rfx/4a z (uhxxz9.l91vod swv3egion of space, can we conclx 1fw (vdhzv/9a xxu4zos.l93ude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniformi f 01ofx06lek magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain region of spa u6q zgx3.bq9h 6fzph8ce are being deflected by an electric field or .3qfgb9qz x6hu8 6pzhby a magnetic field (or by both)?

How can you make a compassj9v*oh j;ldnb i47-lu without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at rifmj5lt1o bo ,*xquhutx(1 m3yca1+* p ght angles to each other, but don’t quite touch. Describe the magnetic force one exerts uy,x p+m h3a (11t*bco ltm1jxou*qf5on the other.

A horizontal current-carrying wire, free to move in Ey9lh1c b-vr+9)i5 y b.3gphpgvs dmn-3x 8 bjsarth’s gravitational field, is suspended directly above a second, parallel,rdyh +g318 s9-hgyn vpb .j35i lscv-mx9)bpb 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 oeo3y0e; wgka-f a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an 2k: r3rx.s77ih-kw o;owbjigunmagnetized paper clip. However, if one end of the nail is in contact wit s r-7oh3k7:wo.gbiw jx;rki2h a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionize l8j r9 *ruo;y4b1g*lova8kyl d and the other is doubly ionized. How will thu* 4l yy9rkj8abo1rgl*l;vo8 eir positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on Bpl r1,kr0iu ;a inside 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 sv d*.li doau g()3;5.oub nksis an electromagnet (the iron rod udlg d nkai5oos..*3;s v)b u(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 the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the fodli s bk,ctt* a8518omrce per meter of length on a straight wire carrying an 8.40-A current when perpendi5tldmi os8bc at,k8* 1cular 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 length 1.q9pjec mix4vq6rr0n9i o m/of straight wire stretched between two towers carryin.6nom9v/9r0xei mpjqq4 r1 icg 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 pnre73i)yv /c3fud6,r.y. ir bw3rojof straight wire stretched between two towers carrying a 150-A current. The Earthiv yf .b337ne,crpidr ow. r6/3 y)ujr’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 o;,j 7rbq y5 ch)svsb*7yf uvd0n it is 0.)uf 7y7bd; q*s,j vrsyvb5ch0 750 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 mby ge2oz*hb s.t, ha))+ztz8 A of current is oriented horizontally. At that point on the Earth’s surface, the dip )za8, thg bmbh2 zo.s y)ze+*tangle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum ti0kf* 2m2aaz of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strengta i202tm*fzkah of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be7 jy bsau5:o8c only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship a7:oy 85ajusc bs it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximuxys6s9xi )1 tom of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “float” horio56mh7naundxm-b p a722p z5 kzontally in air because of the force due to the Ez7p h ak-a5 xdnpb2mo52n6u 7marth’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 gk7-71b nyglu $q\,=\,+2e$ 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 an8ew lp)f z8 anqxfjw,9r8 zb2)d direction 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 t46 x2q 4wmikbhhe force on a negative charge for each diagram shown in (Fig. Beqbkm 46hix4 2wlow), where $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direction.vf60r: pkzwa 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 w7p j8gvtf3dx n1zqg *39oz me/ith 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-Tzkx06lk8n6 ny field, in a plane perpendicular to the field. x8z nkn606 lkyWhat is the radius of its path?    m

  An electron experiences the greajw: m+(kijx7rj8qjy,9 fr p4btest 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 thdf x m2zyj+.3dat go undeflected when passing throughj+fd .dy2z 3xm perpendicular electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium ato phvae(+n500ivne5k + 0wwpm mag9:i vm 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 required for a particle of charge q movin-zb;q0sem w, mg with constant speed v to ma,;qem-wbzs m0 ke 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 i7al/cg5 q53odxrm :b jn a circular path of radius r in a uniform magnetic field B. Show tmdqo r/j:x3 cglb57a5hat its momentum is p = qBr .

A particle of mass m and charge q moves in a circular po+ 20pj-d8r jg+qflg aath in a magnetic field B. Show that its kinelfr8 20+dj -ogpqjga +tic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentuj;gbtbtx+g / z;rrh2) m 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 + uenye)il 8f)5h uri0wggr1 f4/m:xdm/s perpendicular to the Earth’s magneticu )euir/ygdf0nei1 w85f: r+xg4 lh) m 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 magj+ga2 ke q6/)iqx sbb.nitude $0.40\times10^{-4}\mathrm{~Т}$ 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 speedl aep4hvz 1ft6, nqa9* $\nu=2.0\times10^5\mathrm{~m/s}$ 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.q+w ) bjbs,v/ e)jwkw1 How strong is the magnetic field 6.0 cejjw,1wk)/qb)+ vswbm 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 allowela3+-t0f g+jv vstvl4d to produce a magnetic field no larger than that of the Earth atl+lfsgv3 t+v4v -0j $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries currentpa wpqbdeyi -(k-hwd35*6bo 9 I out of the page toward you. Indicate, wit kp(6h beiwd pa-dy*9 q5bwo-3h 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 ur 84z-gfzx*sp pward 24-A current exerts an attractive force pepxzgrz- s 8f4*r unit length of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the force between two parallel wires 8x10r /qh 9w:thkupz9dvwwm dy9t1 8u 0d2tyl 35 m long and 6.0 cm apart, each 9 /rp9tuq 0dhh82 wd ltwdvy9:ktm z8uwx y101carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic s0zmabkx0:+ kfield is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cabl: +ax0sk bzm0ke 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 polesuy6f/ i 5rc,rqs- i9aw07uabj. What is the magnitude of the magnetic field produced by this wire at thes,7/i9 -q 6rcjbuy0 fwua5ia r 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 pe-qneon8 (.4r h2m 8 erf0nbfsame direction. Determine the magnetic field at mrp-fn.fn0 e4o ( e2hbqn8r8e point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass ipe z fkqs,x8t/sw/g9.s placed 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the .ke9s8g/qt/xp,zsw fEarth’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 n9p do.iaab 3c1et magnetic field 20.0 cm due west of the wire if the Earoi 9c. ad1p3bath’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons pasje*s,sg m*d: fses 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 midway between two long straight wires 2.0 cm a .eie7ju1eik,qem) /kpart in terms of the current I in one when the other carriuk eem7ei)k.j e1qi,/es 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conduo4 tb94jp lr4hcts 25.0 A of dc current to, and 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 midpoi494pr4obj h tlnt, 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 9jk:u 5bk7zu zplane of the two wires shown in (Fig. Below), parallel and just to the right. If 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 z5 :zbkuuk9j7nearest 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 23x /7xh5.kbq6qi3b rkw $^{\circ}\,$ 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 wire, as shownn0s 24+ vz2(0 dwryet/oyycd q in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and directio0dysyc2dz/we2 (yrv +q0o4 nt n 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 Adg.65p x1dd4lbx:d y uv.ts 0mq0:mxc5d vrh *. A second wire, made of 2.5-mm-t.dv qd56vus:x rg 0l0bdxd .:mxy5p* cd41 mhdiameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perlw,3, 66 ox+ow,sflmlsdca9t pendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetx om+,swsa ,3tcd ow66l,l9lf ic 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 carrir dcsi,m+m-s3k:9ahybcgl6 6es 2.0 A current. Wire B’s current is 4.0 A in the same direcsbm s g, rk+36h96:-cdlm iayction.
(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 ar vm 3w5zm/xc3ctmmqa58);ys te 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each w)smcc /y x q5z3m3m5t a8;tvmwire 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 direc6-bfs ikqjz6j*6-jn ution of the magnetic field at the midpoint of the side of the trianglej-6sq6bn z iu f-k6j*j 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 I in the3zwxea )po-n4.j7n q f same directio4)o nqwa. fenp7-xz 3jn. 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 t eqz7y)ghd,t+jc + 6xhotal of 420 turns of wire and carries a current of 2.0 A. Calcc+hqtj+hz) y7 ex,dg6ulate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solen55px o/nurvrsup0,7 ot9ua* qoid 1.25 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carr5o rpusqxa7 *p59utu0o /, nvry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long.yuy3hl q92 (wnz;xh) e The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this yhylx() ; 29ue qn3hwzwire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want tob( avo v.8oou5 make a practical solenoid that produces the greatest possible magnetic field for a given voltage v85v.o(bao uo. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shapepo7d2+qksc;b y 23c7i3h rfn)ybg0g g of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Belo n+7fkhc)r3c7bpgys g2by3o;i g d 20qw 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 magnegxoim* . ykzclvv2u.b(v8f1b- 8(xostic field between the conductors of a coaxial cable (Fig. Bely b1go*.m.zc2 sliu88o (vf(v x- bvxkow) 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 o)hjkmp(+ a t:m:c.ion 42rlvq n a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 Ahjo.q )tm2 i4+r m:lkca(np v: flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale forzwhl0-szhn*hgak . :k 24swp1 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 galsoeb6*d m0*j ws6u87)eea kvtvanometer weakens by 25% over the years, what current will give full-scale deflection if it origi0o6jee) k 8etams6d u*vw7b*s nally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torque ch 7:l7nff7 lcww77f nwfl7:wl cange?

Show that the magnetic dipole moment M of an electron orbiting the protyvf; pi-tx30 mon nucleus of a hydrogen atom is related to the yfix3;tvp0- morbital 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 oncsg n2 pqt 2 ;u)jgbnnls6x),: the ground. The Eart xtbg;n6)q),jlc 2u p2gnnss:h’s magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic to0 d)cz(gnuwurw w8 +18-bw d-p3ieifield. What value of electric field could make their paths straight? In whzb+n o wpgdtrewi-)u(c 8d-wiu1083w at direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal to 7i *f:loaqze )21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic 7)o:q ea*l zifmass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectromete2hlvu5x )i (k6w4nrtdq8hz u 5r of (h iuk lh5xt vq5(d8w2rn46)zu Fig. 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 pollutants. It is difficult, yrxkri8z()4nv hz*u7chjm (9 however, to separate molecules with nearly equal mass such as CO (28.0106 u) ah 4 () mkh*x(ri7zu8 jcz9rnvynd $N_2(28.0134u)$. 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 acceleratf,;ur d-h -v i ltkm4gfsk3kjh, ne:(9es ions by a voltage V before they enter a magnetic field B. The ions are assu3jkih4tv-;kse9ldm ,:ff -,u ( krghnmed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops ofgyfrdh6n glvf o ),0r87/ xrr9 wire per meter, and a 25-A current flows through the wire. If the permear)h8r, /7vydgxr 6nog9f r0lf bility of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm lo9 -t a2dyo;k(irp)ow ang and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 - wyk9o(ad2po)tr ai; 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 ;rrvg5,/vb k clq7:jk $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kimfl,nzm:* k7 igf ji9 q7tep1.an5,lt netic energy upon entering a region of constant magnetic field.n:nflkt7ig tfm5iz7pl* 9je 1a,m., q What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal q /: pql6pq 1m;e1a:wrr jsqi5current of 330 A toward the east. er ;/q::15miqlrqwj p 1pa6sq 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 wh:/ywdueeami d qy.6.07x cm -uich 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-, rvc39lo tc8 eayuiq,7a6it points almost horizontally to the north a6t 3ile a8-uv9y7 ,rt,ic aoqcnd has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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, whose3 q r3,u0i2evgljd6gc mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shownq,b2n1bf0 xy 4zzq xzjw*(1ph 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 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 currebx2z411qpqhw * z x (z,fn0ybjnt 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 co ;5abe;q;hdojpper wire and is suspended in air due to the two magnetic forces from ;j a5;ebq;hd othe bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act as railsjl( uediawte fen*45sy2u0,6-1r a fp to support a lw6leerj5(4e-i sa2 ,nuapdu*t 1fy0 fight metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximatjdzyr p;yy .65, )5ck cot*vvue maximum deflection of the electron beam near the center of a TV screen due to the Earth’s rk zv) c tu,.y;yd*oj6p c5yv5$5.0\times10^{-5}\mathrm{~T}$ 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 elementarm v1k91 syxd(qy particles such as protons to high speeds. Particles starting md1 91kqs(xy vat point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap 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, locatedh6wv/-kl+ iyf at the corners of a square of side l, wlkihy-v /f +6carry equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beam stee bcmr16kyp(v+ring”; 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 ext+ kpb rc6m(1yvends 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 coilo) - e09b4 di7rqz4 ,1fb3h zpbscobpy of wire carrying a current I (as in Fig. Below) is 4r 1h7oq 3fbc0z4pe,)bb b y -id9sozp
$B=\frac{\mu_{0} N I}{2 r},$
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 pole6ou on-bwvou tbwi4r8ak/-p8h h6p)/s the 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 t (j*+xxha z3 tq j(g;wug(:uxnhe 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 th;gajuxx3j *u(g zxq+wh:((t ne 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 would make a beam of electrons, traveling to q0geo4njy:,mn /( sakakaw; a+s -.gv the right at a speed0k/v(j4+g: yanna.qsgma , e kwa-s ;o 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 spir zwh s v).s,,wdyj9 ,m,iyag(gal path through a gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Cala yhi .,g,yw)zs(,vjws gdm, 9culate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to producci puui g.ld68*qz 5qw50u7- zw ;tglde a 0.30-T magnetic field at its center. If the maxim u.d6it*u 7ipg u55 w0wldq;- 8clzgqzum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, sn4th evy:/zich00q ) 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 stringst/zhy necqv si)00:h4 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 e b:vfyufb3/t(2uv.wbbr-n -6 8ktpd = 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$