A compass needle is not always balanced parallel to the Earth’s su, /;yqmmguc1 g:mp2+kp qe4y jrface, but onem2y uejg,mq+g4:/ ppq mk;y1c end may dip downward. Explain.

Draw the magnetic field lines around a straight section of wire carr*9 bw8a pzglghs -85tzying a current horizontally to the leftlt9hz a z ws5-pg*b8g8.

In what direction are the m odg0**9-w;cbjg+ +urdvs szsagnetic field lines surrounding a straight wire carrying a current that is z-d* gbwug9;*d0soj+ +src sv moving directly away from you?

A horseshoe magnet is held vertically with the north i2bu- s* a** ipdsry.spole on the left and south pole on the rightsd*i ay2ps* ui*.-bs r. 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 metay aywuft42-7cllic object, or only those made of iron? (Try it and see.) Why is thit-y4fu2 wyc 7as so?

Two iron bars attract each otherr xx2dm:ksi-.w vf)b3 no matter which ends are placed close together. Are both magnets? Exfb)-i wm2xksx:v.r3 dplain.

The magnetic field dues7.(tuljtwe j+rdto. anm5s+ l)ma:* to current in wires in your home can affect a compass. Di n .o ams(j 5+swda e.:t*tlmjltu7r)+scuss the effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uxp e d2 +5n)l-jhmj6ncniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic enpmcxdn-n6 2jj + )hle5ergy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in thohmpry 88 9mwz:8wj:ve vicinity of a current-carrying wire. Formwv8mowypj:zh8 89 r: 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 produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 32cl -lrhn6-u (lf ksf20–46. What can you say about the charges( ulh6lf-fr k-3 nl2c on each particle?

A positively charged particle in a nonuniform magnetic f:7r9* zbt;a,dj fsa5w /p7b m.cmgvbtield follows the trajectfv77 tbagb.mp9/;bsrcdj,* m5: z watory 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 attract a magnet? Can a magnet attract mrt : 3pn 4cr5rfaia*f2pf5vxbe1r*) an iron rod? What must you consider to answer the2xfrp mvft4inp3 )c5r:aeb* *1afr r5se questions?

Explain why a strong magnewynj60 zf2,*ea14koxpn b2v n t held near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest.2xeno*w40 fvj a, np6ky2bzn1 [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 three iron rods, twii(mkg0+ n 1dio of which are magnetized but the third is not. How would you determine which two +gkiimi n(01 dare the magnets without using any additional objects?

Can you set a resting electron into motion 3g0v-e dj/p qqwith a magnetic field? With an electric field? Expl3gj-edq p q/0vain.

A charged particle is moving in a circle und9 fw1;8m.jsm2ksb dlier the influence of a uniform magnetic 8j1bf2km9 m;sw li.s dfield. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electrxpr/b,a(o39z ww,dhfgyx 03 (,lfg uz omagnetic 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 perpx gpffg ,3b h/ da,yz0u3w( ,zrlw(9oxendicular 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 horizontal wire carryfsx gnfq-z 8t 1c.9/cq*gr+fbing a current from left tors.-qg1fcn8f tz*g/bc q 9fx+ right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields cescv.5/kl2/ p u guh5that surround a moving electric charge.v cp/ g/hkc5l.2su eu5

A charged particle moves in jmf0q ix- kj;5a straight line through a particular region of space. Coujixkjf q0m-;5ld 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 8u,zjg5 u aa +hzxvi ryug);3-bvnz9;region of space, can we conclude, fo vz-uua)g8z3x9r5unzg,y+ ;ib v;ahjr certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space therj-ee pns7jo c6zvw, 4* qmx7fxcu82g0 e is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in ao ftz0hans/et,-ium9: 8 + lvf certain region of space are being deflected by an electric field or by a magnetic field (or by both)?z0 e:m,vn9/+ia lh usto-f8t f

How can you make a compass without usixxqyytyfy--h(, +uf - ng iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to each.v7s;7xcb a:b moh ,ue other, but don am 7hbx.:cv oe;b,su7’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move iqe; 6pfi9y/pj0v(pm d n Earth’s gravitational field, is suspended directly above a second, parallem / y(p dep6q9;iv0fpjl, 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;in dn8 emum/gba; t,9 a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Howev) d.d .lutfqg 4scad2usu2,p 3er, if one end of the nail is in contact with a magnet, the other end will attract a paper c ud upul3g4)2.ss2tf,q da.d clip. Explain.

Two ions have the same mass, but one is singly ionized and the other 42p zhk -:etwhkki*l+is doubly ionized. How will their positions on the film of a mass spectrometer (Figk phh:k +kl2etw*4i-z. Below) differ?

What would be the effect on B inside a long solenoid pyj0l;+ m5vyf:tlx , cif
(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 ..u* 6vdpj rkk. A relay is an electromagnet (the iron rod insid.uj rv6.*kpk de 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 force per meter of lengthzu4mxp6 l h6ph heiz* 2e4f;+z on a straight wire carrying an 8.40-A currexeemh4z62p+u 6; zlhizhp*f4nt when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of s pcdko4r1u5d11*es2c f dlj- etraight wire stretched between two 1241r s5edujdk* f eod-cl1cp 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 ahu2zlk5 (8woo1 sd bu- 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field (zsu85-blk odu 1ow h2of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a kz9v 03j70gdofy pez3 wire 4.80 m long if the maximum force on it is 0.750 N when placed9yj fgv z00ez3o p73kd in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4h534+zfn cbgu 2ct9 tf.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnecuf fz9 bctg24t5 +nh3tic 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 carryifha:r;:n vv w c9hy1aemnn -q7;0uz0nng 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If y::w7vnm fcu0a rae0n;v9zh -h;1nq n the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on at,-ccrq r*j:zd; / aif wire is measured to be 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 as it actually is, calculat /rrqj:c tcizd f-*;,aing the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire isyy d*/ c i /urbmy*x3a9t5zgl( 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-diameter copper wire could just “float” horizont-c n4-rx 4se)qk:xdec ally in air because of dxn:-kc4 4 exq-srec )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 charszdo9,/aiq( z 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 o+et /ft7hc, i7oef )b.*z8myb/kl 40wectcm and 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 the force on a negatisd1 nca34u ,drve charge for each diagram shown in (Fi,n13 c rduads4g. 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 directiondxqaer g 4)+7l 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 ves/ bp5mkqwpib( 8 -nv 5y-jb2hrtically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plane perpen 2qj/t) z/rv -/*wfq0x-p f t:kdzpbjudicular to the field. What is the radius of i0p-zb wvk-q/*2/ftr: t f)jjz/upq xd ts path?    m

  An electron experiences the grea,vcnjo11nbz 2pqgw5 ; -er v)etest 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 undeflected when passing thkr3g+u 5ntf 0y(7w1d7ug qcvlrough perpendicular electric and magnetic fielgg+7fnylukt7v30 r(w5d cu q1 ds 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 whose mass isz2pho v :i0jvp((dca 1 $6.6 \times10^{-27 }\;kg$ 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 moa51qo4 c2yfz ooe4(bh ving with constant speed v to make one ci45f4yc1 ohoqez2oba (rcular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radiusepoq5kft5,avo v6w4: a .n/sv r in a uniform magnetic field B. Show that its momentum is p aq:o,4ve6 /5tn vsok.v5fawp = qBr .

A particle of mass m and charge q mrm um) l:nq3vhd+u3 4roves in a circular path in a magnetic field B. Sluvmh+)d4 3u mqrr3 :nhow that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem 21 is uh ,;jkl3wp.mj y+4,i+ bpubb$L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earthksc:e 9m 4swu9’s magnetic fielm :9esw4cuk9sd 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 fieldch8fmynru f d4n 0l0c(e a:y*7 at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with speedmeq 3uofnbq4 3w,p.jg*rk: e 3 $\nu=2.0\times10^5\mathrm{~m/s}$ 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 stalle20/fw44:bmqhlayjv ud vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? lwq02vaf/bu44jm h :y 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 al4 qe4o8yx oc5+eb,kqwlowed to produce a magnetic field no larger than that of the +4oewq45k,o cqy e8xbEarth $(0.55\times10^{-4}\mathrm{~Т})$ 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 towd)-wxi5eh7a 0m k6muzh j kl7qmv(v--ard you. Indicate, wdh0 -mi -7qjmek(k u-vv xmz 6aw)5hl7ith 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 exerts an att/+ckczurf(t996 c8fxxlx t 5fractive force per uncu8f5t tkr(zc/ xf+ f l9x69xcit 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 4)d:gxy1zf :xv j0 blwbetween two parallel wires 35 m long and 6.0 cm apart, eawzglb):jf :dv4 yxx 10ch carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field ienw9mskxwhn.2)ky 16 s being carried out 1.00 m from an el 912xmw )es.kh6kynnw ectric cable. What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A,6w xtgi3d:on 7lw ,huj6)eh ;(lqssr along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of 76i ,elr: uh,w)q6gnlod(s hx3tjws; 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 th2bc.xa xt5idecn3n/:e same direction. Determine the magnetic field at pointd 5tn2iaxccbxn /3e.: P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south fo sfa/g .v(z/jrom a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal componen. vzjo/( gsaf/t 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 ol-u61: 9e atuxy bvvtd+o0hb)f current due north. What is the net magnetic field 20.0 cm due west of the wire if the E ubhe)b9axly0 6- +ttv:1odvuarth’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 m/z))jwag5- gmd:phxpasses 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 -7a*x xqz 9y7bn)axkh wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currents ar7*-azxbn xyk a 79xq)he
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, an instrument. ju50d ty pi*x2If the insulated wires are of negligible diameter but are 2.8 mm apart, whapd*u 2jy it5x0t is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the r8rcn )knxp+ah 87 1egjc8t9x(ztr w/plane 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 eachrrc1hrn t +9)c8 (g7tjwa nkze p8x/x8 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+;aosn lph7p 1u8rht 2s 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straigh 4 pd,qf; :rk2l2ynnwpt wire, as shown in (Fig. Below). There is a current of 2.5 4 df 2;rl wp:n,n2kpqyA in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current *2qivx 4n whu;hd)0ns of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is* n0nvhwhsq;4 idu) x2 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 pkc 5 7(nsoeu4(cb 9r2aufws0berpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below)( 9ssf(una cw7o2b c5r4ub0ke . 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 the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A car y1wx7awqn+cnt- gf5+ries 2.0 A current. Wire B’s current is 4.0ny1wn +gwq-ac7 xt5 +f A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking along themh0p,pb))mh h d, 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 (dh0hb,h)pm ) pFig. 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 direction of w., 9so hj8b9d f4hsm2-rrivsthe magnetic field at the midpoint of the side of the triangle between w8hir2v-sdws99o hmf4s. rj, bire 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 the sk u 0:nnljw;s1ame direction. One wire is at x = 0, the other is at x = d, 1u 0kj;l:swnn(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 tur9krqcxwm-ibh:5)nk .t 0-a qhns of wire and carries a current of 2.0 A. Calcunh-hkm x-bw tq95)q a. 0:ckirlate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to qc q21or4g *mmproduce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of them*1q 4cm2rqg o wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long stz g,tg+o7y) t7uimw b1raight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A currenty7 itmz,gbtw1ug7)o+ downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper 6mk:qka b9sc 8i3o,g6xp6g jband 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, such ag6,sa9bog6 p xk3:qci6 8jmbk s solenoid diameter, length, and so on.

A toroid is a solenoid v7 v4pg4yk-qgzyg4u1 in the shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that qvkp 1-zgyu4 ggv47y4the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the condu-mj qi1bp:yk 9ctors of a coaxial cable (Fig. Below)mj iqyk19-bp: is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed with its face paralleldau- dgq0- qayzh,w9: to the magnetic field between the pole pieces of a large mgyqdz0 qwh ad, 9:--uaagnet. 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 deflectsmecu4 367lfd7g ucezi pd e:*: 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 by e7vgzxd(;z5y vhp6yr dsx*,7 25% over the years, what curr;yz,exgv( dy5xp776rz dv s*hent will give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does (9 aiea5 dqqz*the output torque chaa5q *iez a(dq9nge?

Show that the magnetic dipole momeztgd (jb1 o-)4:3+g tuhjdp lint M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angulhd):pb (1utzjjl3g-i +otdg4ar momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter a yqxicp +,cfij*sp +9)nd containing nine loops lies flat on the ground. The Earth’s magnetic field ,qy*9ps c+cxi+)ijfpat 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 0.5664y+ry2v3 lf j: tb ;ftnw2hz*hkqxewv 1d-5,r -T magnetic field. What value of electric field could make their paths straight? In what dirj v5r+bk32 1: y-,*x de4hlvzf wq2fnyt wtr;hection must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium at9vkd( +8m6 +vvyjrbckoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. Th(+mky+ k6 9bdrvcv8jv e largest radius corresponds 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 3nd54 gs,p pexspectrometer of (Fig. Bel, dn xgp4e5p3sow) 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, dst ehq;)2wkwnt*-cg8s/; 8hmz;buj however, to separate molecules with nearly equal mass such as ;dhmn) ;8h-scbt/28ug; e*wstkw jqz 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 m )1j/wnolcm k524g auvoltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that 4nk 1mj wa)25 lcug/omthe 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 cu9 hu5:)xgb ( (bx lvbia7c ahnsf) k4-a3fhku:rrent flows through fa-xn:gulcbufa )4hh k9a7 :b( h)i(vx 3b5ksthe wire. If the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, ande3qf:iu qh 9 j 44yu0.av1eadjw;n41 pvd)wxv 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 permeabil pyevdwj4ja 9;n1 di xahufu43wv )0.v:14qqeity $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum l/ :ptlh u31fdo:0jc l$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon entering a region * k5zv im)e:ivof constant magnetic field. What is the ratio of the radii of their circular p*i k:v5)zeivmaths?   

  The power cable for an electric trp +8 hihltww qvjjiswy; 211t1 s)*zb5olley (Fig. Below) carries a horizontal curren1 i1w pqsv j;b2t+jzsw 8t 5yil1)*hhwt of 330 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 nvavddk ,w1 erl-: dk;4et 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 m4v1 s49v vy r(x2jhjcnagnetic field points almost horizontally to the north 1(vj4j4svhyr cv2n9x and 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 atomh+ lbb:obiw+g7 zk-af;9 -ssd , whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is show:)bdsy6a 78oh4uuj z jn 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 ra6h y:us 4u)d 7jjozab8ils. 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 tm6h1gkvlm4; f h lu/a/op wire is 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 botto /lh4kml;/ 1mgfh v6uam 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 raiy/egpv 0)o-iz e(fz -0nfjt9cls to support a light metal rod of mas/ j fzv tcg-)y0eef(09nop-izs 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 approximate maximum deflection of the electron beam neadhxu xros.)7:3 *kkfy9gm) c sr the center of a TV screen kk) r fcsgd3m:.*x)9o yx7husdue 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) 9ohz8b n)fbl0 is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocityo89h) bn 0flbz 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, located at the corners of a square5ic lpybz. .+w8,1z )jxp )yzd6s mfjc of side l, carry equalwdb)xz.f1czm8 )ls +z,pyjip5j c .6y 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 forac/ e7c.dv 6+xeyk 3sv “beam 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 angle will a 7 avvs /3e.6+x yedcckbeam 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 5ocga*zj k(eg,,b gr9ly; 8ay wire carrying a current Ioej5,a(k gr;z*g c y 8by9ga,l (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 fv 0y 3d-8*yovy,p:s ujsu:fg 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 the magnitude of magnetic fields produced by overhead.m4i6mb *lci17sqqap power linesipm ms.a*qq6 14lbc7i. 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 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 mag3my,-w.1b ,zf c8rvp ub+aiq snetic field would make a beam of electrons, traveling to the right,1-ayswbrimf3 z8qc+., upb v at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0.01t f /rg*i-j+ kafnq*c4owz.m)0 T, perpendicular to the plane of the spiral, as shown in (Fig+o- * )c4qt/*jgraiz.nmkf w f. 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 P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0dgh.fk8rq( 8j.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the r f .gdqh8k(j8solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.5a6i8p:h0 anzi0 mm, carry the same current but in opposite directions. They are suspend8a:za ph 6ni0ied 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 kqtia7lzz5; p/ 2+zan2ulgb1magnetic 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$