A compass needle is not always balanced parallel to the Earth’s surfacmy-(b wk. /cndqym-0se, but one end may dip 0yw n(-m/bk.sc -d myqdownward. Explain.

Draw the magnetic field lines around a straight section of wire carryinga;:mee,1w o m2;yohjsq mu8(r a current horizontaw;m,2 m:muh1qrj( oo ee8s;yally to the left.

In what direction arhim2fsr k0i h83hp8f8 e the magnetic field lines surrounding a straight wire carrying a curr2 888p0imh 3hikfhfsrent that is moving directly away from you?

A horseshoe magnet is held os ch(*jlob 7/vertically with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the csbh7o(loj*/ wire?

Will a magnet attract any metallic object, or only those made of iron? (Trymy-c2 c8k :dlm it and see.) Why ic mlm8 d2-ykc:s this so?

Two iron bars attract each other no matter which ends: v)k .jiib;.*s/eicajs: y usj*;ppg are placed close together. Are both magnets? Explain..pba; *gsv i kis./);uiy:pc sje: j*j

The magnetic field due to current ie;gq. 7 +3nkcbl9jf bin wires in your home can affect a compass. Discuss the effect in termsgi+ .jl c;ke3q 7nb9bf of currents, including if they are ac or dc.

If a negatively charged party:ma .bn)e3px 1frh-s si+x*oicle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energ.oe3pxh b +1-sr)f*:xymsia n y 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 the vicinity of a cf (a x(q2+8pn rxh5lehurrent-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 px+h n( 58 lh(aqx2freparticles, 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 sho/ 5l ed(it5/9telkun+ p1fxfu wn in Fig. 20–46. What can you say about the chadu1efe+pi / x/lt(ku5f tnl59rge on each particle?

A positively charged particle in a nonuniform magnetic field follownm j248s -qtz imk)tr-s the trajectoryzt jkmi r)t24qnm-s8 - 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 an iron rod? What /0 4zvv hy7uxfqnp1).qtz(jtbvfya b2)v **tmust you consider to answer these )v 7* zq h(y pvna 1f4tv.vx/20tqzf)bbjuy*t questions?

Explain why a strong magnet held near atn hqyu p(oc.(p+w q(, 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. [But don’t risk damage to your TV opn, hu(c q +qyw(p.(tby 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 thw 7u4)dgks ;gvird is nwg ;)kgud4v s7ot. How would you determine which two are the magnets without using any additional objects?

Can you set a restind* wuzrgb4i3 .g electron into motion with a magnetic field? With an electric field? Exiw.z4g u3*drbplain.

A charged particle is moving in a circle under the influenced0skcbh *zss a*v3f,4 of a uniform magneticfabs3cvh4 0 ssk,z**d field. 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 electromagnetic p lga 3vb.-mno6umping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the sa l-63nbm.gaov me direction?

A beam of electrons is directed toward a horizontal wire carrying a current f )5j*olugw2( b xioz-jehv mr28ovm -5rom left to -j v5e(5 2o*h8mgr2bj m u)wvio-oxlzright
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electri):gagrb kxq75w+ otnwf ,08i cc charge.7wcbgf tg, n:5xkr0+i)wo8 aq

A charged particle moves in a straight line through a particular +qgs6rxatx 2)p7yu , kregion of space. Could there be a nonzero magnetic field in this region? If so, give two possisxxu67) p rtgq 2k,ay+ble situations.

If a moving charged particle is deflected sideways in some region of spcc:j 8nvdh26u d.xi;vace, can we 68jh:cu nvxidcv2.;d conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic7(bxrti(9mvez0 0arr 1z*uvb 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 movingoooo/0(wir 3 c electrons in a certain region of space are being deflected by an electric field or by a magnetic fieoowi/ r(0co 3old (or by both)?

How can you make a compass withoucjh c7 0mrn(k ht+-cr+t using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to ;4bzkr-vhgs 3d dn8w6each other, but don’t quite touch. Describe the magnetic force on3hdv4zk 8wg rs;bd 6-ne exerts on the other.

A horizontal current-carrying wire, free toc;pg6se/cv 6z9 g hit: move in Earth’s gravitational field, is suspended directly above a second, pc6gziv6ht:c e /s9pg ;arallel, 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 /g+-)jml gwjizu-fi: unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized papuhv v4 )n si.;y67dpxler clip. However, if one end od7u .yvi)vp x6;l sn4hf the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is douxg :mlpd vnw w64fazs +; jm1r,;0q0gqbly ionized. How will their positiolr4zvmq ; +df:p1aggx0mw,6nwqs0 j; ns on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B ir1+9utc. un f w.mu(.yombl*pnside 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 solenoicuun 0fu1/-ybq ,pnzv*sm* 3yd 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*fn *ym3 z/pu , uubscqn1-y0v 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 6wbdm zfhq;.w f4- +ukw7yq/n the force per meter of length on a straight wire carrying an 8.40-A current mnuwf kyz ;q7w4 b+w/6.dqfh-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 o 58cxhy-ji9o3hi afys :p,kt:q.p i1kn a 160-m length of straight wire stretched between two towers carryingjhsctp h yx5,1i.ao8y :qk-i:pkf9 3i 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 t bxra47.wtuz4, zp5sw re.7zd euq2a7 he magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetq.uaa4ur zbepww ze2s td,z7 .x747r5ic 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 dfdsr;27 w3koq3x ;zpon it is 0.750 N when placed in ; 3 wzrkpd q27xdsf3;oa uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current i)rrev 5iq 4bq5ebbo-4s oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earbr)bb4 re vq4-5i 5eoqth’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-4w7lu+vq :v wrkbzn* is a maximum of 1.28 N when placed between the pole faces of a magnet. If *vl4:u+wb-7nwq vkrzthe pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 359gs3oh*;vv v+rayvem*qv :8 l% 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, calculating a;*lv+3g o:yqr8* vvmesh vv9the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire jw r *6krt.u(hi;9ph tis 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” horizonta snmc;l uf(7pvp*j b:l0:0hhxlly in air because of the forcel:h7x jl(0f p 0:hsp*nv;mubc 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 chfo5xh5qqoftx8k )sb3.vb csba 3+ w;0arge $q\,=\,+2e$ 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 a/y7ti9 rljbu;i fqlv9jt4/8 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 negative charge for each diagraxgp09(vx8poo9xq x p7zn/; sgm shown in (Fig. Below), wpoo(8sg x07;p/q9nzp9xgvx xhere $\vec{v}$ (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 of j5ft7zc7q cx5 $\vec{B}$ 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 39anncm1-qfl;, w ajospeed 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 perpendic r9oo-c0gr7i fular to the field. What is the i0-ro co97gr fradius of its path?    m

  An electron experiences the greatest forb9 u-dapb rdd/v.7t4fbk2 m3gce 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 undeflect ll veu-1ubk4ll mox/) us/;6t4c+lhred when passing through pel/+lu ur)l4tkb4e/cumhs6 1l - vlo;xrpendicular 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 atom whose maurut--zgin4n 3ji +c6ss 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 rg(tb1w*u-mg yt 77 ugfor a particle of charge q moving with constant speed v to make one circular revolution in a uniform magnetic 1tm g7w* y -rubgg7t(ufield $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a unrjl( 45 )l.sbwhsmnlsi1.8f ciform magnetic field B. Show j.sc1lm(.isb 5f4n)wl hrl 8sthat its momentum is p = qBr .

A particle of mass m and charge q moves in a circular paty/ b 9lfgg llz1)ulm+og2x+ 2tx0zx7nh in a magnetic field B. Sho+xg120x bt/l lg9+m7 l zx)f y2golzunw 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 +o* /hagci3 6mw)ngdo particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves wt ): kitmd0d 0yhlxt,kpc) 5:4rf6zak ith a speed of 160 m/s perpendicular to the Earth’s magnetic field h65 x:r tktkmplf)z4id0ca: k) y,d0tof $5.00\times10^{-5}\mathrm{~T}$, 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 magnit1yu5z87o ysp uude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with speed m- w1 4 mq rnar3m8bhc*fv/on :8d c7u3mf/wuo$\nu=2.0\times10^5\mathrm{~m/s}$ 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 20j-wo: yywg4-2cn nvr rhjt0carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compa:y-n2 -vjj42hcrw y0wog 0nr tre 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 klk4b7l;rqm 5m)o(f 1 8bbtidallowed to produce a magnetic field no larger than that of the Ear f(kdkb)lbblt7;q1 m8 i rm5o4th $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight ww0a-b.* ss,k sy7xjzth v6lo(ire carries current I out of the page toward you. Indicaax *- 7,zsks vo0(shbyl.6wtjte, with appropriate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A current exerts an attractive jl(jap*1 a,ttforce per uaj*, jt (apt1lnit 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 ofoq*i5m h0wiuz2w y4a 3 the force between two parallel wires 35 m long and 6.0 cm apart, each uqy* hwam04z3o w2ii5carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m fr*llp x s(skj7un *o-4bom an electric cable. What is the maximum allowable current in the cable if the experiment is to be acc47l s*bnju *px l(o-skurate to $\pm1.0\%?$    A

  A power line carries a cu3wpbhc2vl-) m- 1niq*fdcsx g n88 k.irrent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnglq8n-w i kdhsv- 1xn8c2 b3p)c.fm *ietic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13. f -oa,wzexk020 cm apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).w x okazf,e2-0
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is /g .yviu *wy b7zp2:wbplaced 18 cm due south from a straight vertical wire carrying a 35-A current downw7 b/y*bi.z:gwwv 2up yard. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due n q+19ien0,- qigf qfbiorth. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downwarg-iqfqf91n i beq0,i+d, 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 pas/du -kw.yluu /m,jb4atwz4 u9ses 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 cqydoank1e)kaos , + d(:)bh/ co+hk0 field midway between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 ckndy /1,ha(aqo+ds )+)e:bckook 0h 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 curr1xpl f o9)vti7ent to, and from, an instrument. If the insulated wires are of negligible diametevo 97fx) pitl1r but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (2q jg3 1j9jf3fgn+hfzb*0lo. i p4qtsFig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does itp on12j0q.g3zh4 flgb3s9fij*j qt+f 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 poinj0dax cggu)*hclt8 .,k+1yfwts 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straight wire, 14y c1*bpz0wh)so zqmas shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop14bz m czoyp)0*hqs1w.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a currenb 01fsn,yd fw+c5p9v tt of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, +n wbdfs p19y ft0,v5cis 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 perpendicular to eaco jwpv tbo jce+7 .5)wp()sbh;h other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field atow v7h wc);(bb+o5ejts.pp)j 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 Awo.r(1xk1am9 jv*c tw carries 2.0 A current. Wire B’s current is 4.0 A in th*w( ta1 m.vwrokcj9x1e 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 fromo+le i,a*4j a5)m8piia x7ewf one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, buaif+l47xpjio 8a5ma*,ew i) et 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), dette1 +5bo zhi/,uxewqt6g e y81ermine the magnitude and direction of the magnetic field at the midpoint of the side of the triangle between+1qwgt 6u/ xzyt5e o,hei8b e1 wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, ca 59hnd+j + hascn nboi*t(+vfx/ 5oua0rry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below5( t9osv/cnnxho*n+j +i+daa5 h0b f u). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a3 k+) *4gvfd kw. cy(jzhla4ggla9 z5i total of 420 turns of wire and carries a current o.9(dal3 +jzcfv5ka w4hlkgg*i gy )4z f 2.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce ar jyt.iyu:1 b* i2 j.3h3uuetk2,co sh field of 0.385 T at its center. How much current should therije,o b22sjyi3. utt31k.u c hh*:yu solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. Thr:+/ bp apsm7kv:,scf9vm(z le 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(ra ,:fc9+lbm :sm/ vs7pzkvp downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that produxmi c3ys3y +.tb7mk) *fvozy 4j 5uk6oces 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 as solenoid diameteku7c* 5m3 oyxkzy4j3+)vs 6 omft.bi yr, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Usej t7h8xh: b+;y6cgloq Ampère’s law along the circular path, shown dashed in (Fig. Below a), tb jhq:+cl86h; tox y7go 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 between the cltd.tn2*o: 6 km zv3*zo7 fgjzonductors of a coaxial cable (:dzkzmtz63 o7*f l.g2onjv* t 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 pv/irb*bpn9) grp* o0 wire 22.0 cm on a side is placed with its face parallel to rbp/b9p*gp o* nr )v0ithe magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflecz+nb+sqeg80 9zd*dhe ts 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 25% over the yearw bxss,8jq2rd75i oc)s, what current will give full-sc, 7b ico qx58rd)sjsw2ale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor dslg a*qy br5ww2ib22 )rops by 12%, by what factor does the output torque change?2 b *)rwilg2bq2wy5sa

Show that the magnetic dipole moment M of an electron orb e9seb (h00kryiting the proton nucleus of a hydr( eys 0re0b9hkogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine t /r v4z)2j t0n.a7v;wnwryyw3 ad z7tloops lies flat on the ground. The Earth’s magnetic field at this location has magny nw)a r yvdnvzzw 2/tttr;a04 7.w7j3itude $5.50\times10^{-5}\mathrm{~Т}$ 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 5a),.e 4k*hlaox cind 7 aa/garadius 5.10 cm in a 0.566-T magnetic field. What value of ax*aa5 c) ah47oa ,enlk g/di.electric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, german,.dvap,st2xb b n fc:o4b, yj,ium 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 76j,d vbox .:a y ,pcb,f,4bn2ts u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass sp(ku.hadm 93rwcp ih 81ectrometer of (Fig. .pui(khr1 9 3wa 8mdhcBelow) 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 used9g9 n:hou- uhfa3va1opb3 e5i.msal7 to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO g.3va-il mo19pe s:a ua7uhf9 nho3 b5(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 voltayxbgavne m7ah-effjd07 h+b:,b )v, :ge V before they enter a magnetic field B. The ions are assumed to stav-,j g 7fx ,eeya0hbhfmd :a bvnb7+:)rt 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 of wire7u7h* cqh(kp4s3 m vvv per meter, and a 25-A current flows through the wire. If the permeability of the iron 3 vhh7 musv cqp*4(vk7is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and has 640 turns * ys:/k nqeyy /ayh3hb;srjx5g 1z x93of wire. The magnetic field inside the solenoid is gh;: kr x/5*ssxey3 9haybqzyj3/n 1y2.2 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 momentumq3ea)r/ fo n12k pys/v $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kineticts7)/ nhw 1wjt energy upon entering a region of constant magnetihw7)tn wt1 s/jc field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carr2ktid sl4h 0d5ies a horizontal current of 330 A toward the east. The Earth’s magnetic field 4d s25l hikdt0has 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 p:oe8l8uc,n,s pf fm(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 Ea(,3 igjn3 *ac1-lkpkbzls z8;h mar6krth’s magnetic field points almost horizontally to the north ap1lmkj k nag c* zz,363;slbhri8-a k(nd 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 heliumcyf8+e.gcfqx03i t50 j9uti j atom, 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 shown in (mtaj/all)bk)9cg93 o 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 pl c9alo 3/k)jgtbm)a9erpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and is sus:k: a/3n vln.jq;y7uyse es* epended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required currqsna: s yv/.y7ku ;le :e3n*jeent flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a hor / 8vguf+)rm j:oc l1goix6z+aizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A mag i)1xa6z/u+ jlfo ggvmc 8:+ronetic 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 deflub0 j4 i: m7vpv.tl;zvection of the electron beam near the center of a TV screen due to the Ea.7vjluz40v ;tv :mipbrth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate e5,v))uwar,gy vo 1zf)fel.w i d;ws)llementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dee o ,5vdr)fviy.wswaw)e;l))g , 1 zulfs,” 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-,7f todj h-o+gdhhm2 side l, carry equal currents+-dfghto, dh o mjh2-7 $I_0$ 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 ve6ve2)w mvmkk kizv y:f6+t u;7ry useful in particle accelerators for “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 extenky6v6zvwek+f2t iv)m; :u7 km ds 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 wir 8wnops cv5g)jxdf( /.e carrying a current I (as in Fig. /x.fcg sw)pdj 8on(v 5Below) 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 field is1 4ezzid i.zd.ns/d c7 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 theg*l1rqis 5r , uk8jx.w magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground a1klsg8wr r ji* 5uqx.,nd 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 magnetic field would make a beam of electr 2c1)zpy .l .3tvriruwons, traveling to the rig1ui rvc 2 .y)pz.l3trwht 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 pkj5atuhj3. tb3g,b 2,7dp urpath through a gas in a magnetic field of 0.010 T, perpendicular to the plane of the ta3 ,, duh prtubg2k.p7j5jb 3spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produc2ivrk:(jev9gh f+q 1+wg d4ive a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the solenoid rh2 figi(4dk+9+w ej qg1vvv: have?   $ \times10^{4 }\;turns$

  Two long straight aluminumppy6sa rpz)7c58 nk gi+-g;w e wires, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strg6gnr-c 8ywas ppi;zke)7 p+5 ings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T a2 -qk1 rwl44skm:x evot 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$