A compass needle is not always balat5yl+5ff .w(px waxz1nced parallel to the Earth’s surface, but one end may dip downward. Ewf(.z f +xl5txayw1p5 xplain.

Draw the magnetic field lines around a straight section of wire carryingty, ft3q- v0yz-gn (duq )c,xl a current horizu, 3ly-( qvd )n,0cxy-gf zttqontally to the left.

In what direction are the magnetic f:gpm)zhw a-a9 ield lines surrounding a straight wire carrying a current that is moving az 9gpwm:h-) adirectly away from you?

A horseshoe magnet is held vertically with the north pole on the left and southy-mu50f8vxhrchox:5- t( feh0, os m u pole on the right. A wire passing between the poles, equidistant from the,fft8o5y:5h - ru 0uoeh(mhxc-mv0sxm, 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 ho fa5;p.hn)f of iron? (Try it and see.) Wh.aofh )n; f5hpy is this so?

Two iron bars attract n)g/gbn02h;0z kifbn each other no matter which ends are placed close together. Are both magnets? Explain.) knfnzh/ggb0bi2n0;

The magnetic field due to c;7 +pxa f*i gaaz.z5c.qiin9lurrent in wires in your home can affect a compass. Discuss the effect in terms of currents, including if tgizzqn.c ;+*a i.i5ala7x 9pf hey are ac or dc.

If a negatively charged particlef)s21fp/a jj o enters a region of uniform magnetic field which is perpendicular to the particle’s velocis f1p/)a fjo2jty, will the kinetic energy 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 of5 ld0xqn-*gb1vg rg9o a current-carrying wire. For each charged particle, the arrow indicate1*qrn0-b xgog g5dv9l s 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, ent1qvsneev4g 7mn3 -gn/y l5 wj*er a magnetic field as shown in Fig. 20–46. What can you say about the cha1l ns5nmw 4gy/*3g-vqev e7jnrge on each particle?

A positively charged particle in a nonuniformipqe pz 8op;uf* 1c1;a.hy f m*yvqj96 magnetic field follows the trajectory shown inpf*;1je yqpam6z cu9pvh f 1 *8io;q.y
(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 magn 9e*d*av9 fz;em4qaahju+ l h3et attract an iron rod? What must you c;4hdafje+a*mv93 * e9lzh qu aonsider to answer these questions?

Explain why a strong magnet held near a C8 p e*xn1.pcziRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goixpzc. 1enp *8es completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of whivm92r ab f/y(mch are magnetized but the third is not. How would you determine which two areb2v (9yfm/ arm the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetixx b*bf ya36)mc field? With an electric field? Exy *bambxfx6) 3plain.

A charged particle is moving in a circle under the influence of a uniform magnev1bx; bm5ar:dtic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged ;1bdbvr mxa5 :particle will take.

The force on a particle in a magnetic field is the ide*/4 stpdy.wd wqiu+b7a behind electromagnetic pumping. It is used tot+wi ysdw4/q.*b p7d u 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 6c8vj:3fw )7 au 0opvede.qoga horizontal wire carrying a current from left to right o 8e.6vo:af 3pg0w)v7c dquje
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a movibidmnc* j)gz,,u ir* /ng electric charge.ucjd,mg* z, )i/n*irb

A charged particle mof8cwccj fd +7, e2mtn0ves in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situations0+ j7mfw nc28,tcdcef.

If a moving charged particle is deflected sidewoem) c2*w3.x)cp -t4xc ysgwy ays in some region of space, can we c* c4scw t-yo)y) xgc.mpwx 3e2onclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region.wa q, f8ex:ui of space there 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 a ce7g p*zy-)2j kbdcv0,nus s3 hzrtain region of space are being deflected by an electric field or by a magnetic field,gp0k 7vnzbsyd u3zhc )*j2s- (or by both)?

How can you make a compass without using iron or other f) wx,*wm.tsvx *x g-ha(n wz+eerromagnetic material?

Two long wires carrying equal currents I ar..o48 jtyvvpf klf n1.e at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on thel8f.y ot.1v4kv.j pn f other.

A horizontal current-carrying wire, free to move in Earth’s gravitationalfy1mjofp /6 cw:wru,j 2lb rn 3z18-bq field, is suspended directly above a second, paral bm3n21yr u:6-frcq,8wjwfo 1j b/lzplel, 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 at n)e qte.)-djitract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Hoz o2wfxf 94;w3j kua/uwever, if one end of the nail is in contact with a magnet, k4zwjx;of/ u39 w2auf the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singlysy) 7qt2pj )qgcdy;i28yv p t7 ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Below)) vs7y2q j p pt7gtd8iy;q2cy) differ?

What would be the effect on B inside a long solenoid if p(ube *zk 2wnsr :q;oegusig,c/ ,5 5b
(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 ibu)m ;rmlmazp f.:+fa4u9s(s s an electrop r f.msu4;fm+9u(a sbl:m )azmagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, 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 ofd7fv ebb a-n:1o2pq,x length on a straight wire carryi vq-ex ,o: 27bp1fabdnng an 8.40-A current 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 165i lg2n4: srhune( zn5cfs8k60-m length of straight wire stretched betkinfc8e:gz (5r2n s 46s5ulh nween two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic for l06 gr 5yku2f+ybxj3uce on a 160-m length of straight wire stretched betwee6ykgb r ly+035u2ufjxn two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing g dzgnv.d1jdfjjuuvy -d8+)b8 7 (j2oin a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fieldv8z d+j2(od-jfjv7dngu.jgd8b1 yu) ?    A

  A 1.5-m length of wire carrying 4.5 A of current is orienteia1zwz461a-sd u, 5ety yqf.jd horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnd w-4tf s,ej 1q1uy6azi az.y5etic 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 of-pw: wni snb+(-+i fcp 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 strenf+ bpw niinp--scw( :+gth of the magnetic field?    T

  The magnetic force per meter on a /jce g4gi32pnwire 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, calculating the angle between the wire and the magnetic 4 ge3 nip/2cjgfield.    $^{\circ}\,$

  The force on a wire i9 ge lt+tcgh;6s 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 wir sa;ik*yuv5 )de could just “float” horizontally in air because isa *5duk y)v;of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chargecz gosqh1+ju 7c3oz+nl /b+ +u $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the force on an eg uqe6ueof)qu1f5 amzpc5 ( 02w 9d4lblectron 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 dig-df:s6.mz,gsp s;qragram shown in (Fig. Bel; ds.s6r: pq-gzfmgs, ow), 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 of9*bwzvef:d l+ $\vec{B}$ 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 sbza/ar47 i(7htf 5 qcwpeed 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 h6.bhpm4e*h j0.20-T field, in a plane perpendicular to the field. What is the radius 46jbhmh ph.e*of its path?    m

  An electron experiences the greatest s+v knc/cq x0+q54hlbz6xn ,dmw )s3e 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 gof)84 gr(x0wfnzsk 8me undeflected when passing through perpendicular electric and magnesnm(04ewfx8 g)fr 8zktic 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 atomph l 8e;ceb tzn:in*2mrqi-+y01z h;e 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 moving w eo *g0-rwjszm+-w0b2uox(4 lguyx* t ith constant speed v t0 * u w(sg-y *l4+or2eugzxm- w0xjbtoo make one circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uniform magnl v *o;nbullfa v9l g s53f3;g9*xkal/etic field B. Show that ita glf x;bnsv53lguo;vk /l*f 39*lla 9s momentum is p = qBr .

A particle of mass m ang46 xt4 d7azq+yd4b oyd charge q moves in a circular path in a magnetic field B. 7oqbta xyz 4d6+d4g4 yShow 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 particlui 47/d)ow apci)t0vqkrw6wpd b +9i)e in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s magnek,obn-zhgf c9 it ,u4/tic fie ktb, -4nzchf,ig 9ou/ld 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 mlrg) fnh- h2;xagnitude $0.40\times10^{-4}\mathrm{~Т}$ 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 spe7ny a8,ffm8o1x6 fme yed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 5e7/z ij1gv ax8nhe d*a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away fhv15 xdin/aejg*e7z 8 rom 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 allowed to pl1 ).c7juc odxroduce a magnetic field no larger than that of the Eartc o1l).c7 uxjdh $(0.55\times10^{-4}\mathrm{~Т})$ 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 b7e5euy2-ek7d+ygt y ,co;lv I out of the page toward you. Ind75k d t+ ,-;yblu2y7ecog eevyicate, 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 ej:u4n*thw wh2xerts an attractive force per unit length ot 4nw:h*2uwjh f $8.8\times10^{-4}\mathrm{~N/m}$ 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 paral az95;+gtxbz ylel wires 35 m long and 6.0 cm apart, each carrying 25 A in thy t;z9xag5b+ze same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field,phmrwry8 am ap5 4sy1ge.0g+ is being carried out 1.00 m from an elect4aa0,g r.p mew15s8 gyrmhyp+ric 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 along the t) yscsr vaoy-z4+9)qrh(izq9 ops of 8.5-m-high poles. What is the magnitude of the ma)y(z v4rzaq qh-9)scy9s i+orgnetic 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-u o8kux 4( 3t*iw fgnqrl-63eqllv:z wires 13.0 cm apart carry 25-A currents in the same direction. Determine the magneticvu r-l6wg (iket-334qxqol l8u* nf:z field at 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 is placed 18 cm due south from a straight vertical w30lg;ie* c qpeire carrying a 35c pe3* qe0lgi;-A current downward. 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 north. What is the 0.) mfbakyp)i net magnetic field 20.0 cm due west of the wire ip b)i.f)ky a0mf the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in spacttz 0lk ;uy:1z 2swoa7e 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 strai (+i-mu8fy ;wt-dejtk ght wires 2.0 cm apart in terms of the current I inwuy8-t j-(it +;efdkm one when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of ac60az f 8lz1f77vlx8ll yr +hdc 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 mia r87vx 1l06 clyf+8l h7flazzdpoint, 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 t7914cu)nens3jhk* jdr aqo b5he 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 each of the other two wires? Assume it is 2.8 mm from the nearest wire, center thn j u5c71bn4*k ja9)dorqe3so 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 30k bjxwb p (4v8:id.mnre1nm 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 wig ae)j:.*:j) gh i)ohfpv l2vire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of thejg* ):ve)hohi2:v p) a.igljf net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire cahnz (u-r3f t*kejl gss gd7374rries a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cmjn7k feztrdg*s 3 (3g 4-hlus7 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 perpendicula:r8sj n 91smuveb*u ij 3vbb/ 40ssvx;r to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the m9is x/m8b ; ub0s4bv:jnjvs*vseru31 agnitude 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 carries 2.0 A curren0b5st7h 9 nwdht. Wire B’s current is 4.0 A in the same 9bsh 7tnd w0h5direction.
(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 w5-a,8qns i tgare 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit 85tgna q isw,-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 directi o0*ierufk.b d 56dfj8l w8hr5on of the magnetic field at the midpoint of the side of the triangre6u db.ki58h o8rffjw*dl05 le 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 the *waki+n7 (fnq yz7:qf same direction. One wire is at nyq7nzw7kiq: f(af+* 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 total of 420 turns of wire and 7)oxa*xgbqg e9mlx** carries a current oxog7mbx *lg9)qx*a e*f 2.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid g33 9yy ek593wszdgfd 1.25 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if izy ydgk3w 5 g9fdes339t has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A8bxml, m5-a kl;yxv+ ij0)tsk 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-byvx mas0kmlijx8 5) ;k -+lt,A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and waw*p 6ndu+.bcwuyx)) gnt 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, shop)b )+ uwwncgxdu*6. yrt and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’sz6cslr 7vz kur8disq o21 j2,8 law along the circular path, shown dashed in (Fig.z,6 usq rk8sijcvz72 1r dlo82 Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between t g) gplv3*f 0rjo9 qvw6nf1*cohe conductors of a coaxia*rpjvl) f ofqggn1v960 co3w* l cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed with its f7 d ftzt9ci u-d,1hvp*ace parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the 7ttiz,fd dhp9cv*u-1coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale9 abyu6/ms,63nhm1xrrohx r 9 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 years gdi(a0:3h k4)evk8 jdlyf/ vo, what cuvl h/goav(fe ky3:8d)4ijkd0 rrent will give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a 3sop xm 2+( 0an/vfxx4 k8pcnimotor drops by 12%, by what factor does the output torque chanv8n (xx/mspax 032f+pnco4i kge?

Show that the magnetic dipole moment M of an electron orbiting the proton nuclek3e4l4rfk /1hl. cxoion0 o/zus of a hydrogen atom is rr ok/olxz4k 4l1oc n.3fhi/e 0elated 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 loops lies flat ; 5aef4hav,n,,m mzkcon the ground. The Earth’s magnetic field at thisc 5m e;mz4 k,,hvnfaa, 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 5.1jve;e 9g1 i(ym0 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction must it point9iem (je; 1gyv?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature exmmk5f ppry8 ymeo7b2sg26)/ qual to 21.0, 21.6, 21.9, )xgr2pfs2m 75myeyk pm/ob6 8 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field behpue/sk g )w4uiq8 zp byht53 ;*au(/ktween the electric plates in the mass spectrometer of (5(ahh8zpye;w4bui3 u/ */)tk qksg puFig. 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 : ilor7rl3.pwis difficult, however, to separate molecules with nearolrl :ri7pw3.ly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V befobcmd5y-j6c2ose b7 ;ore they enter a magnetic field B. The iond6scy c75ebo2 m b-o;js are assumed 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 of wire per meterhqsjzz0+s+ y ,o /g2xr, and a 25-A current flows through thezsyxq+s/ o gzr j,2+0h 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, and has 640 turns bok k3sh8uu*p1o k)(j3tbzm5 of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. Whap ojb3h)5kk uos(k 8tm*1u3bzt is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum j cqwiuf q.s;1(xf.. q$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 electrozhfr;a.+o xa :n have the same kinetic energy upon entering a region of constana:. fo +;hzxrat magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below4v9och .964a*:khraf ji7mo c ygki-k) carries a horizontal current of 330 A toward the east. The Earth’6aom9hhvrkky a g :9 . k7i4-4occjif*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 airplanmw*3epd(lx6y sq; ;fce which 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 magnetrph1t1 s(9c ptic field points almost horizontally to the north anpth 1(1rtc 9spd 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 k-tga.; rh,8k*w t -kw.jh( cronlak-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 i)p elw.gx8s :hn (Fig. Below). A large current moves in a closed loop composed of fixed rails, x w8gh)sp l:e.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 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 ;3vlbqjn+l zp /17zi;axh,pq.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspen7;,qpilz/a;j3 hlbz pvnq+ x 1ded wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act ak.e ulv ,j4p-4ccf0bcs rails to support a light metal rod of mass m (perpend0lu-b4v ejk cc,c4 fp.icular 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 y (( )09w 1jhmv19 jgghkp0 xamr;jxf8,qbdsy near the center of a 0j v 90xjk,ha1)p;byw 1yr8((djsf9x mmggh q TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementar,, jr- rycpn c9t;dk)ky particles such as p d yp,9ktccr),rn; -jkrotons 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 “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 hoom(2tdjzy ;ed 7 8n8square of side l, carry equal curre;tjo 872eydod8 m( znhnts $I_0$ 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.rz /w64 du ex yq8weuvs1-b-s 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 extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons tra -z e wdw84e1q.xs/u -vsryu6bveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at thearkg .3f s7p1p center of a circular coil of wire carrying a current I (as in Fig. Below) 3p1gfsak7 . rpis
$B=\frac{\mu_{0} N I}{2 r},$
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 fiel0zj u/n-ai)a ij3c5l3a2sozp d 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 mai9t48 io7 *h apxsthkv9q::tvgnitude 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 po9p7a htsit9h4*: i:koqxvt8 vwer 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 electrons, tra rfv c)vu,q9+bveling to the right at a speedf)cvq 9+ vbu,r 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 ak kjyayw+gd sx2+q 4x0b1st;,c 99 jmuh *p;ay 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 94gk;swkc1jj+d9p,tx * ; byxyqaush 0m+2a yand 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 diameterueky8+dy:iv3u a8j 1jp); 8bbws :sps, is to produce a 0.30-T magnetic field at sba1vub3k y)ps;ip8jydj8+ue 8ws: : its center. If the maximum 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, carry the same c gn)ff.2cz,lpurrent but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Figpg2n,f ) fzc.l. 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 un cdabg:ic 3avpt okj;20)6o i,iform magnetic 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$