A compass needle is not always balanced parales j ;ub/tao89lel to the Earth’s surface, but one end may dip downward. Explain.b u; tes/j9ao8

Draw the magnetic field linqwnx:(/5 r*ogeww r0 a0ya )wees around a straight section of wire carrying a current horizontally x(wr0 oa nww)e:5rg/0*qwa ey to the left.

In what direction are the magnetic field lines surroubm9p3jd 5e znzs va+k7e, c()mtp-k3p nding a straight wire carryingm vbk9 z np7mae-+d5tsjze pcpk(3,3) a current that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left and suvxb6t bxz46p58d9 svouth pole on the right. A wire passing between the poles, equidistant from them, carries a current xx4 b6szbpv9v u58dt6 directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only tho4c:z +t: um2(6 -rdt/rxmntbvhcje :s se made of iron? (Try it and se tmb csre(r m+z:4:cdt/ 6-juthvn 2:xe.) Why is this so?

Two iron bars attract each otherc )l 2hck4dgndo0h- 0z no matter which ends are placed close together. Are both ma0no l2hgzk h) dc4dc0-gnets? Explain.

The magnetic field due to cug7/p+hh 2+ .qdpxicmsp3 ,pksrrent in wires in your home can affect a compass. Discuss the effect in terms of curre p+ hi+.qx ,mp7sck3dspghp2/nts, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magneticwme4:t-usib2 syo; 4g field which is pwoe;bsut44s2g- y i: merpendicular to the particle’s velocity, 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 pa.gbbwt3e pm) - r7mma-rticles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates tbm.p-7e3b- g t)rwa mmhe 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. )ok(d f6)2wdjli9rbdc ze8 m/20–46. What can you say about the charge on each particr )zedd k9(/o8jcdlb)m2 6fiwle?

A positively charged particld4dwwvq;0/ kyqs 2l0xvj /vg/e in a nonuniform magnetic field follows the trajector/xgvd 0sq;4vd //w kjwv2y0lqy 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 ma,p;s hiy2 mq0tsw /dlo9hcu3 .gnet attract an iron rod? What must you consider to 9s0ut.h,psqyd l 2o ;imc/w3hanswer these questions?

Explain why a strong magnet ww, 3a .)euw hp1z,. xydbh1clheld 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. [But don’t risk daxda)wbzhclh.,wew ,up 1 y3.1mage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three + ufr)pyp9t m9er5/woiq:o,viron rods, two of which are magnetized but the third is not. How wouldo w u5t:,iqv9y)mr+ppr 9/eof you determine which two are the magnets without using any additional objects?

Can you set a resting electron into moo xaw*p0g(q *ution with a magnetic field? With an electric fieldougx(wpa q0** ? Explain.

A charged particle is moving in a circle undetd-7t ,pifs m*vl-us0 r the influence of a uniform magnetic field. If an electric field that points in tps7 d0tmv-s,*iu t -flhe 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 behinds c/ ftc6qbb 6n3n7w4l electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificia6cl/wbnctsq 4 f6 3bn7l 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 wk9c v6n mp7-c owdh3.r+ve(vafr94y directed toward a horizontal wire carrying a current from le-yrnw3wv( 769c4m rhfav9v.dok ec+p ft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or j wza57cyzb ,) ii2.dymagnetic fields that surround a moving electric charge. ,ic7y5bd )azziw yj.2

A charged particle moves in a straight line through a particulr(m+zw7q(:n0 rc hqcwbeo2 ; aar region of space. Could there be a nonzero magn0(2 q7h qn;wob cmac rezw+(:retic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space,n/g): lw.r1)c /duwaevmkln( can we conclude, for certain, te lua ln/.kdr w))c(/vg:m1 wnhat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fielpn*d.7xll6 gg4iqj r0)z,qxd * gqu3td $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain regio nz)xgm u (2*d(1kdzqqn of space are being deflected by an electric field or by a magnetic field (or m)zx1 (qu *ndqz(g2kd by both)?

How can you make a compass without using iron or other ferromagnetic 7 dmv5y8 h crz-:qqqcg0xrd v)5.u7qumaterial?

Two long wires carrying equal currents: her0ojq c.d4 I are at right angles to each other, but don’t quite touch. Describe :.cdhrj0e qo4the magnetic force one exerts on the other.

A horizontal current-cig *3):4wsdt sq2wwffarrying wire, free to move in Earth’s gravitational field, is suspended directly above a second, parallel, curren*dsq:w) 2fwit4wg3 fst-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 e el6:qi8o*ue magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetize;o8fq2yo g w;ifc 3o.ed paper clip. However, if one end of the nail is in contact with a magnet,o. ;8eoy2; gio3wcq ff the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singlyyo,vt:q( 2u,f dhhilx8+q ju ( ionized and the other is doubly ionized. How will their positions on the film of aq+u(fx8 d: , luyojvhqh (,it2 mass spectrometer (Fig. Below) differ?

What would be the effect on B insidezb xu;6 u72g.;d+a*gu 3vfxcq uv, nor a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . A relay is an electg2 x*ei4vy8bg romagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of irogy8ex2v 4*bg in 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 length on a sttm 8bzn7, 7,(j/vv4, d)tksv)9 jtnbrcycdmqraight wire carrying an 8.40-A current when perpendicular to a 0.9vq/ cmr t,7)(v9, ) 8ctsmnd,b4vt d7 bnykjzj0-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 magneti-t.oywth29 qc c force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. Theoc.2y-h9w q tt Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitu4 hy1x*lskzuoldtc+u: 7 )ye*de of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Eao kc+t d)y* l lue7xhzy:14*surth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is zj7g - tpx)9ndflowing in a wire 4.80 m long if the maximum force on it is 0.750)z7 9 ptjdx-ng N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 0bx *bfae2g r,4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip r,e 2xbfg0a*bangle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 13nb4ji)o i/ kaj,hs /t ;tpe-i.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what,eittj4;/n ab/hpoji-k 3)si is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wliv 3hznjw rx-a.7. h3ire 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 awrh.-nxli7ja 33v hz. nd the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximhw0)k42bd*ywv2erf 5s jo t(tum 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 t- 3c*sjlj xz :4c gaan*;:xvmh/:gue“float” horizontally in air because hx gtc:j3 :v*: /lnujaz4-s x*e ;gcmaof 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 cha9l di,7 f2wlsbtb/mvbf asl6a78qj 60rge $q\,=\,+2e$ 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 electr,4x(kxus: t 56iujyrfm h5dn;on 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 diagram shoh+: o;kg65ewwazqb (mwn in (Fig. Bel+awm o6( hz5w:eqgkb; 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 of8(:n( 0 fupk0anndz( agxbu+ a $\vec{B}$ 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 up 21pj8mbx,x boward 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 ,pad8( dj n:zr8l8xcl plane perpendicular to thec ld8 raj,8nplz( :x8d field. What is the radius of its path?    m

  An electron experiences the greatest forceol :jl9vp.:gr 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 0;ad 7 wxf:yz+54o fzu r,vprepassing through perpendicular electric and magnetic fields zfdw7ay oue r;p+frxv5 4:z,0of 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 helium36z8g kap y4)5sqb ssq atom 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 al.mi l86wsje;b)93q s cat4gv particle of charge q moving with constant speed v to make9) mwcgqa jt4bs8i.l6 l3 ;vse 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 movesj9agm q yw)h57 in a circular path of radius r in a uniform magneticy95hw m qaj)g7 field B. Show that its momentum is p = qBr .

A particle of mass m and cham1;q xwazb67ky (em( grge q moves in a circular path in a magnetic field B. Show that iym( (1 z;xq7akbw 6gmets kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the parr,tcl02w qs 2jticle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with rjyt(vtueb3;l,f.vls* : s 4ta speed of 160 m/s perpendicular to the Earth’s magnetic fu3r:tbe4tjv st l(v,;ly.s * field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s maoefy 5-:8w 79o8imizl +vvkojgnetic field 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 withakrpqs7jl.hd5qa o7 d2f1, i9 313zlr qne8s l speed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A current. Howh v*4v)(pls( h.dg ziw strong is the magnetic field 6.0 cm away from it? Compare to the Ea iz.h(hdv)sgw 4pl( v*rth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no larger t1) flv5xyjs cn :,:p3gjo qdt/han that of thqpj o v:gs) jx3cd l:/,15fnyte Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I 5b4 qxeburgt1 )zna/n.zd0 k- out of the page toward you. Indicate, with appropriate arrows, the kra.bd -0z1qu)xenn/5 g bt4zdirection 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 ex 5o mxt:mob+ cjek8-;o2kp an,erts an attractive force per unit lenjp;m,obn:o o-a8k2kc+ex m5t gth of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the force between two parallel r bsk3s,)cq-ywires 35 m long and 6.0 cm apart, each carrying 25 A q,sy -)cbsk3 rin the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnet8 f4 j6a crfnjx+0v 2ywzg)4b,zw juf0ic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in th44w )z28bj +gf0zw,fycx vran6jfuj0e cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 wrj /3lgb:)sl w3h pz)A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produpbl)zj)3 s:grl3wh /wced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 2+9wt0rpr pqd5 5-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. Belowrq rw t95+p0dp).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight verticalf9sjtsd( i:r0yl5ns6 xt.yx - wire carrying a 35-A cssdnr -jfyx6 l i5s90ytt.:x( urrent 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. Wh6s i/j d+.vsf+r 8o;bdsoo f6xat is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward, 36o ji xds+6 fs.ofo b/vd8s+;r7$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a rate of.ppg ts pp.;+za;6hix $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wires 2 nlw scab1q 2sb7izd)k9ymnny.8z3- o(g 8 ol+.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these cur owd 1zbml)-kbnl+yyzq28n3i c(oss897ga . nrents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires condwhs,m-s 81scgn5p fus*d0 y. iucts 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. B ysu5. fs gw1c,-m*pihs8dn0 selow)? 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 ingtegn,y:h .f, (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per ht e:g,,y f.ngmeter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points, uip.ofh; zrq+. chn8dbp8z: 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, as j: ii3*wyc qis;d 4;qrshown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and directiqiji: ;y*si r qw4c;d3on of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire, made of 2.5-5fckm2 u49 a, tvksf/nmm-d sfkc atu/,5nf24mk 9viameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are orienn h :k22qb17zre hh*cated so that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one ha bn2ch:1eh zr*7kq2carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wireap br bc 06pqwmo81)8is are 15 cm apart. Wire A carries 2.0 A current. Wire B’s curm8o6)b i1c b0wa qpp8rrent is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking (hux+v yj+63al7vbi +bf u2n mc*7 voualong them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its directionf* aobnb7+c(mjv7 h2 v+uyx3l+ v uui6 in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the magnetic field at yav2*btxlph :8yqk , 1the midpoint of the side of the ayl 2th8b p*:qx1k,y vtriangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d 0q(f8 ufly 2v,2 eiepeapart, carry equal currents I in the same direction. One wire i liqf2 eypvf8e(,02ue s at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and cr vq-fg8x rpg7q 1no5)arries a current of 25v 8f7n prq-xgqogr1).0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoidaahdnetbql,5n36- li 6;tl )o 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 lqinb o3 a5d at6t;6e)lhl,-nit has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-lonig+m7; 6 lvnawg straight wire cuts through the center of the soleno ;vi7a+n6gml wid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper ad-6/ *(vlba t6mre4 bgz- p hri6k*cxznd want to make a practical solenoid that produces the greatest possible magnetic field for a givenemazzr/4c6 xdt*6(b lbp 6gh - vrk-i* voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the ((u vh5lwc-09yexja :nql/k w shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic field h0xkl5w-uc 9v l(y:wnje/(aq
(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 tha1i1sn;j 9g*/qg gyd gpt the magnetic field between the conductors of a coaxial cable (Fig. Below) is* dgnq g9gsj1p1i;g/y $B=\mu_0I/2\pi r$ 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 siedar oj,lf0 1mf-5 +umde is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. Wudlra 0mof- fe+jm1 5,hen 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 deflects full scale q ;fcfh1*b 3uxfor 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 galvai2vhdk -i 61gvsprd))..awu wnometer weakens by 25% over the years, what current will give full-scale deflh6)u)rs wgpv.-i2 d.dv1ikwaection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motorn p xvojsn9q g5fhm:i 1j5(+4y drops by 12%, by what factor does the output torque changey fmj+ 4ignpxns(951q :hov5j?

Show that the magnetic dipol xb(75 spsxipiiyp i2xe1/5w q oz s:m5nm1x-5e moment M of an electron orbiting the proton nucleus of a hydrogenm-5xxip (o s52yx /:7wzsi 11nebx5s qippi5m 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 loops lp )s9g/mx; sxb2jh.gj n)ihl9ies flat on the ground. The Earth’s magnetic fieximh/ n. 9gx;)2 bjslg9sj)hpld at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic field. Wh,s;btms v ksq/rve19/ew, 0pcat value of electri rpv ,q ts;m 1cw/0eskvesb,9/c field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal torn78div 7r(xnc33 qq m 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomq(7i33d rx7n 8nmqvrc ic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass sp (xuruzad81 i+ectrometer of (Fig. Ber+x d(i uz81ualow) 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 u 5a6t nban5v coz9:xz0sed to monitor air pollutants. It is difficult, ho5a onza:6zntx5b 0 c9vwever, to separate molecules with nearly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V thl. g36s7dkd/ cmvr si9 )sm9before they enter a magnetic field B. The ions are assumed to start from rest.hvis 7lmd 3cg/. d9 ss6rtkm)9 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 wgba/bc:s ztg *cdae5i) y0f8) ire per meter, and a 25-A current flows tgi)b)caa 08tg/y: cb *5sfdze hrough the 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.ut o qq,41;clvsoqi;38 cm in diameter, and has 640 turns of wire. The31lqov,to qs c4ui;q; magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumg gv o, h*+5l4vlbjz4f $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 sabkp/ +9qjp, jwme kinetic energy upon entering a region of constant magnetic field. Whatqp b9,jwkj+/p is the ratio of the radii of their circular paths?   

  The power cable for an electric jiflg o.ni4qj6o iv(.g(+)ht trolley (Fig. Below) carries a horizontal current of 330 A toward 6i+ qj.hivi)ot(j(4 nlg . fogthe 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 net chai .o+.4 u lbuc3(m2csw,igaqr rge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points/ g;99gsp o,eurq z*ys almost horizontally to the north and has maposzs,er/9gq;y*9 ug gnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 helfgy1mb 9i h0x6ium 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 (Fac aev49gu7 oiqs1*13*(p4kqsi n fp xig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, anco isi*9ks3 q 1aep7 nvxug*f1pq4( a4d 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 1.00-mm-diameter copper wire and is suspenyh; mvf ,d3wrl,r5/k sded 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 c/ l5f,yhrvrws; kd,m3 urrent flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act asp 2 jt5wv;t/bi7;mqfjyy:td ( rails to supd/yj pb;:j ( 7tyw;5i2tqv tmfport a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron beam near the center5s lyp4g9e:p wu/ nb 5e0lj2hi of a TV screen due2hpij 45p5eyu0:/ egnl9lw bs 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 d. fxy;qydz02pevice used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles aref0yx;d2.pyz q accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of a square of0 /*wg tfcmlfe;-5 bss side l, carry equal cuefm0 5*gwt;/s-l bfcsrrents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “b-ksndw:3 flacu5s0t(b x 06 kqeam steering”; that is, the magnetic:6 c asx( 03k0tnsf5 w-uqldkb 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 traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of asjm/ ev8fax.w: b03wf- iop-g circular coil of wire carrying a current I (avib0xf -w e:fp8a/m j3o-w gs.s in Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic fieldl gci;3in rrv:5;wj bli)i:9k vv0:i s 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 byvcsxt 00u-3 uu/ 6ctib overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you th3v-uu0/ cux6tsi ct 0bat 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 nbgr q rn2w.a/b4ju-*a beam of electrons, traveling to the right -rb4ur/2gbw a*j.nqn 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 f9:f6 +wxw3, uulbu7zv 6v vehyield of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two suh 6l:+xv3yez 6vfw7 u,u9 uwvbccessive 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 diameu46 amvl7zq3e ter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns m3el4za muqv67 ust the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the same cuu/-ypte;4; ey t1rahnrrent but in opposite directions. They are suspended by 0.50-m-long stringsn e4pah;e-y/1ru y ;tt 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 magnetic field B = 0.23*).o hsnx 4unn 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$