A compass needle is not always balanced parallel to the Earth’s surface, b ,69qsoyvvqoplzs)7p:z q)4t 1x q* qput one end may dip downward. Explai):*qp97q 64p ,lv1vy)zqsqot psx qzon.

Draw the magnetic field lines around a straight sectioi 76b )/uwzg1e :jjxq i;vvf0rn of wire carrying a current horizontally to the xifjj; /0i1)r7 w ub vqg:6vezleft.

In what direction are the magnetic field lines surrou9 6qs(-/psxzs * zql++l cbkcjnding a straight wire carrying a current that is movi+ l9p c+lq-s(sx6 j*zsbq/zkcng directly away from you?

A horseshoe magnet is held vertically with t7ocxf kol*x*-xa2av gd.)-bthe north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directlylc. g2td7x*k-ao avbxo)-f *x away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only tjeujy:4x 1q-6 iapos3guk0ltv ;4 d2ehose made of iron? (Try it a 43y gte:;svd1 au40ki oe6 jxj-qlpu2nd see.) Why is this so?

Two iron bars attract each 3dp s )iv.cf68xis4 geother no matter which ends are placed close together. Are both magnets? Explif.svd3ix ge8)6 scp 4ain.

The magnetic field duoq ae*e8o ;md1my4ojtbp(r*1e to current in wires in your home can affect a compass. Dioo d(amt q1mo yj eb8*e*;4r1pscuss the effect in terms of currents, including if they are ac or dc.

If a negatively chargedjo dbh kmk275u;*kx0b particle enters a region of uniform magnetic field which is perpendicular 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 eleo70m x*h5bj ku;2db kkctric field.)

In(Fig. Below), charged particles move in the vicinity of a cu1nwex+kykx *x0-on af.bwm:5 ig+a2d rrent-carrying wire. For each charged particle, the arrow indicates the direct*mx2n+0:n dwbw-ka1x x o5igya k+f .eion 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 F7v7fkr px59c i dbp4d8ig. 20–46. What can you say i p4pr7 f57cdkvdxb89 about the charge on each particle?

A positively charged part-)ph w b6i7gx e(h.indicle in a nonuniform magnetic field follows the trajectory sho)-pgx bh76ed iinhw .(wn 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 musrjh;86kd -vm 5ao1 kitt you cot a dj;-1om6iv5r8kkh nsider to answer these questions?

Explain why a strong magnet held near a CRT telesa;s xe- +gdx8vision screen (Section 17–10) causes the picture to become disdsx;x-a +8se gtorted. Also, explain why the picture sometimes goes 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 which are me zr*/fb-(w4e rttg t20u cna/0 1ffquagnetized but the third is not. How would you determine which two are the magneu4-zbu2r e/rqft fg wft/1t00 ea*nc( ts without using any additional objects?

Can you set a resting electrg/j3f r 7okmkqo8 3dy;)w 4ixton into motion with a magnetic field? With an electric field? Expla;3w4 yxo7 qrgd8k i/3otk )fjmin.

A charged particle is moving in a circle under the influence of a uniq60 3xw ow3pbsfg:lb :form magnetic field. If an electric field that points in the same direction as theq6bl:sg: wo x0p33bwf magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idub;dih( g+0*wmhqko9 ea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic ; +0(uq k mwhdhobi9g*field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horirqogdajndh90;df : * 2zontal wire carrying a current from left toaog :rnh9 d0jq*;f2dd right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surrouny9.sh 62)h1)ofs0rsj1xk ixz bisr;d d a moving electric charge.xr1sy)f6sd 2bs;j s.ix)ikroh0 9 zh1

A charged particle moc hbu;w,:xcjfzf7 : mm7n4rb4ves in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so:7 ubzfwf;,mr7 x4b:chnc jm4, give two possible situations.

If a moving charged particle is deflectedah; s/asv 6db qt8(ys u)(xck1 sideways in some region of space, can we conclude, for certain, th1d a8/sakh);cx6vby(st(uqs at $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space ther5)*n* 6likek bymzxk, e is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a iv0m m ll x43wvfl6:8qcertain region of space are being deflected by an electricvm38 xi0q6 wll m4vf:l field or by a magnetic field (or by both)?

How can you make a compass wity4nj+l,k ywduedrw-7 .)6e b ehout using iron or other ferromagnetic material?

Two long wires carryi e8+z2ta 4hqrdng equal currents I are at right angles to each other, but don’t quite touq a+tde8h2z4r ch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational fielsd)/wo m-lq*.x* * lyoy;nm fgd, i)o;/m *ly *d.xno- f glwqmsy*s suspended directly above a second, parallel, 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 unmagnetized piec +qk;ol:bfp 5h8clr:uqm ;t4ie of iron?

An unmagnetized nail will not attract an unmagnetize-ihj sq6a 9a4hjs(xspq/h s4 (d paper clip. However, if one end of the nail is in contact with a magnet, 4hjq- h his4ps(/(qx js6a9 sathe other end will attract a paper clip. Explain.

Two ions have the same m9vaq g*l vt/0a 0at1p5x9uvbtass, but one is singly ionized and the other is doubly ionized. How will their pp* 1ul9 0b0t ataqtxavg9v /5vositions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solmxh82o 0gy p;denoid 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 sim n.x6vrlk+ct 4ilar to a solenoid 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 on a pivot. Design a relay to close an electrical switch. A relay is used when you need to swn4k xt6v +rc.litch 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 thk6a 2t p5cunl0e force per meter of length on a straight wire carryingu0 2pactl5k6n 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 obcr2 xo:g +h,rf the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The E obrx+rgc, 2h:arth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of straig7u x035en) ) iucmft4vyfuh.0 ox1fabht wire stretched between two towers carrying a 150-A ci1c.e a)) f5uu47o bxthy3 f0fn0xmvu urrent. 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 in a wire 4.80 m long if the maximum forcj aue n8zy5r/3e on it is 0.750 N when placed in a unifoj z3uan y85er/rm 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of c,ma1*j d2q kf ho,a-s*ge rpq)(zb *gwurrent is oriented horizontally. At that point on the Earth’s surface, the dip angle of t m, 1gpeas*2,b ok*q(-dr*gjwf)azq hhe 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 magy(x7;+yc*n ) 72osdblk-t hu7vah iwximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what i2h7 lxgh+dy bs;(va n-cw) 7k7ou*yi ts the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% okoxb* i.or 6-z.zq tgu (xp0xi(f5mr: f its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch themqu gok:z xb*rp ziio5(x0-(r6 x..ft relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximus oczle(xdcml 2 t*55/m 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 n6e(x1kxhk*zrg1,f.wr l9 q f.00-mm-diameter copper wire could just “float” horizontally in air because of the fo z xhrqf lf. kknx61w(,er1*g9rce 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 charge +x)uw6v2t4 eupjcf-d$q\,=\,+2e$ 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 electron h3v w+adf o9k.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 onw*bsbh rxj h(*wo/6ndw ,n/f9 a negative charge for each diagram shown in (Fig. Below*s *wbf ( hhbj,wown/6xn/dr9), 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 directr irx6p .p;;g: xejt52vaak*gion of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertica zwn jrbte e:n)syus; 1q.73j2lly upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plane , qg je7-a+u8 d 02bmqtt0afesperpendicular to the field. What is the radiusm,a02 fqs7jtgb 8qeu -t+0 eda of its path?    m

  An electron experiences the greatest force as it travelsp x 5(1l ywf-99;2,ot hls*jdrvife4jhvkx1p $2.9 \times10^{6 }\;m/s$ 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 e9rqmy9c bh* (zlectrons that go undeflected when passing throughm b99*ry( zcqh perpendicular electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom wwc/4kmjho68 + ownsm6wy *)u+ / lyhsnhose 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 forrk2; a-pdj-svk b7joyco //q, a particle of charge q moving with constant speed v to make one circular revolution in a uniform mag-dys/-o;, jkvr2kc p 7 aq/jobnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular paths;+lg0vn csa*3a , kr7q.cpa n of radius r in a uniform magnetic field B. Show that itsr;*vag 0a3ac lssnk+nc 7 qp., momentum is p = qBr .

A particle of mass m and charge q moves in +c4gc v.rg 1iea circular path in a magnetic field B. Show that its kin 1c4gie.gvcr+ etic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of thiylc+8 ,26. hm1mx5h tlwjlkcf6 z/oye particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s0v35:s* d bcxfijibsa(n8zp c*1e;t z magnetic38tnb:;xb0pv z c sz5c1afei jisd** ( field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equator has magn5v-amu ;x*vxv itude $0.40\times10^{-4}\mathrm{~Т}$ 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 spe-u8m0 d7*0ershg5kpkyj dpf 8ed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 cu1injj1g.ktg t; o/ ae(/la/ exzl d./rbak o+0rrent. How strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field.a(ot d+/o /tekxz 1k .ei/jnrlg/;.ga0b 1lja $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to pr5g5 axj26k8lxhsl j+9; uuqukoduce a magnetic field no larger than that of the xja 65qlku2l89 xjskhgu 5;u+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 carrd e5y 4vmu5irtlv9l xlz1r,k v:*9ft +ies current I out of the page toward you. Indicate, with appropr9v,lt fm41kdlr5: il* 9vevxrz +5yu tiate 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 tuk:y8mecyh p):ow:h 2 -ux qi0flt 5,24-A current exerts an attractive force per u :2 xk0lf toc8 ewphuu:,yymhq )5-:itnit 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 oe355krcytnw vf:p2+q f the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same direnv ye3f5 wt2c+kr5qp:ction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried ob gv36 8op72thf :olfput 1.00 m from an electric cable. What is th76fltp o oh3bp2g vf8:e maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 959 kc7g 7dr bh*dpei1-o A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the -i 7*debrc kp9dgoh1 7ground? 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 t/+dm fs3 dcm6kvh2:x13.0 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 6 xmdc2k fsdh/ m:t3v+cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm lqsez58j) qm1p s: 1p m;r2djqdue south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s fimj:pqq qd8;p1 j)sez2r1l5m seld 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. What3+9bk :sk lmbmw 92ja qc-f1vd is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there poij c1qdm wkbm2- s+fb9k9l3va :nts 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 space at a rax n:sv4k*mrnt4 o)u1z 4 fop:jte 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 beyoxq 7+)j7 /jtsa okg; qw(ftudki(3, tween two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currents af)ikoj 7k(og( tqd;s/3 ajt +,u q7wyxre
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to,b e 49p.byg9x3cqwub , 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 from9uyxpgb bbw, 34ec .9q 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 ykuq6l++y5rb 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, cenr6u ylqb+ k+5yter 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 poigq((uh.cmd +l 03g q)y nt8+wp w,jvgbnts 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 wi5k:fqo9ylr o /re lies in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both 5oy:9 f/qr olkwires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carrig,;wseml+4 p-9qb c cxes 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 cm below (Fig. Below)pbce x,+;sc9w-gm4ql.
(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 thi4y)o9*tumcw. xp k :cey 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 carries 5.0 Ai p yco4ut c:kxw*).m9?    $ \times10^{-5 }\;T$

  Two long straight parallel wiresi 1) uurnkm1reh26 *gb are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same direction. 12 g *u6mhk)1run erib
(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.,g 5j1l/ws2w;rua ji f8 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 pfjjrw2a5; su1i l /wg,er 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 a83+s aspmkh ,6f(brhqf/ex c 7nd direction of the magnetic field at the midpoint of the side of the triangle between p7hbshx6 8,qmkera s/ 3 (f+cfwire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, qyny nbp5:s++ 8ynm-xcarry equal currents I in the same direction. One wire is at x = 0, the otnpy 5 +yyx+b8-nn: qsmher 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 as obwfai99-f8 total of 420 turns of wire and carries a current i- wfo9sf a8b9of 2.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.22bkq..g xjud -5 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 .xkduq2. j-gb turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-lon(boeo 0m8 1fy:ih7hdbg straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires thatofi 078 oeb 1hdmy:(bh 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 produ35 n )v06y wiao:ni67yjr/3pzuispzjces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something es3i5joj:piinuz /0 vyry6a7pn z3)6w lse? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shapey-z p6vv1w1 thfn 9r8d of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determihf1-wnt8vp 61r dvyz9 ne 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 tyit(fqfd24 h/ ugs6 cfa he.39o show that the magnetic field between the conductors of a coa g.t ffqy69(he34hfci/d a2s uxial 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 placvn03 f z1aqvopl3n4y9t:5wq s ed with its face parallel to the magnetic field between the pole pieces of a large mnpovaszn59 w:t3ql qy40vf 13agnet. 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 deflects full scale fo28x3 6yr+jjgt0mng x 4g tturk:w(sxw3d gv8 8r 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 j4 9szzzid4 s6bl.v7cgalvanometer weakens by 25% over the years, what current will give full-scs9lj svzb 7446zcidz.ale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torque chkxo0*j/ths5,ae6uevl b2; vbanvox;tke5l2e0ujhsvb/*,ab 6 ge?

Show that the magnetic dipoatj17b,1 z ytjle moment M of an electron orbiting the proton nucleust7jzbyj11 at, of a hydrogen 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 lies flat m3lwyg5,8 +2yptn iqgon the ground. The Earth’s magnetic field at ty3 w,5 p2lgntgyq i+8mhis 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(pv8y/mr,s4osd2u 5 v illq .o radius 5.10 cm in a 0.566-T magnetic field. What value of electric field cuo sip oydl,v2 5r.l(4v/8qmsould make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms havebt)g 5igr l6;z 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 76 u. What are the atomic masses of the other isotobz;6gtg l ri5)pes?

  Suppose the electric field between the elects123n k2vqkg aric plates in the mass spectrometer of (Fig.3qksav2ng 2 1k 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 1zc uh31wlxp4 being used to monitor air pollutants. It is difficult, howeverlhc4p31u x wz1, 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-h inn9aqof,b8 0 -jux a voltage V before they enter a magnetic fielh0q b ,jx-nf9nai8o -ud B. The ions 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 meter, and a 25au+b6: t5c gzs-A current flows through the wire. If the permeabia:zb+s 6 ugt5clity 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 turnl6)zse)v r8 we epj*p.s of wire. The magnetic field inside the solenr lvw.8j) )ezeps6*epoid 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 momentuk0zu+p7oebhe )e-0 d nm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energ3r.uz . e6mnpcy upon entering a region of cons6c.nemu3 pz r.tant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal currcli +bi h5 61rvlp2r u14gmco)wqx4l,ent of 3b)1 +12m5v4xchigiqplru l, 4 o6 wcrl30 A toward the east. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which i-y7 y, 82cbpbs.vhmohas 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 Earthrjja12;y dty:*p/.z ex*unya.7fekz’s magnetic field points almost horizontally to the nou7 *tz1er2 ejda.. ykf/anzpj:yy*;xrth and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium at w 8s3g2k1kiko,altfw /l:6 t st)dd)iom, 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 (Fig. Below). A large curr3 s vs/y ,o2fplhwt*m:kx/;ajent moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm,l*: af/sm pykwoj2sx3 v/t,; h 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 1.0;zg4 a:uwhrc7+zq 6:f t.p12eupqmu9p7c usx0-mm-diameter copper wire and is suspended in air due to the two magnetic focug42huz fm;7a qz+qt6r:cpup9. u :wp 7 1exsrces 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 suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plahm qx iwd ((j t77yon5-a+/ywcne act as rails to support a light metal rod of mass m (perpendicular tow+o/d ya 77yjmch(q5nwit -x ( 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 ellyqf i964voq.w*twzgp)4ir2 y;5q pdectron beam near the center of a TV screen due 9)qd rq w5f gi4;wp*6y.2vzipy otl4q 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 elementary parvo3 lh bmw*j/(qw ,y6vticles 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 “dees,” where there is an electric field E. (There is no electric fiel whbvy ,6vl*qo3/ m(wjd 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 straik)h8x3 t ycau3ght parallel wires, located at the corners of a square of side l, carry equat8ychk3x)u 3a l currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle akkfkfndl67 */y )eqm6 ccelerators 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 t7ledf/k m f6)qkk6yn* his 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 a circular coil of wire carrying a c-c ;zie n:5n( wajdg m/g.p3yvurrent I (as in Fig. Below) n /vmce-a5 ping3 wg.(dj; y:zis
$B=\frac{\mu_{0} N I}{2 r},$
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 is about 1Gg h30ycvthbkvs7lw 96w7d8d7($ 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-hhu+zzg4 fnju;8x:vw:n. gvo;q fj; magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you mightoh; vw fh84gfq .uvjzj:;-+znn; gx :u 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, traveft:eiuuun z82jj);2 cz ut3w- ling to the f-tz8zuw:uc nu 2ej)uj2t 3 i;right at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0.010 T, tg x7ejy.m4xu.*x bf ;v+rsz, perpendicula;xsr yfutj7bgx m,*4. z vx+.er to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magneticud yf6i/iv8k 3.fn9m g field md39i k u. 8fgf/i6yvnat 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 curr ookidzlva9yh dd i/g:ujzy*7jc/3 ti;, 72k /ent but in opposite directions. They are suspended by 0.50-m-long strings as shown i7:ddy*2 a,3g vjtikdo/u /i9k7 /y hozzjli c;n (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 unif9- dfbhgoe -(qorm 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$