A compass needle is not always balance p5p+s vitrc(o+4bv+id parallel to the Earth’s surface, but one end may dip downward. Explain.v4po5pt ir+bic sv+(+

Draw the magnetic field lines around a straight section of wire carrdve9+x g 8ly5qying a current hor5+lgxy edv8q 9izontally to the left.

In what direction are the magnety x+ +;iinnn9ym: t8 1apn;yhmic field lines surrounding a straight wire carrying a current that is moving directly aah;9mp+yny+ iyn ; tn8nxi1m:way from you?

A horseshoe magnet is held verticaze +op5i+ jn9olly with the north pole on the left and south pole on the right. A wire passing between 5+i one9zo+p jthe poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallicw;yl,,9 /zofbi.ufgst gl b25 object, or only those made of iron? (Try it and see.) Why o.bgz2bif/ty,u w 59fsl ,lg;is this so?

Two iron bars attract each other no matter p44,nboojwc raw6h+*gn6j5 kwhich ends are placed close together. Are oj4 kwr 6pjbgn*w +5,h4 can6oboth magnets? Explain.

The magnetic field due to current i6bugpjm8) 9w5+mff uy,dz gr +n wires in your home can affect a compass. Discuss the effect inf6+9,druzfb)gjp g58mmywu + terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field pt6kvf-0 pl 1;n ohf)mwhich pk-fmp n)06of1;tv hl 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 electric field.)

In(Fig. Below), chargec059qebvw cztyvskr6p0 8j; 5s;tm 1bd particles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the marspm0t65t 0 ewkjq;b9ys 18 v5zccbv;gnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fdiqkqe;a40 +y vdz*r,ig. 20–46. What can you say about thea dv*e, yri 0z4dkq;q+ charge on each particle?

A positively charged particle in a nonuniform magnetic field follows the el 4fh8(.inv najup-6 jl2(hztrajectory shown nhae-h2( (f64n8 ljpu.vzij l 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 mn2lz mwny05f tt05jjp 7pz 5:kagnet attract an iron rod? What must you consider tojy 5kf0 5:m50znjzt2p7l ptwn answer these questions?

Explain why a strong magnet held near ezsp9-51 lvg6 9o)w .tx fnrhta CRT television screen (Section 17–10) causes the picture to become distorted. Als9w 9gvlrte6.-)zn5ofpxs1t ho, 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 magnetized but the thirdstx*a:1yg6v e is not. How would you determine which two are the magnets without using any addition1ve g6xts:ay*al objects?

Can you set a resting e nqvv+si rxfw;xxu ,wk80w/):lectron into motion with a magnetic field? With an electric field? /iv+vxxr:k wfw sw n,q0)x;u8Explain.

A charged particle is moving in a circle under the influence of a u 5 dwtawwm9xi;8 m48lqniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, da d4wmwil59mwxt 8 8q;escribe the path the charged particle will take.

The force on a particle in a magnetic field is the 0w de::jx7nklidea 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 bnw0 j k:e7xld:lood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wicyue23 juzx ktjw8.8 z3z-4fb9a6 nd pre carrying a current from left fuapzk 3nb2y8x6- j dj 3wu4tze.z 98cto right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric.ep26q(z/5 b24kxdbirce j ff charge.e q4f2k6 ej.5rdcfpb/(b 2zi x

A charged particle moves in a straight line through a particular region )po,q,v75riopx-z vhjw 6 t -jof space. Could there be a nonzero magnetic field in this region? If so, give two possible situairh-vj,xtz7 q)o ov5p6 , -pjwtions.

If a moving charged particle is deflected sideways in s+i p8nze. n ;ma7pvavvip8+y8ome region of space, can we conclude, for certain, t7a8pvvv; i +8ie+.nynp8pamz hat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a unifoul,btur59 j7gj,is o+rm 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 movina zpmd3;5nn79ku)ycxa3l ut6 g electrons in a certain region of space are being deflected by an electric field or by a magnetic field (ordnxka3 7z 9cu65) uap y;ntl3m by both)?

How can you make a compassyy0 :i,.( c/r)ehor0gn z ry1kmypdi* without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angle. yla.4tqlam; 4jn2ad s to each other, but don’t quite tm4l.2j tq;.4a y andlaouch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free tssqsu.d 6 )aiw;5 hnqw6a2h )tzqw(3so move in Earth’s gravitational field, is suspended diszahs;q6( q).d3qsw5isuh2t a w wn6)rectly 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 unmlxqhs j(0o5j-agnetized piece of iron?

An unmagnetized nail will not attract an unmagnetizef; ct*d(me j u47fqum;6oyyo5d paper clip. However, if one end of the nail is in cc*uq(f uommd yj;;6yt7e45 ofontact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other iswpoxai k8l/pp53+i:b s-ko p 9 doubly ionized. How will their positions on the film of a mass spectrpokio +aslpx3k- :p8bpiw95/ometer (Fig. Below) differ?

What would be the effg;tij,l x )uw9ect on B inside 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 t 59smac p/lq, (9zv t2bql2d/f qqhu9co a solenoid is a relay . A relay is an electromagnet (the iron rod inside the cohu q 9c9 dllb/p 2q9(q5fm t2c,/vsaqzil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straight wire cau ++tf4qw4ay9 +pvr lrrryingqfp4+raut9 +wyvl4 r + 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 160-m length of straight w3 h 8og/amnn ;.3ledo;icqe6yire stretch .omyne igeh 6qa/3nd c;o;3l8ed between 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.t e f in.:/muw*jkza 2 qgh(2tn4zt+v of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Eartqtnekwht:2 zg.fu2/vnj+m.ti a( z *4h’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 5vs eenn/: ry5long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T field? 5nynv/e s e5r:    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizoazxf.7f+ )rlpntally. At that point on the Earth’s surf 7.)+rxzlafp face, the dip angle 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 1.2/ bi*j*(5u4en; wa5rd kpjljfdaz/ est8x.i28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is5 idxnpa*e. /ji84 (j2b/l5rf z*jk etws;uda the approximate strength of the magnetic field?    T

  The magnetic force per meter on auevirbs; o07k2 ;0a ky wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a mk2;uyai;v er0k bs7o0 aximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum yyuvk: az 9/8xity67uof $ 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 w.r1f7isldbk7d bl6(q5 gn /m xire could just “float” horizontally in air because of the force due to the Earl / fdq7di .r(lkmxn5b1 s7bg6th’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 char8a y. 7qy5xudf /ao f.b8,waqcge $q\,=\,+2e$ 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 magnitudgg d2;i:v94m7 tu ppwu6m 2gpye and direction of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negay*ce sq1,xy /qtive charge for each diagram shown in (Fig. Below)*1 sq yqe/,xyc, 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 of y k*wi-: -;xoa3ooqax$\vec{B}$ 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 upfje a:9kw*v/roumk *( k0cl+vward 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) ./ cl eboxqr(it /41hyproton enters a 0.20-T field, in a plane perpendicular to the field. What hc qbxi4 t/(o lr1e./yis the radius of its path?    m

  An electron experiences the greatest force as (rt zah1k+g80y)mg tjit 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 pas /bwn o;*,ogm6vw h.nosing throug,m w*/;n.ovgw 6b oohnh 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 whose mass r d,v/n-3qtypzzwrakmi7 6)4 lx)1 y tis $6.6 \times10^{-27 }\;kg$ 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 chargo)eppf f/hc/ 0c5e va,e q moving with constant speed v to make one circular rev eh0/ af,5 e/fpc)cpovolution 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 radiu-+6ksj n,y havpz-7gto,m.k is r in a uniform magnetic field B. gn -6 ,7vsz-kkj .mtp h+y,oiaShow that its momentum is p = qBr .

A particle of mass m and charge q moves in a c051qm23 syb,kr4 gdm bq9 avgeircular path in a magnetic field B. Show that its kinetic energy is propb2r5 9eag 0q3g k y14m,dsmvbqortional to $r^2$, the square of the radius of curvature of its path.

Show that the angular mome gc82ke)rda 3entum of the 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 Eaj23sa( xtnaw +pa 4hg;rth’s magnetic field sgp( ja ha23;at+nwx4 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 magnitudeqy16pz5kl g*u- /-xiipi5)l obv d:l w $0.40\times10^{-4}\mathrm{~Т}$ 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 spej(so v *lb7xs7gw78vxed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehiym )qe1 tkg8s9cle carries a 65-A current. How strong is the magnetic fiem891 gsytqek )ld 6.0 cm away from 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 produce a magnetic field zht *xu07f h3yno larger than that of the E3u hy7xfhz t0*arth $(0.55\times10^{-4}\mathrm{~Т})$ 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 Ia qwado:ewy( p x.5hku-uf7b( /5upv. out of the page toward you. Indicate, with appropriate arrows, the direction of p / ba uy w.d-f5ouke5wuv7x:h.q (ap($\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A current exerts,iupuyge -8d/e ( sktp1 ;yqj; an attractive force per unit length ofeg;;u8jyk( s/y, de 1pq-ti up $8.8\times10^{-4}\mathrm{~N/m}$ 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 a(9 wy(gvdmx3q;vhfvw*s 95 . tr8akgrnd direction of the force between two parallel wires 35 m l(w98vw;vfggy3*(qdt mxa 9s.kr 5v rh ong and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is b6ljeo: .cvhb9eing carried out 1.00 m from an electric cable. What is thel.:6v j9bhe oc 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 top e qiu5.sfd4x8ll)r 1ritx-gm26v4 .mu rj5i xs of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare wituir glv4.i.dqmi8sut546r 5)1ljxrxxf-em2 h 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 25-A currents in the saed4eze;dg( )zhcl) j,*orks i( +f+ssme direction. Det*dc 4oe)ers;z kf ,+l(js(h+iszd)eg ermine the magnetic 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 cmd b 87upx6og3u2unim 8 due south from a straight vertical wire carrying a 35-A current do6o p8n3 b8g 2mxui7uudwnward. 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 thaly +3mf2 1nr9tfdo2u(cheb: e net magnet at21 c 9obfle:drhy3nmu f2(+ic field 20.0 cm due west of the wire if 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 space at a rate o: 5-l ykpk/aelf $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long str,1pt (q m6sw w/w;hswvpj ,fo4aight wires 2.0 cm apart in terms of the current I in one when the other;(6sot fv/w4w,1q ,jwm pswhp 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 dc cfadu q-ip xw i4+b/2uq-pv+ a8urrent to, and from, an instrument. If the insulated wiresfd2ui+xq-w+qv/u48 -pb a pia 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. 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 v /qkz2)y akq u19vux 0bg/vx9in (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 othzb ukxu/q9k1 0 /axgq)2yv 9vver 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 k ws5wso+wvp-/u5 z0r23$^{\circ}\,$ 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 shown y-vnq2 (vfwa5 in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force v(aqfv25n wy-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 uahn3fi-dgm7k :5yb5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fd35gh ufa 5-y i7mnk:big. 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 orientn0sgxwj 4.vagw 1b/.ynt22hb ed 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 yb .2t1x.avgh /wnn4jw 2 bgs0carries 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 carri8.yrn ml w2:ufes 2.0 A current. Wire B’s current is 4.0 A in the same di ryu f8lnw:m.2rection.
(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. (Lookt upjov 1m4n am+0;,v9cc q.w,o yf4sving 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 isc yqv, , +;9p0vcfso1 44am.vjoumnt w 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 tdc z1y(oda s -1ebk,k,he magnetic field at the midpoint of the side of the tbcsdeydk,zk- ao11(, riangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d x q6ns;wb h +39ine.ioapart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below)b n+6qhwoi9.;e3ixn s. 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 kowpb.7 )y)wqof wire and carries a current of 2.0 A. Calculate the field insidq kp)y bwwo7).e near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0wcw5 qvi.wtab( 031p 65u yopw.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wire? p.qicwtu 5ww boy a563vp1w0(   A

  A 550-turn solenoid is 15 cm long. Tj:bp.biwj -+ehe current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and ii jjpbb. :w+e-s 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 coppeqynyos3g a et3 lg;5eq5 ;z:)lr and want to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copperq;: ye3tesqz3n log )g;lay55 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 shape83bp: bu*sk3(ukwjg5vp9sqt of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in pbssj q 5kpwu39g8*:ub3 v(tk (Fig. 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 (r m7 ggy.; zl70+eu-heh6ulrwn3mxw the magnetic field between the conductors of a coaxialgu;ehg-mlrw eu x6hwn70ylz3(m.7+r 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 wgx 6.rplm )wmins0,0uybr*q(5f/ zgy ire 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6. *f,mb5gy6 pu0/ iy)0xrwqsn(g lrmz .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 deflesyd d1gj s.jj0a 1/p6vcts full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer - a+ zpe:d.a00cv aermweakens by 25% over the years, what current will give full-scalzce0a mda:e-r av0p+. e deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does th8m/j5ol pcke3h8 z-5:wj ofvkjw a:)ne output torque chaw j8pfov5hj a 5:onjek z:c)-/83lkwmnge?

Show that the magnetic dipole moment M of an electron orbiting the proton nu xxnxb6fuq f0z/3.*tscleus of a hydrogen atom is related to the orbital angular momentum L of the electrf0tn * xu/bz3f.x6qxs on by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter 0 ;vu u42f(xhidj)dq g)gy3 dvand containing nine loops lies flat on the ground. The Earth’s magnetic field at this location has magniud(q4f 3d)2h g;ix 0v)ugv djytude $5.50\times10^{-5}\mathrm{~Т}$ 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. Whc it*l*a*g1 s1 /voii/ dupo,iat value of electric field could make their pathudl*,i/o1tc ai o/ si*ivpg*1s straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, gerthwtox:s k2 /9manium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic mass9 w h/okt2:txses of the other isotopes?

  Suppose the electric field between the electric pl paugm u 0pwy6;aw*7c7ates in the mass spectrometer of (Fig. a7 gwmu;pc06y a7uwp*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 ikl p. b37 cmwucz4z;bz94ru*vs difficult, however, to separate molecules with nearly equal mass such as CO (2vzl3wrz7z b m.9k4u4uc; bcp* 8.0106 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 as)rjd658hyj accelerates ions by a voltage V before they enter a magnetic d)rs6j58ay jhfield 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, akluc5 /w q.jo :zt7* 0mlu9pamnd a 25-A current flows through the wire. If the permeabilit5z/m.clwa: jkolup mut9 *07qy 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(wx l1phf113ykjdqb2 1.8 cm in diameter, and has 640 turns of dq(fy3jh21 xl11 bk pwwire. The 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 momentuffs4az0 k1hh303err gm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kinetidzuyw3 vc b/77 fx06tcc energy upon entering a region of constant magnetic field. What is the ratio of the radii of thf/y03w77c6tu x d zbvceir circular paths?   

  The power cable for an electric trolley (Fig. Below) carries ahx g5r2d c65 5i2gswc6o do7nk horizontal current of 330 A toward the egr6o ikc7n 56 hwox5d d2gcs25ast. 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 charge ofh6gl d8 .c67 tzuj-gmtqk6p2j+( xkup 79lk nk $1550\mu C$ 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 magne.x5 boe*haok4.oi9* de+pfjz enka .: tic field points almost horizontally to the north and has:eobapn.*ohe4 ok5 k x*j9.diz af+e. 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 atom, 5wl8 jge+jr1q -;z0mg3rs rmqwhose 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 current moveih (( wn8kjt,i* (tefcs 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, 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 magn,k( thec (jwi(8tn f*ietic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top )sp -qqnc7sj. wire is 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the re-q) jn. ssqpc7quired current flow in the suspended wire.    A

Two stiff parallel wi4wbxtv7j6 9kq res a distance l apart in a horizontal plane act as rails to support a light metal rod of mass 6kqw bvtxj79 4m (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 center+ +aslvqyc hkrg,i8*/ of a T+y +,k hcs8ga/vli*rqV 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 elementary particles c0cai ve0/j d0such 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,” w0 / cj0ecdavi0here 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 wij a yt9yaty/ 6.)kbuszy*.z i3res, located at the corners of a square of siday z/yk6tz)j3t* s9b .ayui.y e l, carry equal 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 acceleak) *0sug ahi7ck::pj-6remk rators 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 wickkgre7ua -6asjm:kp*)i :0 hth 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 currenoxv l 70phz6hc6:8i rva aw2c,t c6wr:v xv627,hai8l p h0zcaoI (as in Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic f b j:,m9 da,cibw(,oyjx g;g*bield 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 mag 7(a )a9siuqih(dv :kgnetic fields produced by overhead power lihiku d )aiv g:(q9s(a7nes. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic fieldv :wmuvn+m/o4uwu7e j0pkq )) would make a beam of electrons, traveling to the right at a speed oqvj )0wo+/4:unkwup vmue7)m f $4.8 \times10^{ 6}\;m/s$ 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 da0mnb5m7 w;;l vh)st 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 and 8.5 mm, respectively. Calculate t)m n;bham5vstw70dl ;he 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 magnetic fi,tzsmm b )+/gield at its center. If thegb,mi tm )z+s/ maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires,c+w sjhn. z(h1 each of diameter 0.50 mm, carry the same current( jzcsnh. +1wh but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform ma;s0jtuoxlt q3tymx p (fj62oiai ;6bv,27ny: gnetic 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$