A compass needle is nqh*m 5f,lmw ahud8dx1 4cb3r:ng6ld *ot always balanced parallel to the Earth’s surface, but one end may dip downward. Explainf6*8lua* 3l4rhmbn 1qxgchd 5: ,wdmd.

Draw the magnetic field lines around a*esq: x2 qe5kzbdv ;l1wh,y-hi vbd: , straight section of wire carrying a current horizontally to thx:d*2q5i1q wvh;b ybhe,z e-,:k vdsl e left.

In what direction are the magnetic field lro,8io/ 4co chczi 81i)iot. 3vbuj (pines surrounding a straight wire carrying a current tha i 8iop.b/vhjz8,4o( o itc3cr1)c oiut is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the lefth/t0+0m9pm ,4wako dxmr e.ac and south pole on the right. A wire passing between the poles, equidistant from them, carries a currpmmeaa+/w 00t, r.d9k ocxm4hent directly away from you. In what direction is the force on the wire?

Will a magnet attract any cjb8- noin/sm c8 (d2vmetallic object, or only those made of iron? (Try it ad/jm- cn2vsi con8 8(bnd see.) Why is this so?

Two iron bars attract each other no matter which ends are placed close ady5/o6ui.h c fd5wj-z;vj/n together. Arenj ;z dod-6c.//5avijwfh uy5 both magnets? Explain.

The magnetic field due to current in wires in your home can affec.;gedhkmdt.j b3 q ,z6)hog 7kt a compass. Discuss the effect in terms of currents, includind)h36.gkk,eh .7 q tmodb;zgjg if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field we )qb;t r7vfg(hich is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Expletfb;g v )q(7rain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-carrying uc e0nzf i9l.(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 magnetic field produced.i(9lc f nuz0e by the wire.

Three particles, a, b, and c, entn) f6pg/jult 4er a magnetic field as shown in Fig. 20–46. What can youlp4n tfj6)ug / say about the charge on each particle?

A positively charged particle in a nonuniform m xrdmb(t/m x2vdv0)u*dr02 ru agnetic field follows the trajectory shown in txmd)rdr 2 *x2/v00 urd v(bmu
(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 ani 12fhk v/4(codnoce 5 iron rod? What must you consider to answer these questions?n k41oc2i(ve5ohf /d c

Explain why a strong magnet held near a CRTv7v- up0uiw w) television screen (Section 17–10) causes the picture to become distorted. Alsv07ui)u ww v-po, 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, twons /b q7nlb:4mkx7hq - of which are magnetized but the third is not. How would you determine which two are the magnets without usingnq/4k bs-7lx:n h bmq7 any additional objects?

Can you set a resting electron into motion with a magnn6y5fs 1q 1wrwetic field? With an electric field? nr 161ww sq5yfExplain.

A charged particle is moving in a circle und s-z8j7azdkcc (y+dq;er the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particccz-as7 k (8zd;djq+yle will take.

The force on a particle in a magnetic field is the p iiz9 1nhgfwnqy;7,;idea 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 sh n wzqi9n1fp;,g7hyi ;own in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire c)nby9fuozcl 16- s h7zarrying a current from left to ryoc 69)zuszh7-nl 1 fbight
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric charmxjt7ui ;t 4u ;j4vi oniw;o6u2 ,cpp5ge.6uw2j ijim;pc7;pi4tnv t5x,o4 ;uuo

A charged particle moves in a straight line through a particulatq :uwi8gzsx 5 2qdvyqj2)s:4r region of space. Could there be a nonzero magnetic field in this region? If so, give two possiblevguxq s 5qsyi)28:q2 tjd:z4w situations.

If a moving charged particle is deflected sideways in some region o6gxyyebqh6 m u7(y58vf space, can we conclude, for certain, that m6h bey8yu7(yqgv 6x5 $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of spaced9 zs8l 9j;ng10gzaej there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a cer 12r5z,raqm g(t20a zsg,dgm dtain region of space are being deflected by,zdagzrm2d (,qa gsm10 25gtr an electric field or by a magnetic field (or by both)?

How can you make a compass without us/k,,p *omqpty knj(p 3ing iron or other ferromagnetic material?

Two long wires carrying equal currents I al/u), co,f33 inb70a kml dxnbm)co0 wre at right angles to each other, but don’t quite touch. Describe the magnetic force one e/luinmo,ax 3f)7d0 b,b cl3mo0cnw) kxerts on the other.

A horizontal current-carrying j6ep 2ch(a0j4q3gct pwire, free to move in Earth’s gravitational field, is suspended directly0jctq pe 64 3g(hpjac2 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 piece of ironc*uy(f 0+uc sckhz1eg(ug7s ey7 )i9 h?

An unmagnetized nail will not attract an unmagnetkk q47eipp kaf++1r +f+c7un jized paper clip. However, if one end of7+jr pkf 4+p1 f+ e7ic+kauqnk the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized aj9e;kx9bz mm0-36bfbd eob5 8vy hh:hnd the other is doubly ionized. How 6mxz8 -; bh0eeko by:5b93d m9jhbfv hwill their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside0j cz4:(i+*s5bdl d ) pra fjfdf42hjt 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 relayn62tith73ydx4q rki9 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 switch on a circux4r q2tdi6h9tnyk7 3i it 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 perpe(9,n*8 tr ipx wsq8u meter of length on a straight wire carrying an 8.40-A current when perpendicular to (8ruiqep* tw 9p8 sxn,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 magnitu,vnm x,1nnyueb-y8 / unuj0*l de of the magnetic force on a 160-m length of straight wire strun- yjn1bn8uuy x0 */,,lnmve etched 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 of the magnetic force on a 160-m length of straige)yv m4y rs8c2l n4tte09o q)vht wire stretched between two towers carrying a 150-A current. The Earth’s q)v n9eet42l4vo )crm80ysyt 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 maximq q-e(em3caxt9: :wqt 6h rvy+um force on it is 0.750 N whhc+9w3x-m eq v6tytrqa(:e: q en placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is or7 nln 1 5krc;:hjuyw(: lip;nxiented horizontally. At that point on the Earth’s surface, the dip angle of theyhnlpru::wnc( 1;;jk5x n l7 i 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 ca3v tzmna u* kd:t1ih64+ z9tkorrying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter,419kt+ nao3 6vz zhui:d m*ktt what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of itgms4 *993vll6j xzunn s maximum possible valulgx*4v6sljumn z9 9n 3e. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is :jqxdvu2 +8ewfpg j f50yp -*ea maximum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-md78x7ak,uqlr.5qyk w ;lb.r j9,nkc r*hwr*a m-diameter copper wire could just “float” horizontally in air because of the force due to the Earth’s maq 5j rak unk .8hlcrwxwl ;, a,*rqr7.97y*dkbgnetic 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 char a/6we l0+98uiqpzxqnge $q\,=\,+2e$ 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 b8zklh(( ii r:qe ck:bts,fh6z:.u5lon an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for each diagram s on r0czx1(;- x l9ngw;gbtpy/hown in (Fig. Belowx/ytonn -r0( 1zbw;l ;gg9pcx), 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 directiongt0 l 3 8vepn8dx5v,rk 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 projectrr d9xio2hrt n 0)8i-kv pg-4eed vertically 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 pi,vq u j(qh2w4erpendicular to the field. What is the radius(hi q2ujqw, 4v of its path?    m

  An electron experiences the greatest force as it trave)ado 7j cl*9uvls $2.9 \times10^{6 }\;m/s$ 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 electro0s2 0x+n(j6i 9:camr on5ybj r0tywpt ns that go undeflected when passing through perpendicular electric and magnetic fields of magnitud0rx jrby t0 tmosy6c w59 :nn(a20jpi+e $8.8 \times10^{3 }\;V/m$ 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 wha4z c(ob/5mx c40; 8yqo eoaaaose 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 for86u)g okl ju;7bc;niv a particle of charge q moving with constant speed v to make one circular revolution in7 ;b8c oviukl) g;nuj6 a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a umbjg/:*rv -zr.kq vf5 niform magnetic field B. Show mr.5v*kq/r:g zvj bf- that its momentum is p = qBr .

A particle of mass m and charge qw )mlsjpi: :s: moves in a circular path in a magnetic field B. Show that its kine s: milwps:)j:tic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angulasfthpe ik 5p1omy 4sd..gitop v 6/*.1r momentum 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 1(l-0edq1fs.ce chq8s 60 m/s perpendicular to the Earth’s magnetic field d-efs(cqeh q1c0 .sl8 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 fxs efqwa2,zo6bq v -p/jn *8m9ield 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 withmea+ou 1: k6zx2brz 2g 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-v0w a6*mwt ,s:qt.yxoA current. How strong is the magnetic field 6.0 cm away from itmyw: 6.qwv xt *osat,0? 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 jzk5*c5sdc )oy x63rgno larger than that of the *c55xrgjy3ks)d zo6 cEarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long str 0mq*ha5a9haq aight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction q 5mahqah*0 a9of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wir k;fhymsut( 8lwqh q,)q;f(l ;g+dy q,e carrying an upward 24-A current exerts an attractive force per unit ;h f8fl;q(ky) dl mhu;sqq gw(y+qt ,,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 direct*e e 7,yfe85zmkk fdi.ion of the force between two parallel wires 35 m long and 6.0 cm apart, ee i ,f75k.ef* k8eyzdmach carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m fro3oe :h*cofg:c m an electric cable. Wha oc:c3heo:g *ft is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current o1s )54v nhla5 3sjftxjeo/mh* f 95 A along the tops of 8.5-m-high poles. What is the magnitude of the mnj4as h/oml5 fvex1)s5hj *3tagnetic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A curre 5xyphhxu.z mmak8p:k z- (37onts in the same direction. Determine thhz.mkka y( m7puz 5h x:o-8xp3e 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 cm due south from a straight abp8vv9q 9 7trvertical wire carrying a 35-A current downward. In what 97a9vvt8rq pbdirection 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-mbp/pe wo:6w is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but db p6/-wemwop: ownward, 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 i z*4jryv gxn)8vw9j ,hhk+rb +h+*f/gubm g0 a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wires 2.0 cm aparv8 m:,-t nm6jo tuvp,xt in terms of the current I in one when the other carries 15 A. m:vv6, p,-mu 8n xtotjAssume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and e4 7r:0kg: bxxa,ljr wfrom, 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 midpl4,ew rk7: xxjg0rba:oint, 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 pl k6 m*7to3xjjfane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other x7 f6mj okt*j3two 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 pointsc au s .hpftr5oqfdv,.d**89ldsn s)2 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 te:8kq;. ar,sbjeq3 idhe same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in ks;eqqb:e aj 8,3rdi. both wires. 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 carries a current of 48 A. A second wire, mav;x0;zwoe 0uvh8ko lp)1u x-q de of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetickwuq;0po)8v xz x vh-e 1ul0o;ally 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicular to each othylat 7 e*v)d1ier. 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 1vedl y)a*7ti 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel y ekq fam:uhl+ .lsg38,m1:ax wires are 15 cm apart. Wire A carries 2.0 A current. slu. a: kqalxe:y,1m+8 fh3gmWire B’s current 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. :kycd2c) zsq8(Looking along them, they k)cdc zq :sy28are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit 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 06j3oh(; p.lms j zp ;xbtu5e)0l coxuthe magnetic field at the midpoint of the side of the triangle between wire M a.0 zp6ljlco3j 0;u be xpox;u ths(m5)nd wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I in thp mjcupp+9m 9;e same direction. Onep+ m9;j mupc9p wire is 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 solenolb jb/ x glhv+*d x4/(vaw.vq x:mu2;oid has a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside nehvxxx v: bo4/jbgv/l2* uq (d; wa.+mlar the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diz8 13s5lhzxar ameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if zhzs 8 153xralit 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-ct8h+c1e z4g9rsb zgoc6f02fdm-long 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 wcs 9ff2zr c1dbg+64o gez08thires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practh:h :hv pq.8,3wacbbxical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat,w ::h av3 bqbx.8p,hch or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape o3)t+kapcss h+f a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine tk +p t+3cass)hhat the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the cov;.o w4.tibt m;1quj4;wdu minductors of a coaxiawbw motd ;m;j4u41 qti.iv;. ul cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed with i v4+w:rh (1vr7 qm0x0tha2 fl0tq2 e qnlorcu(ts face parallel to the magnetic field between the pole pieces of a large magnet. 0 + 22(fev01v mon4xtqrlua(hrlq t cr0wq7:hWhen 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 for z 03gm.3euh. nli, roxa $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% over the years, what cugj yakyhu u 096(fsy,*rrent will give full-scale deflection i*jh0g6ufsu (k yayy9, f it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, byt+9gsk )ir*. geiqjx7 what factor does the output torque chgj.q* ks7g)i9t+x ie range?

Show that the magnetic dipole moment M of an elev49e d vk31.a lasp3qpctron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the elecde9als41. a3v vppk q3tron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and kcap ;h5:y5lkcontaining nine loops lies flat on the ground. The Earth’s magnetic field at this location has makpc:lhy ak55;gnitude $5.50\times10^{-5}\mathrm{~Т}$ 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 m/qnh 7x.+x/m fftnk - jlrc(/a 0.566-T magnetic field. What valuh/kjm+f( x7mcrn. /f /l qntx-e of electric 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)yd a*xwrixt* (ja3/kpy-ypp 6 90.h3jx rzw c equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of yxaw)3kpyp / j9*pyx3xr -hjdwtr0z6c.ai(*76 u. What are the atomic masses of the other isotopes?

  Suppose the electric fielfc6abcmk4pg u0r9kbm3 9/d9l d between the electric plates in the mass spectrometer of (Fig. Below) m/9mcp bc9k6dug3l br0fk49 a 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 moo;j )f3k 0yup +jn7xyunitor air pollutants. It is difficult, however, to separate molecules with nearly equal u;p0k )3uxf yyo jjn7+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 spectromete3cb,fsd ( 03ho6iryjgr accelerates ions by a voltage V before they enter a 3bjo( sf 3yg60d,rcihmagnetic field 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 me0b )r21qiar1wh4k2fwqr( kj2tefir 0ter, and a 25-A current flows through the wire. If the permeability of the irob e1ki42w)a qi 1frtj0(rq 2rh 0rfk2wn is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and has 640 turns s)8+wp5zkdvw0 uy 7j+tx qmt6 of wire. The magnetic field inside the solenoid is 2+0y7ut6 p8 +5)wsjdmzvqt k xw.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 momentum vo c6 qihtm*in062zn 9$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kingz.ddegf+b93xf81 qycc 1 n4netic energy upon entering a region of conf481 bx czdgnyf9qdg 3ce.1+n stant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig./w4 h*s6+qdjxuks ee ;0fkv*g Below) carries a horizontal current o* f6;x w+k04hq/sejdk *ugs vef 330 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/r;dxqnpab8 q :; xas h( k;mnoy5+x+k an airplane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Ejx u.lo*ja(b8 arth’s magnetic field points almost horizontally to the north and ha8ax(uj jl*.obs 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, whose** .(h.owzjg mssqbk9 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 cur6:/ lo kc3ez5m/ :dxu*twdt bfrent 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, a mass of 1.5 g, and is placed in a field 5tzb: 3wf/:x kl m/cte*6u oddof 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 ptopvo4x u5j6 sj)3 k-p)-rf gwire 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 required current flow 5)txpfos vk-j-3 p4)6jprgouin the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act as rxv3 p21w)al m oxmv;k-ails to support a light metal rod of mass m (perpendicular to eachvk x 23ma;-1wlompx) v 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 ma +qkdjj0h )7g 0:nfu8krm9nx qximum deflection of the electron beam near the center of a TV gkukh08xm )r9qjjd7 n+0:nqfscreen 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 s.,e0wd)lwo8ud )ck4 b5nvz uuuch 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 field inside the hollow metal )w)0vnoul 8,zu 4uc ded.w5kbdees.) 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, l7:4y 4dc.gg jounw6mjocated at the corners of a square of side l, ca. 4jwy4jc:n7ogd ugm6rry 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 verjzo+i qr)vq -2y5-p gmy useful in particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that arej2- i+qm vr-qp) g5ozy 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 cv x 93m5s6z)tngqxh b/atu5(xenter of a circular coil of wire carrying a current(qv9sxumh6)3t5 g5abxx / ztn I (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 fier464j(zyj5be i4f j dold 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 magw+),e uyt2z . xmlun/qv7w5v hnetic 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 might experience walking undew+,q7l2ynzx v)/m 5w euv th.ur 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 electrphkpk3d.7hnuv7) pt9y5coq(rm( r -pons, traveling to the right at a speed (kp hrh97n3)yotq7-vrm.pcpud(5 kp 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 acmv+ h;az-y;; hg-vdm gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at po+ vm;;azdvhg ym h-c-;ints 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 magn7+gu m zenj5y8z )5ws pw5(oso1r:pfpetic field at its center. If the maximum current is 5.7 A, how many turns must the solenoid hav:uf5wspro(ngj1mpo 5zwe78y+s p z5 )e?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry mgxzw v4gs5n-. dy:u, the same currentsy g4gmnw, x.5dv:- uz 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 magnetic fieldds-lzyk 1;s *96vmjlc7ne q6o 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$