A compass needle is not always balan b 2c h,+:pf)4oxawjlnced parallel to the Earth’s surface, but one end may dip 4npbf+ho x 2cal)wj:,downward. Explain.

Draw the magnetic field al4,.y.d nr;v)rw0k 2a.(gsn asy* nicz1wpj lines around a straight section of wire carrying a current horizontally to the left.s ja rzd4) c1a.;ps2 g(,k..nnvn0ry*waw lyi

In what direction are the magnetic field lines surrounding a sezla -8fe3 h5utraight wire carrying eue-afh5z3 8la current that is moving directly away from you?

A horseshoe magnet is held vertically with the,;s b+ 3wvhh aism-np; north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wir;npshh3 w+,bi-;avmse?

Will a magnet attract any metallic object, or only those made of iogmd rgq)y9( 7:d(t dtron? (Try it and see.) Why is g t7d) (dt:9odq(y grmthis so?

Two iron bars attract each other no matter which end5f-xblpr: )vm e- 8fm; ph+ntds are placed close together. Are both ma eftmx-n;f5r)m-h bp:8 d+vl pgnets? Explain.

The magnetic field due to cungsug06/h:c- x(ak qzrrent in wires in your home can affect a compass. Discuss the effect in terms of currents, incluxq: z(/n-kc g6s0ugahding if they are ac or dc.

If a negatively charged particle enters a region of uniform mathb vjzvq+.i746w,zi gnetic field which is perpendicular to the particle’s velocity, will the kinetic ene.q, 4iivz+7 zvjhtw 6brgy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a curreuhvzj b :478ebnt-carrying wire. For each charged particle, the arrow i84uh:e zb7 bvjndicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as show 2p,j xp65ctgxn in Fig. 20–46. Wha 52ppxx,6ctg jt can you say about the charge on each particle?

A positively charged5vsg uqejxa/- wq38-o /-zpew particle in a nonuniform magnetic field follows the trajectory shoj -3q/guxz- e e5vaw/qp o8s-wwn 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 attrac q (+ldgeait.;t an iron rod? What must you consider to ang; t(d.lei+q aswer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–109w / q:q4s3xodv6 satn) causes the picture to become distort a 9/tq 64dxn:sq3voswed. 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 mu( scn8. uh7qgagnetized but the third is not. How would you determine which two are the magnets without using any additional objec snq7g(uh.8u cts?

Can you set a resting electron into motion with a rs p:kanf25w+w p /c4ib9 rdd6magnetic field? With an electric field? Explain f4a:drd 2 9p+b6/kswc5riwnp.

A charged particle is moving in a circle under the influence of a u0) 1odqi jpfs- rj+(diniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, descri+(jrq 10sd ip doj)i-fbe the path the charged particle will take.

The force on a particle in a ma 9*cz8picu6qjgnetic field is the 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 shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magn9iq j8z*6upcc etic 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 carrying4rbw2 ybs, *el a current from 4*ywbeb2s ,rlleft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric charo-35fif k c+ykge.k5 +fciok-y f3

A charged particle moves in a straight line through a particular regioe x4: 7btkq 8wjttp +phy-x;*hn of space. Could ther7yt btqpwh tkjh84+p ;-:x*x ee be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected 4mf1mrlfnl4- zd.qy+9 z sr:wxw6e3msideways in some region of space, can we conclude, fd+zwm. 9 -lxf qrwm63enm sy:4 lz4f1ror certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space tht,0i-yi -m 6i:(xltpeozz*0f/uhltt ere 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 certain regi4jq05ngs a)-aq *.mzy mmgdw5 e3j q:eon of space are being deflected by an electric field or by a magnetigmdwa* j 55mq0sq:ymg 3z.enqj4) ea-c field (or by both)?

How can you make a compass without using iron or other ferromagnetic material.g/nn:rbow t w fbh187?

Two long wires carryingx-b*0b74b hqpm:xpf m equal currents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts ox xpfm- 7hmbpq0 4*bb:n the other.

A horizontal current-carrying wire, free to :fqdsn:s++wk0 *.eb *qql gfz move in Earth’s gravitational field, is suspended directly *:q sdfzq .wn g0 ek+f*q+:lsbabove 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 qb.na jlm(v1t (,:ydi piece of iron?

An unmagnetized nail will not attract an unmagnetized paperc 5eu,,cj ssv7 clip. However, if one end of the nail is in contact with a magnesjv 5ue7,cs c,t, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singksq 9i2 (bh 3i4o1vutfly ionized and the other is doubly ionized. How will their positions on the film of a massv(uib2k o34fqit1 hs9 spectrometer (Fig. Below) differ?

What would be the effect onufris *6k y11i 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 to a solenoid is c;p2sy 8za-xr 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 uz;rxc 8-psy2 ased 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 p;qb doffsr*:1d+2d6lz mr gkx8/ nc 4length on a straight wire carrying an 8.40-A current when perpendiculam8d f bo;gfrx/n1 c2*p 6:srkz+ldq4d r 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 lengthh k 8cs313;:mljy pfqe of straight wire stretched between two towers carrying a 150-A current. The Earj;hsk8q 1e m:pfly3c3th’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude oi.4pqj:qn j 8wist:w3 f the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetici:w q84jsjtwiq:n .p3 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 6j2skuw3 bz/glong if the maximum force on it is kg63j/wu2bs z0.750 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At ct)p 0.y h4wkme,zvv/ that point on the Earth’s surface, the dip angle of the Earth’s magnetic fieltkc0,vp . y/z h4mvwe)d 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 5 p di)om xx4s6 wpwk4c1o5v1iis 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, what is the approximate strength ik)wi4p6wvo x 1 d451mosx5cp of the magnetic field?    T

  The magnetic force per meter on a wire is mc uc :xw:6dle,easured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum,:: 6xce,u lcwd and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire i318o*je+umzr yz.z/x qr b+jc s a maximum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “f:cp4y6it 98m dnrh7ruloat” horizontally in air because of the force d6dnt 8 y i94hrr7ucpm:ue 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 zy:eih5trz*4t20 -xat0hu kb $q\,=\,+2e$ 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 travelbfca q42wg7 c7b,; oop2 dluf4ing $ 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 shuuf x tei6g;t056k; r6tmmrv5own in (Fu 6tv ;tufrex55i gk66 ;rmt0mig. Below), 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 ov.7dkra;zy7q zb-/qq aurm 0 2f $\vec{B}$ 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 proje.*k w90fxm ;uzikrx6 zcted 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 fiel+ hu8pazabgrs* -(:eld, in a plane perpendicular tpu8z+-a *sehla rb:g( o the field. What is the radius of its path?    m

  An electron experiences the greaoxyh+9n 0v9t:net +5 cgjcm2v -o)wc htest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that y0 8a6xwz c blp(ji1k+go undeflected when passing through perpendicular electric an k+(l0x y6wzj1 bica8pd 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 uwz-:.se;: tn (yhsoyatom whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

  A proton (mass $m_p$), a deuteron $(m=2m_p,Q=e)$, and an alpha particle $(m=4m_p,Q=2e)$ are accelerated by the same potential difference V and then enter a uniform magnetic field $\vec{B}$, where they move in circular paths perpendicular to $\vec{B}$. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton. $r_d$ =    $r_p$ $r_{\alpha}$ =    $r_p$

Show that the time T required for a particle of charge q moving with tpiz*4w+uc:aw oj/r (constant speed v to make one circular revolution in a unr(4cp :iozjta */ wwu+iform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular pt(zw/;xxgy o)a81 tso ath of radius r in a uniform magnetic field Bg)1x ttxwaoyz8/o (s; . Show that its momentum is p = qBr .

A particle of mass m and chac)o( fsq;da7j rge q moves in a circular path in a magnetic field B. Show that its kinetic energ co;aqd)sf7j(y is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particlz 8tr o-hn-q1x+i-jdfe 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 perpend5,*fe;enq n/mdn kjw4icular to the Earth’s magnetic nf/ 5,e*nn ejwdkq; 4mfield 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 meu-5n 7em n*zi )sx hm60j3wxuagnitude $0.40\times10^{-4}\mathrm{~Т}$ 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 speeuu5e/6 z kzao/ h3ru4ud j8j5fd $\nu=2.0\times10^5\mathrm{~m/s}$ 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 uc fhv/*hp, 6gto start a stalled vehicle carries a 65-A current. How strong is the magnetic fieldhug/h fv,cp6* 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 alloweqoe7uiz))pjtj 7 ph34 d to produce a magnetic field no larger than that of the ieu7h4qjz jt)p7) o3pEarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wirx t.hx0il):;riuo*lh e carries current I out of the page toward you. Indicate, with appropriate arrowsl*xhr :.oxti i; l0h)u, 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 carryini+p; t her:j0kk; zvq- 3kah)iic -5bbg an upward 24-A current exerts an attractive force per unith;c v- p:ta+ ie)0bbq3k i iz5;hj-rkk 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 of the force between two parallel wiress45h m/7 ai l+y krr0i.zy8cxgkcf()p 35 m long and 6.0x kgcfi s0+c5rr7)(ypi4zm8 haykl/. cm apart, each 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 .(ue.kq (oq 7r h,mk/luv fazuga,m8/ from an electric cable. What is the maximum alk,o l (uv7z(m8r. a/fuhauq/.k,e mqglowable 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 tops of 8.5bzr0w7k1k(( cvsf4 ae -m-high poles. What is7 v krbakw(( e0fcs1z4 the magnitude of the magnetic 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 currentsv-)tg )7cz0vwq2xf1 xorr - jk in the same direction. Determine the magnetic field at point P, 70rc wx2v-kg)v) jqx- zrto1 f12.0 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 oi34kv(wbzkof5u 9(a2 m(p zga 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 field at thiogpb ka5z2ifo4 ( v93(umz(k ws 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 currqxa1b -68qa,v xul4nvent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downwardavnq41-a qv, 8bulxx6 , 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 1l4umxq4;(s 6bxifwc 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 longxk)ki)e; umr(o57g. b.jkl bs straight wires 2.0 cm apart in terms of the current I in one when the o bi(orx .7;s jbu5kkek .ml))gther 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 current to, and frotlt..r ,1rll im, an instrument. If the insulated wires are of negli1tt.,.l lrirl gible 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 shom rgqh4y yhgafg3o/ k(5z0fq ,o,o9t)wn 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? g zqho 93/o,k)ry 0ghfgom4y5tq ( af,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 23m-.6hzoj+l j h7)f ffig0w- ik$^{\circ}\,$ 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 3o vcgr*ern z+74c k3lplane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine thz*4r oe7+ 33ccklgnrve 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 wireboty x 32e4mjvxsh j ak2r,628, made of 2.5-mm-diameter copper wire and parallel to the fi43 x tkmsj6 av2 h2erjyxob2,8rst, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are pe 2zhpx sai7w5y*nmn01rpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magne*nimhys0 zxw5p71a 2 ntic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.0 A cuc:j;bg;6zj4e kys)5nn5lz rbrrent. Wire B’s current is 4rj5b5j; 6: )ylks 4nzcnb;gze .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.99 a0:h kw.)berr0k-xwjtd nm (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its directah-0b0jkdw 9 nwxer:. k) 9trmion 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), deter+)x ,gwapt(l mmine the magnitude and direction of the magnetic field at the midpoint of the si+a mx(g,tl)pw de of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, m1vj*rf:i2coy + v/pna distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig.n2ivm1/j*f rv +op:c y Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of9qyke kn8 07r22fbadg wire and carries a current 07f nq ey2k9dga2br8k of 2.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoi :zv-2octjq* ld 1.25 cm in diameter is to produce a field of 0.385 T at its :jtzc2o- qlv*center. How much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm;x6f,jjy* wb.lcph*e w gd5y9-long straight wire cuts through the center of the solenoid, along a diamet; lbfj e* wgy5p,* c9dxyjw6.her. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that produces th 2 -wmxgl2/el5*9myelamw tr-e greatest possible magnetic field for a given voltage. Should you make your copper wire long and t5 rx9gt2ae* wmmm l-e-/2l wlyhin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle76n 7au )3wdbp (ucl;tlxi2 bs (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determianx7d p slb27 tu(u6wb );cl3ine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the conductors of0ox)/ g qcmm7wsif::a a coaxial cag:/o a7 imwfxs:cq0)m ble (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 itsu:8itk1ljkx sy .4 j-y2aavl- face parallel to the mylsa.vit-k8:2ujjakl 1y4- x agnetic field between the pole pieces of a large magnet. 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 for a1v y-dzjf:;ui $53.0 -\mu A$ 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 rdc8 4e0ajjuiv p5xk+yh14t:by 25% over the years, what current will give full-scale deflectio+ap5 8d:41r ut0 4jhvyxkei jcn 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 ch .pv+vsu;;a 5,it9d*qqv nspr angsr;p; anvv. *, utq5dsq9i pv+e?

Show that the magnetic dipole moment M of an electron ddgxlm84y-5y orbiting the proton nucleus of a hydrogen atom is related to the orbital angularx4y8m-dd5g ly 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 on the5ktlzd+d o x(2 grodtlx+d2zk (5ound. The Earth’s magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm han0kfxn2v5 m6(d6cifa ; j9u in a 0.566-T magnetic field. What value of electric field could make their paths straight? Inc9xfn2;mih(f6n k u 0 ava6jd5 what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanieuvzcctb-(7a+ecj k3bw)* s- um 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 7b)tc ukw*cbsee aj z3-cv +-(masses of the other isotopes?

  Suppose the electric field between the electric plates in the* p b:r;vukq7yto;c 7g mass spectrometer of (Fig. Below)q: c* r7t kv;7bu;gyop 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 is difficugr.x: vv)ho;c lt, however, to separate molecules with nearly equal mass such as Corg .: v)vcxh;O (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a vollysdslc3 ;v35,nl :i1mz l8 wt2npg d7tage V before they enter a magnetic fiems d;iygp3l53nt vw1 , lc7n2z dll:8sld 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 mehvmla rzv k2 7- o5,::wbfm*loter, and a 25-A current flows through the wire. If the permeability of mk 7r vh25m zowb:-*:lalvo,fthe iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm loho-xukv a,t2mf5m( +wb-6hyq ng and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field insidhmw(fvah+u -5mkb o-yxt, q62e 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 momentum 6p):)zq;gnvsbx dp9w $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 energy m,l cn 06+aqklupon entering a region of constant magnetic field. What is the ratio of the radii of their circular pa 6kmaq+ l0,nclths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal curre1 z ap)*-wcbrdg-ls/ dnt of 330 A toward the east. The Earth’s magneticzla ws/cbg pr)* 1-d-d 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 air l;g 1 o;8c5rt-buzavuplane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s mag4qqrny t gfo5qe.)-70 +pypwy netic field points almost horizontally to the north and has magp 40foq +wp5qyt nye7yr-gq.)nitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 massijzkvt/) z1qt fi.l 21 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). Arln21 tj0;z1vy4qxix8i q1x v large current 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 of 1.7 T, what constant current flow is needed to acti xx01 zqljynq ;r2xivv1 841celerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wi:yfd.( (ezrso re and is suspended in air due to the two magnetic forces from the bottood (rf.(e sy:zm 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 s 9j -9j ob49u,ncfysmapart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to ef bmu jy9-n sjoc,994sach 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 deflectionj0l- +( rd2jd 1(oty+mghrz hqc gg4gw6o py.+ of the electron beam near the center of a TV screen due 61porgj c(h+ gmydz+dj4-0hgl2.ry +qtow g(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 particler827n k.ekrt xs 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 throug.kkrn 8ter7 2xh the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of epkl-+ (o2p jls;,hd(iqx*+znc6t d l r5 n9bja square of side l, carry equal cur-l+jp2o ( +ijnbd,k hxd;q* 5t69c(nse zlplrrents $I_0$ 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 1kl(i61a h4k ne2 avhwuseful in particle accelerators for “beam steering”; that is, the magnetic fields can be used to change ta(4kk nhaih 62l 1ewv1he beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a c hlodr )llq61lm/e;w:m;gzb fc (+-i 4tjry)lircular coil of wire carrying a current ;t 1d fl( rl+;l4w/l-rijyh qe log))z6mm bc: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 mas raii8)vr0 p c)(3 bpd(kutx7gnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fiel; gr0r (w *iqe6xvoc7fds 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 arwri7o c6 ge *;qrxv0f(ea. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a blj)c1/)vo;l f;eg s3lmw9t mm eam of electrons, traveling to the right 9t;l eoc )lv/j3;lmms1 wgf)mat 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 ohv0n8y/ 4y pc-cvlv)h f 0.010 T, perpendicular to the plane of the spiral, )vy-hvyh4 pv8 lcc0/n 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, wto0,0x: hp/vff1dwh1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns1wt 0f/x vh0p:dhfw o, must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight alumtb3 ;uot 5bu7:rodw/w inum wires, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings /o37t:;budru wwt 5ob as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T at a2qj+kr +f z*ee 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$