A compass needle is not alwaysh7e zd5 ma2ye2ng8.hy balanced parallel to the Earth’s surface, but one end may dip down.adm2g725hny zeh ye8 ward. Explain.

Draw the magnetic field lio m.6idywfn)j,.(y kunes around a straight section of wire carrying a current horizoyu y(n k).ojdm wif.6,ntally to the left.

In what direction are theh6l6 c-(wet bvrrv 6t1 magnetic field lines surrounding a straight wire carrying a current that is moving direct t66rher 6tvvw( 1lb-cly away from you?

A horseshoe magnet is held vertically with the north polehr/ x40mzh oflx2*;lrfi) 5,rd) ebld 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 f *borlm )rf4de5x;i0z hl l h),d2/rxwhat direction is the force on the wire?

Will a magnet attract any metall4vcctxt -m5.p-t dl 8iic object, or only those made of iron? (Try it and see.) Why d5 xpm8l c-c 4it-tv.tis this so?

Two iron bars attract each other no matter which ends are placed close0idmi: zt.k m1 together. Aidm:0tk.z im1re both magnets? Explain.

The magnetic field due to current in wires in your home can affect a com aoi( ngj1w*ura+dyb11s b4wod7u ,d7pass. Discuss the effect in terms of currents, including if they are acb w*i 1b+,g1udju wdsya4o7 aon7dr1( or dc.

If a negatively charged particle enters a re0d10 g;yahi dygion of uniform magnetic field which is perpendicula1aiy;ygd0 h 0dr to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the viciz,gbwcf 1eq r 8ed;gv+ut1(0cnity 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 ea gwccz 81tr0e+ fb(vdug;qe1, ch of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 21r mqaa6/x4u 8 or5bbu0–46. What can you say about the charge on each particluabu5mo /6 8 bxr1qra4e?

A positively charged particle in a nonuniform magnetic field xw pinf .-qcz(6xdo1-follows the trajector icz oq.f x6(n1px--dwy shown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnezg3da +0x xq iqa;,3ycei4,b it? Can a magnet attract an iron rod? What must you consider to a giq+zciy3,qaa3b4e ;, ix0dxnswer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10) cawor/+0f ,ml-zj8 hibm uses the picture to become distorted. 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 thi j i/ml0bro hfm,+-wz8s.]

Suppose you have three iron rods, two of which are magnetized butjdqzlxgv zq( k5i/jy)7z r6h 307l op7 the third is not. How would you determinhd3y)xlq5k6 q7pl7jgio r z0 7zvj /z(e which two are the magnets without using any additional objects?

Can you set a restin ) m50r ild8v *d-dklw/yg*:ekhzdcl3 g electron into motion with a magnetic field? With an electrilv8r) 3 wz-dl:cdlkdgd50y*i m e* k/hc field? Explain.

A charged particle is moving in a circle under the influence of a uniformdmn8vp5jw .6m magnetic field 8mn p5wmvd.j6. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea s)y kx(u s9)ypbehind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to p(us9x ))yps kyump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic 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 horixd afcj:zg:5e/ei 2o;zontal wire carrying a current from left to rig z:g:2fec i5/xa;eoj dht
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electrgrvubgr oa6( /d83;y7x :aaakic charge. agvrou a6 8ak;xg73d/a:yb r(

A charged particle moves in a straight line through a particular r:wdn7q.wp y( aegion of space. Could there be a nonzero magnetic field in this region? If so, give two .(w7:pqn w yadpossible situations.

If a moving charged particle is deflected sideways in some ro n/;;zy v6pazegion of space, can z py/oza;; nv6we conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a un4j h+o4.hp6p qnrwo9aiform 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 region of p0c4aayl t( a7*b+n ijspace are being deflected by an elea*c 7(bptj +4nla0iayctric field or by a magnetic field (or by both)?

How can you make a compass s3h6v 2dhn:tz without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to e.e hj;rjyc 1vvqb,23 n7k3zun ach other, but don’t quite touch. Describe the magnetic force one exe1uerv23y khncbj3 z j.7;nvq,rts on the other.

A horizontal current-carrying wire, free to) k2)lnp)b6sue2 w1e6 eh wi3in)wqmt move in Earth’s gravitational field, is suspended directly above a secotww1nw)) 6)2lkqsubin 3) hp62me eeind, 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 unmagnetiz rf q*8gvm.s +xlg.t.jp20dm n14:pqo kaf9p wed piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Hy.iy*)*o ajajcf -a+cowever, if one end of the nail is in contact with a magnet, the oth*j).-+yc jy*foa aac ier end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionizi( nwck5ght5 6h /5jmhed and the other is doubly ionizwhk6i5j cg (htm5n/h5ed. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solmw vg(3p m0 7yyp-sqg9enoid 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 2t+acoaqhhw b8 i9 o58similar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you neeba aqi5 2h+98ct o8owhd 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 magni1dv--hz:;bg(fm*c i f- fhzettude of the force per meter of length on a straight wire carrying an 8.40-A current when perpend*tdb -fm 1-h- (;hg ifce:fzzvicular 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 forx /mei5jj6rfu(nb5 a4ce on a 160-m length of straight wire stretched between two towers carrying a 150-(f nm /5j j6x5erabui4A 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 a6/)fzvz6 -pz y0r pgjg*bemy0h r/1n s 160-m length of straight wire stvzpjr r0ep-zhsfgz/6)g m16y0n*y b/retched 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

  How much current is flowing in a wire uetxptb03to8 sp0qn.wvocyi )(:0q3 4.80 m long if the maximum force on it is 0.750 N whenvc:3 .s00n0tbext(u yw piqqoo3 p)8t placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of 6xas dt3 .cs,--wex)bv54kgocah+s h current is oriented horizontally. At that point on the Earth’s surhoas scs-4v b,a5t -) d3 xkghcexw.6+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 1.282 r//.ixx revnl ae,6y N when placed between the pole faces of a magnet. If the pol iyx rlex r,62vn/.ea/e faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force pbug 2noih( 3-dr7fp8l er meter on a 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 maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field. rgdbpl3i2u-f(n h o78    $^{\circ}\,$

  The force on a wire is a maxh1ma:pyf5gingtx/rb((f 2 /kimum 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 “float” horizontav y8a0i t2,jovlly in air because of the force due to the Earth’s magneticjvt0,8vyi 2o a 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 chay3qd yg-:yu+) (bnw-7z. c iut9rjjkp rge $q\,=\,+2e$ 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 h8 oox(3detg, 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 forn)tz w67*l.pd*caegoi 4v *bfce on a negative charge for each diagram shown in (Fig. Beloiv4ld a 67cnf )*ogewb **.ptzw), 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 o w;zxis+u3: c9qy+fd of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected verticallnn cwm.9oez3gn r1*3f*y u8g ty 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 perpe:z ex/auq 3pw2ndicular to the field. What is the radius of ae:2zw up3xq/ its path?    m

  An electron experiences the )y vv q0 f7/k1swbus+dsy 1d :s,zy3wygreatest 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 go undeflected when passinq:(l, rib tq8zg through perpendicular electrlqzt8:iq b( ,ric 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 heli lz kz*uf;p71kum atom whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge q moving with constgo8ml71i6 br aant speed v mg la 17r86iboto make one circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path x:hcv h t8lg.0of radius r in a uniform magnetic fil. 8tcgv0h: hxeld B. Show that its momentum is p = qBr .

A particle of mass m a ,;zd ud(lpdc(q u/t:l5ygn*ind charge q moves in a circular path in a magnetic field B.c(d ,(yll:/*u pdq;tgn5iduz Show that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the partic-k +orn .wn+nfle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves wj1.o m3zifhb lrvbd1j,3 )mx8ith a speed of 160 m/s perpendicular to the Earth’s magnejl13mfrm 8)o ihv1,x.j b3dbztic field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at thuny9 8n6qezyf(c+9 gfe 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 with speed 6zmo*+lnnqnw;fdr 05 1jd7 qy $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A currq),s;lvq;z cv yn :o;rent. How strong is the magnetic field ;;ocyvnq, ;vlz)s: qr 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 magygnn )8 7x8/ptmkmz/ 0+p1flh9vkk uknetic field no larger than that of the Eagh9l)u 01+ 8xm8k/y k7ftvnkpm n kp/zrth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire car w086h a. bi0md7aqrvxries current I out of the page toward you. Indicate, with apr6 8b0ahmd0. qaw 7ixvpropriate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying roo4p+,fr g q7an upward 24-A current exerts an attractive force per ung,p4orq+7 f roit 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 31:uei oav6haof the force between two parallel wires 35 m long andoi6ua:hae3v 1 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 being caft 66lnu2z ,- hl,ktx)vc4eqw8 euv9 hrried out 1.00 m from an electric cable. What is the maximum allowable curre96qtx wz )kf l-,ee8lv24htvchu,6nunt 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 topstk;b6mzf2jp+i;b aa gd 0t0fbcv:s40 of 8.5-m-high poles. What is thb pd 0 bm6s04+ivkfzta;0gf ac2j:; tbe 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 wsnvhmaq() i: 1ires 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic fieldn(s i1: mqhav) 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.s+t) 17m ar3wx xouux due south from a straight vertical wire carrying a 35-A current downwm +) 3rou71.xtuasxx ward. 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. Wha(km78azd )r,f x)k sptt is the net magnetic field 20.0 cm due west of the wire pf)xa,m(tkzsr kd7 )8 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 poi9 f7xm:+kjobyypx16r nt 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 fie2 b+7x ,2j:dra ihvd x/nidi;lld midway between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume thesxid a7v+ x:/jd2 ,bni;hl i2rde currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc curr k3m*aw/e*n u65oms zkent to, and from, an instrument. If the insulated w*mso /k5mua ek*3nwz 6ires 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 in (Fig. Below),0 :obdx :n7zkg paralledz :0b:ogxk n7l and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, 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 pointsbpxg4h8fbh54/ q 2cq vizz;:t 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 l lhkvor;,x*. l+8rxy aies in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the*l, k.hlr8yvo x rxa+; loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 Ahekpyj x9cm3vy( d05+ . A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below 9 vm0pxy k(5+ch ejdy3(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 o-yb; w ,ns2ayj1b1k -qrm vr,tther. At their closest, they are 20.0 cm apart (Fig. Below). Wha,rbvy1s k2b-1 jtraq,my-wn; t is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wik3ct 4.6n h 6q8;s1v ;zxaz1uvnwhuhy y,p-f dres are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same directh qd116p,vt4;z8c3. ayfk ns-h; nuuwzx hvy6ion.
(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. nez1t+e7(x 10 wg:k4 uz1jrqhuem-oy(Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per ujmz4 n(tqy gwee uuz170x+1eko1h :r-nit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the magnetic fk*xzhx 9kh 0ho 1ythi-y0t ;.bndf c;5ield at the midpoint of the side of the triangle zy- 1h tx;cdk5 nb x9;h hk0t.*0fyhoibetween wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires,o*g ;hp. g*t3* u:lgoct)kl 3omtkcf6 a distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the 3f;u) gkp k*c*c*g.ohto lm3gl6ot t:other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a totalp1p4* hazf:0wif 2vos x10k//xi qpe oz,y+wy of 420 turns of wire and carries a current of 2.0 A. Caiz:h0vpes 21 y*pz1f,0qpxf+4yi /xw kw/aoolculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is tovbnyn9 ;oyrk1 cezzg-q73+4l produce a field of 0.385 T at its center. H 3nyon ;7crvy1 9l-z kbzeg+q4ow much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long.xusu g9:9a3 ev The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. Thv sx99ueg3:a uis 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 so6y7oi l2v (w6 utwzc+hlenoid that produces the greatest possible magnetic field for a given voltage. S wh67vul iyc(w6zo t+2hould you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoiew8ri;:v 0q2) xwofar d in the shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shwai;qef w:v 80xo)r 2rown dashed in (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 the magnetic fiqn4 dun (v*wj)eld between the conductors of a coaxial cable w4jd *vq nun()(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 2dju e*9 -q;:k*lvrhdw rj yo8placed with its face parallel to the magnetic fier*d2oyl8wv-he9r uq jkj*;d :ld 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 deflzs q6k3o-by wj((/oduects 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 weakefbm46s6sp1c q8znx ; l.mn x8(y8jat dns by 25% over the years, what current will give full-scaldq(4mbs86 f6. 1m naxxnpzlcsy 8t;8je deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output tor x,e)po+x 9chgyqu+ggq0;y l+que ch +0+pxeg;y,gxy u+) qlqhocg9 ange?

Show that the magnetic o /4;xgxik s4cdipole moment M of an electron orbiting the proton nucleus of a hydrogen atoos4c/gk 4; xixm is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing ni4-zdgl l2vtc4w/+t-mel g af,ne loops lies flat on the ground. The Earth’s magnetic field at -wtzv, l+/ed 4 llf tg4g-mca2this 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 cm2hv- wjbe j0*q in a 0.566-T magnetic field. What value of electric field could q-*ehvb 0jj2wmake their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal to 21cbc .wq 6ln -oz-12k ;bcaozt9.0, 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 massesok 9 nq1lob. 6c-wb-;zac2c tz of the other isotopes?

  Suppose the electric zk6j,/aho c 3thy9s+k field between the electric plates in the mass spectrometer of (Fig. Belokz39a6o h+tksjy/ hc,w) 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 pol 2 hxobr:;1ybflutants. It is difficult, however, to separate molecules with nearly fo1yxbb ;:h2r equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrom1)k yfxry(8b 1 vfnpqq4: ro5deter accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an ion is oyqbfd1kvynfq1( r54r :)px8 $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 l: p1w dnftzixlzgx)85*p( ul1oops of wire per meter, and a 25-A current flows through the wire. If the permeability of the iron il xp tdxzg*151 ()pnzflu8w i:s $3000\mu_0$ 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 81blcf 8 da 9cev;hmc(640 turns of wire. The magnetic field inside the solenoid is 2.2 T 8 m8ecavblhcc (;f91dwhen 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 1v.mfazh (e+z$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 / m45cuas;1ur hrqlw3rc-9vy -f+jia the same kinetic energy upon entering a region of constant magnetic fieldc-jq+ -4 af rc r5yrh3 lmsu;9/u1wiav. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal cc b;x l96grm75dv/r5x e s6joe*ix b/zurren/ji;6 se/ge z xcorl5b9x6m dxr7*5bvt of 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 an airplane whi8c12/z m e:bxjq a*8uh3xc wpich 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 magnetic field points almofxm 8 ,s.gu3mq cd+.5hpzo/pu st horizontally to the nortgh .+, o5uq3f8zm/p cmsdp. xuh and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mahaa0ln)v:84oki 5 jpb ss 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 moves u2tr ocm:ut/cg1tcf) e6x7n *,q( pje 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 fiel cutogx6n:1ceu 7q*/ )p f emt(2c,rtjd of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and is suspended in*reo q 1a21zxp air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 2o *1rexqzpa1A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a di g-d s-4h pwif36/tmwwstance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular /dtpfi -w mhw 63g-ws4to 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 deflectiokbe 8btm7.;6zx- rc bqn of the electron beam near the center of a TV screen due to t6 r;zkxtembqb .87bc-he 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 elemeng7i b1qm o:g.qtary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles 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 metalgmb.7 1o:igqq 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, locat9 1k,nipurk; tve)f7 xed at the corners of a square of side l, cvrk x1;kfp)u9,i7tn earry 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 accelerators for “beam steehakt g,/1iwb 8ring”; that is, the magnetic fields can be used to change the beam’s direction wiwg/1th kia b,8thout 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 cev1bwr w-4bl 0fnter of a circular coil of wire carrying a current I (as in Fig. Below) ibb14 -lvw0r fws
$B=\frac{\mu_{0} N I}{2 r},$
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 th/ri 9ux;w-i ote magnetic 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 vwktb p8.)ge: magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might).8t:pvk w bge 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 bea r/se*hqbblq5y7j4y t :zo1 h(m of electrons, traveling to the r4ejylh tyb 1q5z(r/o:*hb7qsight at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral patvpnzq+ *q*7mde *h ks6h through a 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 points P a7z*me +h*q qpn dvk*s6nd 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 pro)kqesol) t8b y7h;r6wjr5p0qduce a 0.30-T magnetic field at its center. If the maximum curr 50kyro))6 qtjhw8lrspbe; q7 ent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each ofsiq) .i 2,j-.z bqr qf3nfjho5 diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown ii.n.j)52s, f fiq ho rbjzq3-qn (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 u xsrl (e f6o k1e+z.1(lutqr7fniform magnetic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$