A compass needle is not always balanced parallel to the Ea0x -*ohkn9u kprth’s surface, but one end may dip dowpo9 hk-x0unk* nward. Explain.

Draw the magnetic field lines am 4/vzva:3 rairound a straight section of wire carrying a currentiz43mr av a:v/ horizontally to the left.

In what direction are the magnetic field lines surrounding a straight wire carr( q7g z0y n;6rhmbeho8ying agq8eh7zymbo 6( ;r h0n current that is moving directly away from you?

A horseshoe magnet is held vertically with the north pijy7ct m /ppdh 093:quole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current dire9hq:3y7ti0jd/ mp ucp ctly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those made of iron? (d- sk r*c07edtm6fns*Try it and see.) Why is this s7d*6defs-nrsm* t0k c o?

Two iron bars attract each other no matter which ends are placed clk vkp*s/tyh01 vcn7 o 5i7mqpzh-e7x)ose together. Are both magnets? Explaiqpyh0z/7 nskx 1imkcp) 57v*ve - h7ton.

The magnetic field due to current in wires in your home can affectnpx+ r/qe,0 ki2 ln.m1dzm am2.(hyxo a compass. Discuss the effect in terms of currents, including if eh/xo .ni.r,k2dmm a(+z1 qmpl0ny x2they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field -t)gho9y /egk which is perpendicular to the particle- 9egk/yhgo)t ’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 vicinity of a c1lssjfi /(aev3og 3m*urrent-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produe*1m s3aof l3g/v sij(ced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fiitsh/vei1tdm6gs39,turf g7, /cf 7vg. 20–46. What can you satfd//97gsg m if3e6vi,,7uh r1sv ttcy about the charge on each particle?

A positively charged particle in a nonuniform magnetic field follows the t/d,ztc o p .p*mg3vzx+rajectory shozg.cv,px /+tz pd 3om*wn in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract ano cq6q5r52xed6uqqkqjz.*o / iron rod? What must you consider to answer theseouq 6.o5 5ed xk/qjq6cq2zqr* questions?

Explain why a strong magnet held near a CRT television screen (Seczr0xp9, oesca 2d ur2-tion 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes compl sz9,d2ex0ur r -a2copetely 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 wh04ed w 9- cm)uvctgf+uich are magnetized but the third is not. How would you determine which two are the magn)cuuce w d+4-m9ft0vgets without using any additional objects?

Can you set a resting electron into motion with a magnetic fg-cp9rcgg*ex1m43 c hield? With an electric fiel ccm 9ercgpx *31-4gghd? Explain.

A charged particle is moving in a circle under the influence, nq2w0 xl8lud 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 c8l,l n2ux w0dqharged particle will take.

The force on a particle ie0v1c h/ ftf0in a magnetic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heartf/ hvfice100t 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 horizontal wire carrying a current alxvg)da -bf8 . 8;e e:k5buqnfrom lef. db88u-afq:5ng;levk)x e abt to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surroundfmk*1 a6* rhgv a moving electric charge.a mrv h*fg6k1*

A charged particle moves in a straight line through a particular region of sbv64j a*w0rywcg z2 urj5pr46pace. Could there be a nonzero magnetic field in 5prwjrwryb6*64va02cgju 4 zthis region? If so, give two possible situations.

If a moving charged parti;-dya :(lhoas:cr 1 dxcle is deflected sideways in some region of space, can we conclude,:r;a1y-d( c a xslo:dh for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uni*7 rnw (pl-zpf6kum)qform 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 monyzflhhgr ac7k+*z v0./f:l:ving electrons in a certain region of space are being deflected by an electric field or by cy lf7:z*h:v+r0 ghznf la. /ka magnetic field (or by both)?

How can you make a compass without using iron or other ferromagneti z 787szjpth: sey 8ag;d4jn+oc material?

Two long wires carrying equal currents I are at righth8shdc*ci m*ep o35j, 8gvw+q angles to each other, but don’t quite touch. Describe thsj 3*o qi,he+8wc8m*hpd g5cv e magnetic force one exerts on the other.

A horizontal current-carrying wire, free to mo/jce a.pg7gy)m-yd( pnimbp6gt3 8m5ve in Earth’s gravitational field, is suspended directlycpia)5. gy6 /pdmtmgej7 bnpy- g3 (m8 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 aug 8 n;ly43olv magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, i )g8nfq9nsyny )39hdcp6k 1dmf one end of the nail is in contact with a ma1ks d f8nc gy)9pdqy6nm)9nh 3gnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubly . b6xxa-d* c0yeoofz*m -1c krionized.xcox - bme**f-10dcz. yo rk6a How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid 58.t +q 8y*mma msam2hzgb0 neif
(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 sp 2;6/y+dufp xh; lwiqolenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to 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 currex+p dw2;pyu lqh/;i 6fnt needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude tf*s1b uynf0*kh j4y( of the force per meter of length on a straight wire carryi0yy( th *s4fj1fkb*u nng an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of spcpj ow b a5q4p6gu 3hiz6/)jdo/z:. straight wire stretched between two towers carrying a 1zdsg zi. o/:pb apq3 4p/ocjuw6j65 h)50-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 fot:rk (w8l* /tt 2ukcqcrce on a 160-m length of straight wire stretched between two towers carrying a 150-A current. Thcl tq:2tc8tw u(*/kkre Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m loks/h:z -oh15tk (logpng if the maximum force on it is 0.750 (so1ht5 l hk:g -zpo/kN 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 g b4w mde k,deer)c:9-horizontally. At that point on the Earth’s surface, the dip angle of the Eebr ,-)emc9d e4g: dwkarth’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 )( z j9ml:- sxd6(ah8hkuepw zA 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 dias zmlh)a(-9j6p:dh uk 8xzwe(meter, 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 it, 6gsru 4lsin)s 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 fiels4s ,uln i6gr)d.    $^{\circ}\,$

  The force on a wire is albxh42 c7 ra(k6qbxo4 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 s+vsba 0h :+sff wx/o,hpav3mbd+2h (could just “float” horizontally in air because of the force due to the Earth’s magnetiov,hmds 2h++xfv w/:baa+bs 30hsf p(c 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 cs8wx (i y0bic,harge $q\,=\,+2e$ 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 a+le l+s / 9zg.zh0bqcend direction of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negativv/le 60wz:f xxe charge for each diagram shown in (Fif6x/l x:0zevwg. 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 ovc x; nbvhju x+2xk+18f $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward with a spslj ma ,/fez/;))va u i05bjzneed 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 fieqmwg,8 i +h5wl5ap) vdl2*f zgld, in a plane perpendicular to the field. What is the ra d2pv+a hli8,)lw mg5*q5fw gzdius of its path?    m

  An electron experiences the greatest force as it xv9hnca omwi yp:h u 49.9lr61travels $2.9 \times10^{6 }\;m/s$ 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 passingbpyr95wf ji 3;s0 a r*/mb:/xvgufb ,g through perpendicular vjfig: 30 x*us5; ywbrarb/9p b,gfm/electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose mass vene: k6 j2r,mw;0 zcp)sfp1/h 5hsuxis $6.6 \times10^{-27 }\;kg$ 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 requirw0 6r4 ccnwr5thoue2ai(b fj4+ji k57ze*)fded for a particle of charge q moving with constant speed v to make one circular revolution in a uniform magneticeb*f5u675 h)wd +r wcot a0 kjrze42ji(4c fni field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radi2(e)*2hpphsinfvf )l us r in a uniform magnetic field B. Show that its m s(vefl )hp2hn2p* f)iomentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetic fgg lme6 dn+c;/b s8s)gield B. Show that its kineti6esggs;lc+d)bm g8/ n c energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the b3* y;7w9ca kh fwl15h5bts fiparticle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet movesxf xn.kf 4.fx5*o t ar:;f1rhc with a speed of 160 m/s perpendicular to the Earth’s magnetic field;1h .x fk*a.5 norx4f:ftrcfx 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 ha77 c mnjv/,hip u,o v(/mr)ekasp ;4rks 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 d*( y yuxr*spxpl* i1tn*4wwdz0)*gdspeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 current. How stji id00 pp i+js1in/oh:(b+fbrong is the magnetic field 6.0 cm away from it? Compare to the Earthii/ojb hi0 fbsip1 (+j0d+p :n’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 mok)blmrl 9auf6 ,1 (dsagnetic field no larger than that okls f9 r a)(bmd6lou1,f the Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current - d8 iq927 audf3,2ds,l ff:uvde4 9qvhqpmrs I out of the page toward you. Indicate, with appropriate arrows, the direction of udfq ,qs,3i fde9 hfq2 ds92:p dv8m- ru7av4l$\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 3v.)y yphs.sbi76 o;dsb8u t 0hxoh)u24-A current exerts an attractive force per unit8ohb0u ;t.shubpvxd s is37 h.y) o6)y 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 magnitudcvh 7to fc icv29;8imq2:r3 dq cr3ct5e and direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carro i2dh3ricrc 72:;cc5vqtcq98t vmf3ying 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 mjfnb pq tvbc /.6t wpnzlq,vh *-5./(j from an electric cable. What is the maximum allowable current in the cable if the ex/.jvch nvn-5j zb *qwtf qp,p (.bl/6tperiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along tho db)8tclz mc j/t:/* wzk6z1ue tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wirej/zcz16:d*m/ )t8oc t kuzbw l 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 currents in the 5)osz6deqrnj wb: )+)8 lkbedsame direction. Determine the magnetic field at pointd ws nreo: )6be+ z8)j)ldbqk5 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 placv)feha7 0qp.yic )q *ced 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the 0hcq a qe*.fi) cy7pv)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 cauai1b x:v. o8lgyp n3s evktc4ui;w 3zt-1*k7rries 22.0 A of current due north. What is the net magnetic field 20.0 cm due 3tu1kv k: o.wne-4lg;*1typxz3i8b7c a s uivwest of the wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given p a4v7nmn)q3pz oint 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 b- wt31 1u .xcycmzk:xietween two long straight wires 2.0 cm apart in terms of1wu ict.3xy:cxzm-k1 the current I in one when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducyfe/rybc31c,u*- t (s ia s+ xwv3np xzjy324kts 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what*yy v jzwpycin(a/334s+u- k 3ctxefr s,b12x 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 wir3k3mudwvx) 5pes shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does itdmu)k5w pv33x 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 pointozpp6+fo8 vfb) y5kbgb:b3-vs 4 u1pss 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 the same planel( k5f9(mgtatlwn +1g as a straight wire, as shown in (Fig. Below). There is gk5+fa(g wm19(llnt ta current of 2.5 A in 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, mad*xgc,z pv.lca.w h1(ue of 2.5-mm-diameter copper wire and parallelv ,xcc(hzl.* awg1.pu to the first, 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 perpendicular to each other. At 5zfy wzk90k s5their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field k09s5fzwy k5z 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 2.09pj9 +qonj /bx A current. Wire B’s current is 4.0 A in the sam99 /onqx +jbpje 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. (Looking a0byo kws7 ) ppe,3icm4r6x(qalong them, they are at three corners of an equilateral triangle.) The cupi b wxq 4,pr03c)aks76ye o(mrrent 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 magnitu/lq3hcm )o :xede and direction of the magnetic field at the midpoint of the side of the triangle between wire M /e :lo) xmchq3and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry eq wr tnp2 los(r9.g9oljn8gr ,:ual currents I in the same direction. One wire: 9wsrrnj82lt(nlp 9ogo r.,g 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 solenoid has a total of 420 turns of wire and carries a curc2,- m)8 otjrdc fwpe t.izo2w*s,g*r rent of 2.0 A. Cal.o r*f8cdj2m c zwp-i*2or w,segt)t,culate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.w+kq 9v slao,z.j2c0g 385 T at its center. How much current shoul9a v j0oz2s, +gclqkw.d the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The curre2)tr65 d7mlztu; arb mnt in it is 33 A. A 3.0-cm-long straight wire cuts through the center of lz2 7rdr 65mum)t;ta bthe solenoid, along a diameter. 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 copphokxg+s, lmj/ ,z6jr : c;8jlzer and want to make a practical solenoid that produces the greatest possible magnetic field for a given voltagr:jz, 8km ,6z;jl chosl+x/gje. Should 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 solenoid isswp ac4ni s3sm:8;x-c5v--hyiw 4f h n the shape of a circle (Fig. Below). Use Ampère’s law along the circular pathawschw ;:4 nmixpvsfic4s hs3y8-5--, shown 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 shx9g rwgo-i s/(9m8vx xow that the magnetic field between the conductors of a coaxial cable (Fig. Below) iss mr (xx-g9/oiwvgx89 $B=\mu_0I/2\pi r$ 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 wird*0k9 *yye l,omb:paue 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a lardym 0*9e:a uo*y,b lkpge 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 f j0 q3e6,isjlocfp j8b5 m :t0tbl/p9xull 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 gal n, ;emxzq50mxqpa(w 8vanometer weakens by 25% over the years, what current will give full-sca8qxnp0 ,;5exq mm( awzle deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the o2f (+ fholbq5putput torque chan2fhq (b5lf +opge?

Show that the magnetic dipole moment M of an electron orbiting the proton nucqx*tci 6s9. smleus of a hydrogen atom isq s i.9*ctx6ms 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 nzg0p/ye9 ;hv containing nine loops lies flat on the ground. The Earth’s magnetic field at this location has magnitg9;z vne0h p/yude $5.50\times10^{-5}\mathrm{~Т}$ 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 ci0 ;-(klj p3 w8lsccf0q )0xfwk b8tiaercle of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction must it pwxlp 0a0f3 ekj-k t ;(q8) c0i8cbswlfoint?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germaniumgl6 :3rogmajs)5o7cn;0c lg a atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds tlca37s:6 m);jalcgg r g noo50o an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field beu3eku (iif4 nf66q2jw/vu(if tween the electric plates in the mass spectrometer of (Fig.3f24v ku66if iijfuunq(e(w / Below) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is beinge(7 5ww+ . depiohicn6p*in6 g used to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (28.0106 u) andi7hw icn p.niwe 6(p* 6gd+5eo $N_2(28.0134u)$. 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 voltage V before they ebfuvi )kh-* h.nter a magnetic field B. The ions *)khfivh b-. uare assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A current flow 8pmoq ipecn *:ndr4/q,lc to2k14vx :s through the wire. If thnvqc px4ot*,do:n:e 8 qcmi/1 l 4rk2pe permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1)t 2r 42mszuwlok+:ghhw/g5 k.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2tumko+2hgwh 5gr/ w sl4kz:)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 momentuj07 u: /qbuslxm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 upon entering a regih-4( ;ka+khlzts*w r6q mvdg:e,n3 wxon of constant magnetic field:-v h gke qm;,dn*63sw4z(h rtkx+awl. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below)t8- :o:i2wqcfefm yr( carries a horizontal current of 330 A toward thec- : o2tywqerf(:mfi 8 east. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a1dcqf8h eq7qd9u; o 9kt8sf 0g 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 almost horiz4:xr4ebhdf8j2/so - nny vinss m.w8:ontally to the north bvh:j/s ei sxodnf-w8n: s8y.r42mn 4 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 maskmyaz, pk) cow i9f*0,s 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 launafh1d:(vw3 ,y t5lan icher” is shown in (Fig. Below). A 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 conl(fay:a n5i wvt1h3,dstant 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 wijg t b/qx(k.q1 -gg7kcre 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 cbjqgq /-x7g .g1kk(tin each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance ldkpqxzk6;zhl vh: ,(w5 ,ha2 e bd*caosg:9;p apart in a horizontal plane act as rails to support a lig5 aklpe;p6kz(:h,v9 db; * cqh gs,how zda:x2ht metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maxi vumpw14qlv2vuj7:r2 mum deflection of the electron beam near the center of a TV screen due t:p4uvw 2mr2v7 1jvlu qo 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) -afh-h p4zsd; icqk8bt3:7nbis a device used to accelerate elementary particles such as protons to highd zt hk -b4hpf-8qci:b;7a3ns 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 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 a square z/sfy38 po66vkaef1a of side l, ca6yzo6af a/sfk 8 e3p1vrry 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., vmad; .yhhnard /vjk4qli-i(mt) - 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 thi(rdvl,n v4)h /aiaqh--jmkd.yt .i; ms works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire cal(ti1e0-a9ys f6vy: kpvj q0frrying a current I (as in Fig. Below) ise9 iska0:vjq 06f-fty(1pv yl
$B=\frac{\mu_{0} N I}{2 r},$
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 fiel*r.go.7t vwvssdgt /7v4c f p+2rb qq2d 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 fields produce-w6odbgfg(j0x rnhe.u-( 34 4vd uoz pd 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 under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic fieldd0(ox4g6jph 3edob (w4ugf.r-uzv - n will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a ben)fzftnl 1h -dpp)v: ;am of electrons, traveling to the ridz fn)h -:lvn;)ptfp1ght at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path througmf*az *dv y*8orfgw 91k m*/roh a gas in a magnetic field of 0.010 T, perpendicular to the plane of the spirk *8/1ozrr*offm* mwdg *9 vayal, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, isr5t(o6b egul0siz3+ qd5y( h i to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must th ((+ u63gtr5osd0iib5hyz qlee solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of g-*djw *, uatpo+2fl+c1qlbkdiameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings mglwdbjaf p2++o,k*ul1 qc -t *ake an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniforj /o vr3yy j::5juqy01fqyv-sm 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$