A compass needle is not always balanced parallel to the Earth’s surfa k m0 on2qcn3fl0hz3tyu)ek 1e0 et+*dce, but one end may dip) e* cn3uldy0zet0mn 1k3o+ht0fe2kq downward. Explain.

Draw the magnetic field /6 dethafnw,0lines around a straight section of wire carrying a current horizontally ton t,wdf6 /0aeh the left.

In what direction are the magnetic field lij( d d2srl7kbe)0rlkt im503o nes surrounding a straight wire carrying a current that is moving directly away from yr3 s 5k( l0e)dd7imbtr j0lk2oou?

A horseshoe magnet is held vertically withr;lt-y6k,f i x-q :x1 zoh2 dbi/c1fbn the north pole on the left and south pole on the right. A wire passhcdkb-x 1li26;yrbn:ffo zt, / x-1iqing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only tho/iz)hazt 4avk gd (06l po*wx;se made of iron? (Try it and see.) Why is this so? o4xzzha i0w;)gav(p d*l/t 6k

Two iron bars attract each other no matter which ends are plawvy1b (u fj(8w. u.lnqq 32tezced close together. Are both magljz. fn eu81qy2t 3buq .w(v(wnets? Explain.

The magnetic field due to current inqkimd y*+za*4 wires in your home can affect a compass. Discuss the effect in terms of currents, including if the zmq*4y *kda+iy are ac or dc.

If a negatively charged particle enters a region of uniform magnet2 y3wj- vhj )2iavjmg/ic field which is perpendicular to the particle’s velocity, will the kinetic energy v jaw3y /- mv22ji)hgjof 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 n:z974 hfdt rfa,n3kn+xol +athe vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the directi h4n t9ndnxr7:k f+,3f+zao alon of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic5xbl6q 4gvv :sd xf2v/ field as shown in Fig. 20–46. What can you say about the charge on each particle: xvvx sf42/q6dl5g bv?

A positively charged particle in a lux+4b0 ryl 5arm4*de nonuniform magnetic field follows the trajectory show 0exy*ul rb5ra4+dm4l n 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 ma/xdtfx1o qt*, (8dsbpd6h4f zgnet? Can a magnet attract an iron rod? What must you consider to an,8f qb zh4xs6dod/dxft(pt *1swer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10) cahbq;0w i(ol7x t1 tr;muses the pic 0;;qlot( x7tw i1brhmture 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 this.]

Suppose you have three iron rods, two of which are magnetized but the third isa f 2sa6g/89d6m wy9lkt4yqcs not. How woul/6aw2maf4 9kl6 yc9st8dgqysd you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic fiv8nkvm -p *z-seld? With an electric field? Expp z8sk-v -n*vmlain.

A charged particle is moving in a circle under the influence of a unh-q53jahu:g g cyrh- 1iform magnetic field. If an electric field that poinhg3j5qh-r :gy1achu- ts 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 behind electromagnetic ps7nze4v )i 0quj i5nnctb+4n7umping. 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 magnetic field. Explain how ions are caused to move. Do positiv t)0 n ni45qiv7ej+znu4 cn7sbe and negative ions feel a force in the same direction?

A beam of electrons is direfxb:ivekck6zw- n2 ,zeup /:2 cted toward a horizontal wire carrying a current from leftc nz:fw2 6 ,:zkuv xbie-k/p2e to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or ma u*sw/b2 ges5pgnetic fields that surround a moving electric charge.52sw/bg us *ep

A charged particle mokws( /hyfk6l4v8: jy-z)crgs ves in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so-/sz:sry)kjkgy8(clh v6 w 4f , give two possible situations.

If a moving charged p xx*fs34 7pryb.mrxn so3j6y4b)ldy-article is deflected sideways in some region of space, can we conclude, for certain, b4xxynpyys3r jm -sl*rx4. )odbf763 that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic y a9f fho0)n3dfield $\vec{B}$. 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 whethe;wo 3obnu ubt,dy) q9.r moving electrons in a certain region of space are being deflected by an electric field or by a magnetic field (or by bothbq;d no,. ub yu3t)9ow)?

How can you make a compass wi n1s8(;okuig;;9 en yjb bnzl*+ dl4wsthout using iron or other ferromagnetic material?

Two long wires carrying equal;ntiso+ j z 9.jcy;l;i currents I are at right angles to each other, but don’t quite t;z jic +.;t9n ;ilosjyouch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, 7 9wuvj4*xlga free to move in Earth’s gravitational field, is suspended directly above a second, parallel, current-carryinga* l4gwjx9u7 v wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized piece of iro(96fbnj yd od), o,dt,wv0uva n?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if :/nvk qydvn tw etn-nn **(i-(one end of the naiky*vnn-nevw :/nq*d( t-i(t n l is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one5 cyx44snuxcmb7 q:g: is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectromete x7 yuncxg5c :44:qsmbr (Fig. Below) differ?

What would be the effect on Bu5q/hz7wr zy5u(6fwr wp e 4-g 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 a relay . A relay is an electo) )3ytk ;m*gc b scisk342; vm4fojqdromagnet (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 d3q4oc;3 sg2imvy*bk sf;4 ckom t)j)main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straimhi0nk/ no(,zm1fchveweq b62 .67 vgght wire carrying an 8.40-A current when pe e6hn gmmkq0 /cze.i1nvw h,( 6fo72vbrpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of straight wirecg :/no ,o,jdxj w3 zto+h8q1x stretched between two : tojhjqwd, 38oxz cg+1xno/, towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic e*o-2nonl(5omx a0 iiforce on a 160-m length of straight wire stretched between two towers carrying a 1ix*-e 2ao5oni(mo0 nl50-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 z c5+lq,(b-a*fz0 vep z+daga 4.80 m long if the maximum force on it is 0.750 N when placed in a5za+qdz+eaz,- a*gb fl0(pc v uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5g2ttrw 8gyvutxuwzv )22 8 ;6k A of current is oriented horizontally. At that point on the E2t 28ug2gv t urwkw8ytv)6xz;arth’s surface, 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 b(;kqq 7a yih6; e5/+bum ;vcyr/wenq 1.28 N when placed between the pole faces of a magnet. If the pole face cuweh ir7b;nqea5v;m6y;b +y/qq k/(s are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a,;qm teha,: hd+jbp4lt4k v4d 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 actual+:;hp,dtal4v4kq 4 ejbhdm,t ly is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire isru4+4/6 zpdjhj9xmub 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 “float” horizontall*yj9 gdd.tx,p y in air because of the force due to the Earth’9dtpxj*g y.d ,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 chabds./ hjz:7 fsrge $q\,=\,+2e$ 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 ;(tbvmtrl(k0of 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 t3tnn l pqkds528bs*ei z-53np .9qfih7qv2nche force on a negative charge for each diagram shown in (Fig. vlft i -qp7 nsn3hk*8 s5qcpqz 2nn3.2d5eb 9iBelow), 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 oasj,3sgsu 02( vaqni+ f $\vec{B}$ 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 upwardxjmgg,vze) 0 fu72a o5 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 u 4 aytkvo3ch5ntj0720qib/x a 0.20-T field, in a plane perpendicular to the field. What is the radius of its pathtkxoib2u4 n3a 0 /jyq 70vch5t?    m

  An electron experiences the 6qe /mdnie)a86;v kqngreatest 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 wy84qtyh9,s i, bp1 qgpk/j*zphen passing through perpendicular electric and magnetic fields of magnitude/1yp*kzqg9 i8pyjsph,4 b tq , $8.8 \times10^{3 }\;V/m$ 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 atompp5ddnu- h17l*6nd m/6-x knyyoi7ml 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 mov7 n-( sn( bdtkplm*m,z-;tzj cing with constant speed v to make one circular revolution in a uniform magneticbj7p;t-,z(nn- tkc lmm*z s(d field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge qb: y/f2x,p--zxgcxlou3h;;cz kp0 v c moves in a circular path of radius r in a uniform magnetic field Bxzupb0 3kc2zogl /-;y,hxc ;p cx f-v:. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a1cyu57ssp-wi :mnbd ) magnetic field B. Show that its kinetic energ:7dn-b umwi y5)p 1scsy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of yc+q:x3b0vt4l )+p ja kv8p ye:cwa:y the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Eabqr ccxj.k3+o9wyf : c).of8 qrth’s magnetic o3qr:c98qwbj.f yf+xk . )coc 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 b+* 8oc oqwn1pmagnetic field at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with5vf v;otry h ;ws)00s7veee.j speed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vs :3h8f zr8gcuehicle carries a 65-A current. How strong is the magnetic field 6.0 cmrhz sf8cug3:8 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 producbi n.xajqa25x wd0vuxur3;s- 3 p( ,iu;9kvyte a magnetic field no larger than that of theprvj3uiqu(.sa 0vi tx ;udwbyx3- 2,ka95 nx; 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 I out of the paas32r8(6heir s dwiwl) 9k iw,ge toward you.siar)kelr8i6 hws( i3,wd2w 9 Indicate, with appropriate 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 an upward 24-A current exerts an a 3l/h04ief:ucoyxbj vn+4z, i ttractive force per unit len: zf+j4c4ivxl3oyi/n0uh,eb gth 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 paravo 3u o.a/-nuy hx5e7qbj39sa llel wires 35 m long and 6.0 cm apartuqx /jsy7 ea53b3a.ooh -unv 9, 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 from (,t;(c kd xobpmf8sz:yt()g;:epsiej,p( xban electric cable. What is the maximu:fk(pxj;:eg),op(pxi( ;bet,sb cst m (8dyzm allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a curre5zyw1y blo(-80 d xqjsnt of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Eart1xq d0 5 (8yj-yzbswolh’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 0rxm.h5kd d c0cm apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Bed.00cm5r hdx klow).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 dvi-r, g2-feebvccuq,:hzkze , c *29cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this l,eq2 v,*zvderhf 9,u2 -e :c-bckz icgocation? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due north. What is the n nh uje+w46qk)et magnetic field 20.0 cm due west of the wire if the Earth’s field there points north bwkjqn+ h)u6e4ut 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 a0d +zkvmteub nx q j6jy2:z,5) given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field ck7 gu3q85ym fb))od hkokblo 2z4+-lmidway between two long straight wires 2.0 cm apart idb72ok 8 o)- q+flkkycuhog4mb3) lz 5n terms of 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 conducts 25.0 A of dc currentu 0l+j-q* 0 h)bdd sd)*zqntd7xjzoc1 to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from tjc*d dzndt uh7lj) q1bo sqd)0 *-x+z0heir 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 showzhr9,o:j5jlypy 6q c3 n in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does itrjy q63 5clyz9jp,o: h 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 pointsrn,i.4ueytkie gxl-)7 u oy(6 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 plane as a strai4 ekyd18jws :xght wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude ands:wj8ke y dx14 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 i d0 :jtj4mz m )wn6vtfi+/d9mA. A second wire, made of 2.5-mm-diameter copper wire and parallel z+mi0/m 6t dnftd9m4j:wijv) 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 w3tyu(mezn./ tk,;m kperpendicular to each other. At their c my/;k m tu3kn(w,et.zlosest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 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 curre(dr,v9x qz* jvnt. Wire B’s current is 4.0(,qx vjzrdv9 * 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 w)5t u5p i4nrefrom one another. (Looking along them, they are at three corners of an equilateral tria)w iupe4t5nr5 ngle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and dis5g6o/mmhv9jsd 6 /kqw0,alyrection of the magnetic field at the mdywms 05al/qs m9 ho6vj g,k/6idpoint of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal curredc/5r ok+he,mnts I in the same direction. One wire is at x = 0, td,5+/kemrohc he 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 42hb0+j1. h*sfxbuz3 tcvc 5ck,0 turns of wire and carries a current of 2.0 A. Calculs+. hbv0hz*5cx,ukj ccb 3 t1fate 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 0.385 Tedm(-lhj/ md8cti o9 o.. 2jzu at its center. How much current should the solec2j.h( d9-/imz8.um e o ljtodnoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in itzq yv/-e4ha83 oodf0s/r1 mrg is 33 A. A 3.0-cm-long straight wire cuts thfery 3aordh qzo s-m4v01g8/ /rough the center of the 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 copper and want to make a practical solenoimiiahhy 7ooe(5/:a/ l d that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such : alya iohi/7e5 oh/m(as solenoid diameter, length, and so on.

A toroid is a solenoid in y2n7y-,f*sw sla4buk8 ;hn.rg xf*c sthe shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to dek n;r7,fyac*lfu2 swy sn4gs*8.h-xbtermine 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 o u1.jlr4gg:a ;dmk;bw v j-kp*f a coaxial cable (Fig1d-4kbju.ag :lrjvkm g*p;w;. 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 s*nlu wtumd8q :,7a4phq)rh/ its face parallel to the magnetic field between the p8spu7h ,:4 ntlqw/r*)hqmd u aole 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 scq pyrz-z.o -7hale 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 weakens bj q5qlc2v 3t6j6qhhh+s/k y;cy 25% over the years, what current will give full-scale deflection q5 c+ qcyhqk3j/2thvjh; 66slif it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what f8cfkl;z 1al0 cactor does the output torque chang ll18 cf0z;acke?

Show that the magnetic dipole moment M of an electron orbitin aiieyj: :osoal pkcvwa* )51em+-+, jg the proton nucleus of a hydrogen atom is related to the orbital angular momentum L ofcl -y po:i+vj+:waj5mi )seeaako ,*1 the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in dia.l+j*b ; lu0*tbknqs jmeter and containing nine loops lies flat on the ground. The Earth’s magnetic field at this locb;+s*lj u*b.ln0t kqj ation 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 circt*uv6pn fb4y1 z9r--e. g)ihgbfy; gb le of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their pathyn*f g 1 uf.b6bi -b;g4e-prtvzgyh9 )s straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii wjbz8p00i t g3z:drc8 ;(aujvof curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic ma0pvrc(:zab 8i; 0w 8g3udtjj zss of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field betweveg ofj8 +s rx60h;w,08sigvr;axu8 aen the electric plates in the mass spectrometer of (Fig. Below) raxxsf 6880 ivs je0o ag;8u+wvhg;r, 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 033;6i5l vo4e fsnmm*ui kua p2c*tjcto monitor air pollutants. It is difficult, however, to separate mol*v2 f6 itouml*ick5e ;cp0s3nu3j 4am ecules with nearly 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 spectrometer accelerates i wvb;g9x5.kxzons by a voltage V before they enter a magnetic field B. The ions are assumed t;x9 bwzv .g5kxo 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, andy jdsq 6dq-4x/ a 25-A current flows through the wire. If the permeability4qqd6ysj/x- d of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long20 6qczuas9tvjk3wm 4 and 1.8 cm in diameter, and has 640 turns of w6 uvj4cm32zk0t saq 9wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum om zam6c6g5k 4$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 energyea8 hkqp8dp7zibciu8 1 e2x zsy138.r upon entering a region of constant magnetic ficsi8 ei2 71hzp .1ku3 88az yd8bxeqrpeld. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig.kqf1- ; hm la-c. vg/(c(e6b zjkfj4uk Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a stbckku1c(-f/he .jmk-(f z46lg qa jv; rength $5.0\times10^{-5}\mathrm{~T}$ 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 acquire0*er5 m8rrp2e wyu: god 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 almost hora vnj :q*jhp :4k4.w.qf;ocjuizontally to the north and hahw 4qa n :.pjj. c4ojfk;:*uvqs 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 mass is +a 69hksec3jm $6.6\times10^{-27}\mathrm{~kg},$ 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 laur9 ukic+co604jxic8vr/yf1.c pn1u n ncher” 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 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? vrnc81iu / 9 4 xncu.0+p1icjyrc6okf
   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 susp z0my o0pcrx1*4xsvdxh:ql- +ended in air due to the two magnetic forces from thx 0+hq1*ox -dmc:s4z0pvyx r le bottom 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 xo)l t.cyvn18xh oa6 ,apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to eachot h61ynvax l,.ocx 8) rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electr(z yw t/ oxb1 wm/t*.,uvbgb3ton beam near the center uwb,/xb(tg 1*3tot. ymzbvw / of a TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a devic87y zxgzq) yldw2 *dm4 ck4ecnwl/5 u;xv1m m;e used to accelerate elementary 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 thermv/8x4l 1l w4mdyw ; k)uzc e7;yxzdqg*5c 2mne 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 parallel2pg ncua9i db1ti6fy9f7 k2tgm2-j1 x wires, located at the corners of a square of side l, carry equal j k9c9ani1 dtif 2 7xptm16u2gbg fy2-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 veli6lah( dys mj *29xk3w x2u(38krubfry useful in particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are3b63klu2id *x2w m syr akh(f (jl98xu 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 circulakfxm8-), on d+ lbo*qyt ser)uf nz8/7r coil of wire carrying a current8sq*+r)ntm e no xo,y7zb fdf8 lk/-u) I (as in Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic field is about im6 q2iy:bl- k/oefkarm5u / +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 cex ;c i-dmuhk3*2 :grthe magnitude of 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 macg32:u;h* cxdkm ie-r ximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of electrons, traveling t2snvg.s1l/f vo the right s12/v.glnsfv 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 pathv mellglf8jtgan7 2*+4a ph8m/2 zqy / 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 and Q, the radii are 10.0 mm and 8.5 mm, respectivel72//ma *a+48g efmq zlyh2ng jtvp8lly. 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,m56g ,o:zonscezg ocvu6.52f is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, ho6 ,mc2ofg 5sn6 coeg:o5vzu.zw many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum )3x+dkganowip* 4aw5wires, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspe p5k4) naawxg*+diw3onded by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T awqk9p, .ahw d iaj.;0ot 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$