A compass needle is not alway:qnduw p7f 7*us balanced parallel to the Earth’s surface, but one end may dip downward. Expnuqw 7ud*f:7p lain.

Draw the magnetic field lines around a straight section of wire car ni(y w,1 e(mvy(ecoo+jo /r7grying a current horizontally to the 1g(mywveo,i(/7n(jce ooy + rleft.

In what direction are the magnetic field lines sun::h jb )/uhd3lhebep)l8i*r rrounding a straight wire carrying a current that is moving directly a e bl8*je)phr l:ihhn3:)/dbuway from you?

A horseshoe magnet is held vertically with the north pole on the left and bu o,mk6clk(b9a-r )p- qih9 wsouth pole on the right. A wire pas9 )-6qip ,ru-9 kobahbmklw (csing 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 those manotmuzbo b(w:d-0p e c12ln)ke). 6ekde of iron? (Try it and see.)d-e( kt p1. bw60mbl2 )nonou)ek ce:z Why is this so?

Two iron bars attract each other no matter whark)rka/ ffo; ,.7 kniich ends are placed close together. Are ba.nfr akkki; /of r,)7oth magnets? Explain.

The magnetic field due 72wnjzf, *y7)g kw-8itm9iw (nv gjpkh8c,dlto current in wires in your home can affect a compass. Discuss the effeg- df8w7*l)wm(8gktn2 hz,7iv yk9i nj ,jc wpct in terms of currents, including if they are ac or dc.

If a negatively charged parti,b,,-py8xdx :0pc qp +mmkyz ccle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the,p,xybc8z :p d- k+xc qpm0y,m same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged p8l5p/o0gqb gsn* b+de articles move in the 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 direction of the magnetic force duq +p0nd*/bsbg5loe 8g e to the magnetic field produced by the wire.

Three particles, a, b, and c, enter5ww 512 vh7og jh7cq;si,yxz f3jwjv pl 906nv a magnetic field as shown in Fig. 20–46. What can; f12lp6o7 ycjsj75v w h,vwwqx59jihv 3zg 0n you say about the charge on each particle?

A positively charged particle in a nonuniform magneo.e/3r:bygdy i c k*j+tic field follows the trajectory shoc k+d iyb g3e*o.yrj:/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 ma-;c y-ko /qxxwgnet attract an iron rod? What must you consider to answer these questions?; /-okx ycqx-w

Explain why a strong magnet held near a CRT t* v xp.p t5-pwaaz8biq d/nj:+elevision screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes compadpi. +p-jv bn*tpw :azx 58/qletely 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 fs ag5g +b-vnv/v5*+;buen cxmagnetized but the third is not. How would you determine which two are the magnets wig*b +bn5v- exf/;s+nvcv a5ugthout using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an electrh e,5y 8kw-8nvln h9hz;azn,cic field? Explae-hvzlwn,,yz9 hnh 8; kn85 cain.

A charged particle is moving in a circl0lli(*uyh5,x /v wsrb e under the influence of a uniform magnetic fie,lv ylb0hi x/*s(rw5 uld. 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 iho,xxeb9t hh g 1 yvns/,g5f(,n a magnetic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) gtb h1,s/ ,hevh5fygxn, 9(xoand 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 positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying 7iu19tdw-q/y/v/d: h e wqvuvzm;3 fpa current from left t vwfq tv;hz9//d-/ :qv1upem3dy7 iuwo right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/; x7z2nylg/ z s;gr*skor magnetic fields that surround a moving electric charge. ;72sk/;rzx*ynlzgg s

A charged particle mov)q5e muc :ky6bes in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible b:6kumce)5y qsituations.

If a moving charged particle is deflected sideways in som/s i0;x(kc e( cfczi2fe region of space, can we conclude, for cerk e2c fc/f(siiz(;x0ctain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform menp u3kt (2 bpucp/)5iagnetic 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 wx3yhf5l xc1;mm/s9 8o*rtyd so 0 t*nhhether moving electrons in a certain region of space are being deflected by d1tym3shto* mx; c5y 9lxf8n/ro sh*0 an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other fer3,wa y nh9(z api eix.4h*lx twr1s:vu9vrd4-romagnetic material?

Two long wires carrying equal cuyk fs 4ca/kv55 j v93vwx39hcm:2qvwgrrents I are at right angles to each other, but don’t quite touch. Describe the mav4vgq/23j avw c3km wc5h9f5ky 9vs:xgnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Eadj pp. mtc.zr.j;,y aliy* h/2rth’s gravitational field, is suspended directly above a second, parall,2y*jdmc / ayzj.p;.lhr. itp el, 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 magnez g a49p2p9z7/k8qu mrm:.wt it9wm cnt attract an unmagnetized piece of iron?

An unmagnetized nail will njm*olji584 z3 vdmg1+ um*u)elom i8fot attract an unmagnetized paper clip. However, if one end of the nail is in contact*m48mm 8 ojl ivo1ugl ued+z)m53jif* with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same m i-2x7mpo8zi2 6rwy e lzb1wx6ass, but one is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrx6wr2ze x8wb-impyo16lz2 7i ometer (Fig. Below) differ?

What would be the effect on B inside a long solenoan f87f7)tlifid 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 cr e60 :inm q:r.e .yeqrox+z(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 ro nqi.+0r(r:ee m: .q c6ezyxswitch. 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 current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length 5q8mvyg: wf 1qon a straight wire carrying an 8.40-A current when perpendicular to a 0.9vg5yq fqm w8:10-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 straixqmp :ts9++is ,8rn g2 cyvgq8ght wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field ofigq+ gcr9q8vx2p8sy,mnts+: $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of straight wirep+;zu7 ks. gv:8dp4cnhy 3eys stretched between two towers carrhppyen7 kv;4. zcy udg83+ss:ying 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 gl0/ (eude2r-h:hid cin a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a uhhg0ir/c l 2u:e(- dedniform 0.0800-T field?    A

  A 1.5-m length of wire carrying isiw3 tpk 77edks*nb 14 h4jz84.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle of 3d 8eh4kb w1 tp7nkj4i is3z*s78 $^{\circ}\,$ 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 1.28 N when o l*rzxgia,xx5z:d8 7placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, woadx i7 :gxzx58rl z,*hat is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measuredh/ 3kej1 vzi /jr*yyo4 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, anz jyyhoej k* 4r//13vid sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum cs/j/ag+cue. 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 coppk kqkhm* (p d93gda4qvutwq:/;7l7 fuer wire could just “float” horizontally in air becaup v/a7m u dufh ;t3kd:qkqk9qlwg*74( se of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of ch4jvx) /k 8tx zoll/3+e9 p8kcy hlwq0qarge $q\,=\,+2e$ 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 andk5+8u -u .acq*p9sc6dpom fq c 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 negative charge for each diagram shi 51w4nsccp a s4.zn.hown in (Fig. B5wzan h cin1c. .4pss4elow), 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 directiltwv yzs x8x0(mw +fwp: a7d64on 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 t-,46mwjb kx3el.nzy vertically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energyd- bm9-vf. dwn(xf ge)) proton enters a 0.20-T field, in a plane perpendicular to the field. What idgf- be- w9)f.x(dmvn s the radius of its path?    m

  An electron experiences the gre80qnutk8 ed ;yatest 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 undt* lqdi4m8cc+(1h+zk jpgi j 7eflected when passing through perpendicular electric and magnetm7 14 k(cj czq+lhdji*itpg+ 8ic 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 fm0h .z8+oki:)mdjyq 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 charqh 47bwac5 24cpl01eo1eee ddge q moving with constant speed ve5lwp 1ecbq47cdo de42e 0ha1 to 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 i +t xy4p4l3vdw47lp ba circular path of radius r in a uniform magnetic field Bbwyd4lp4x7 4ptv3 il +. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circ,l5-n zwwbilhfc0 y.( /3wt jtular path in a magnetic field B. Sho 5fitnzc0lwb(wt, h3. y/-jlww that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular m26bt4s g vnx+womentum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to theg ; d(89ftphgadb.+ot zt*.hhpw8 fe 6 Earth’s magneticegd+ 98o.b paf;wtthp( d*h h86z tg.f 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 the equator hasp e6ku80:; eqtxglx i* 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 speolczpu2gy/ +l;94pye ;u gbp8 ed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 cubr+jbuf,8sopv6: m9pt u47: mop ss,orrent. How strong is the magnetic field 6.0 cm away from it? Compare to t8 ojo9,ps+r mftus7 sup : vbpm6b:,o4he 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 +bfw fvng.: ) x-egku1a magnetic field no larger than that of the Eart+g gxf.1eb v kw)-ufn:h $(0.55\times10^{-4}\mathrm{~Т})$ 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 page toward smd1b b -2sofra o/.h5you. Indicate, with appropriate arrows, the directiofoo/. rsd shba1b2m -5n of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carryir 9btg:gjy/,y ng an upward 24-A current exerts an attractive force per unit length ofjgt:/, yr byg9 $8.8\times10^{-4}\mathrm{~N/m}$ 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 beti1) r3uewg)jl fkn7n0ween two parallel wires 35 m long and 6.0 cm apar)k 1njl)n 7eiwg0fru3t, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic fielu;7opul8z y*mpq16psdi 8* f ld is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment i;q8pzl8p ip6*fy7*du lou1sms to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high w-kp qfvm,0c :poles. What is the magnitude of the magnetic field produced by thisq c,-fw:m0v kp 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 k/,87byb d.qym6t grmwires 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic gm.b ,qt dymrkb/867yfield at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a stazq3;f3dbrfg- 2x k0b raight vertical wire carrying a 35-A current downward. In what direction does the compass needle poix;f3-brb qgazd fk032 nt 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 nortr if4615-b (ocx e+fekt hw)wt2hmt7th. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but d6otxi w5 14)+(et-r72chhfek twb t mfownward, 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 zenw e hnkpl;m30hg1 270sv /rprotons passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two lb n-qgt 6qqt4h3kmh. 2ong straight wires 2.0 cm apart in terms of the current I in one when the other ck463-qh.mt2qqn h b gtarries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, anuu4l,yi + jso.d 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 the .i 4+ul,ysuojir 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. Belj. e)woodv;vl9wx8xd3 5ig5 eow), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the 5evj wd;5go dow3)ix89elx. v nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points 2 ,iz igi4g0(dt3$^{\circ}\,$ 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 straight wire, as sho*jensx-l i0qmw0eyz 043 gggve ;; 4xiwn in (Fig. Below). There is a current of 2.5 A in both wires. Determine th0wgz 0 0* qgv;i;xseye mlj -44ein3gxe 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 w:kshxj wrdiw)ty8 . 7jfq97c uy+(f -a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetf7f-txw )y d.ckrj wuh9s7w8jy:(qi+ ically 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 ne ;s:0f y) 0f:hobvfwwmy ,q.to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carri :)smw:b f wqf0ny;0foey, h.ves a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15k/mkj: .j tlv1 cm apart. Wire A carries 2.0 A current. Wire B’s currj:1v lt mkkj/.ent is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one anotez0h1++ ruhq-u g1:wp6oblen her. (Looking along them, they are at three l01uzqrneb6 op uw 1+-h:eh+g corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the m4uo7khijeg6h -ur7 0. c;p xlbagnetic field at the midpoint of the side of the triangle between g7o kh i74h0pjub 6rl.-e x;ucwire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal cur1, dbqh fqng4*ej+8f+*ax dfnngc 51orents I in the same directih4qqxfd8 +*nnagbf1c,1enfo +*gdj 5on. One wire is at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420i bp,nzk/ /z5a turns of wire and carries a current of 2.0 A. Calculate the field inside near the//az ipbnzk,5 center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenpcl w 7d(;k9heoid 1.25 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turnseph ld7k(;w 9c of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. 4*dh7me-rm4f 3aqqy l A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current dow a4dyfe3ml4q mh7-*r qnward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that prod7 ig m,f1ek4xmuces the greatest possible magnetic field for a 7im , k4mx1feggiven voltage. 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 in the shape of a circle (Fig. Below). Use Ampère’s la3b, iw-eq/ 7m;gck mzbw along the circular patwiezm73b q;m-,/gbc k h, 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 show that the magneti81irp k 7h-ku k l.mxi7x5ptx2c field between the conductors of a coaxial cable (Fig. Below)71lkrx-8kx2.u xp thm5k 7 ipi 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 looph0)zza9p(tt k of wire 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torqupazt09)hkt z (e on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deel b:4 3wjx0zdxbbr* j2e*xm;vnaoz9,y-la 5 flects 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 ofgyglf , :. xwkokmt78; a galvanometer weakens by 25% over the years, what currentk7.,8:;y otgw g xklfm will give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the ; bio 5j;ke9 n;ncp*pkoutput torque ch;k *no;p5ncke jpi ;9bange?

Show that the magnetic dipole moment M of an electron orbiting theowj98j s2v/ as proton nucleus of a hydrog8/s9 av2 jjsowen atom 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 nine loops lies flat9zq y v;bv80aj on the ground. The Earth’s magnetic field at tavj0;zvq8b 9 yhis location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic field. Wha2eskwx 5) 5ls)c(ye:rnj1b syt value of electric field cour5x5l 1b se(2: kyj)cnes y)swld make 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 2uru q aur*g 2u5nhl2))1.0, 21.6, 21.9arg )u l)2q2 uu5r*nuh, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mx23;ds qs lj*vass spectrometer of (Fig. Be;s2s v3ldjx*qlow) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pollutants. It is difficult;i xq vltx3;:e, however, to separate molecules with nearly equal mass such a;iqe 3x;:t lvxs 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 acceleratethsb1.(mk/ox*cx le bltj;r t10* uy;s ions by a voltage V before they enter a magnetic field B. The ions ares hexl1y0mt/1ktb u;(; * lojc.*rbtx 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, andy5t -:l4vore6a+m fjxgk d89iv e1. ik a 25-A current flows through tk68lv+1.mxevt9dkij i 4 5-ea gf:y rohe wire. If the 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 1.8 cm in diameter, and has 6403xk2o adl:(;lvm0h5i r r q*:bgepz.o turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permea o::blaor (edmi*p.zh3ql5k vx2r ;g0bility $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu5fjcvf*4ep r5 m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 havejvgm:mo 3 o84l the same kinetic energy upon entering a region of constant magnetic field. What isl 3 omv:om48gj the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a ho2p.et3 i-z*o n/ tcgfgrizontal current of 330 A toward the east. The Earth’s magnetic field ha.e tgtn-gf* zop/2ic 3s 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 airvimd ajnf0: 8*plane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s+ wsib0j :yv6a magnetic field points almost horizontally to the north and has magni:ywbsa0 j 6+vitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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, bhr;on. 9 *8z: rghkldwhose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A larb m it ) rq8alco+ pe-7rnce*9.yk/6nvge 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 ple c +9i tr)k6. valqm 8r-/bne*cyn7opane 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?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper w .rubds)*jgk 6ire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flour)b. jgk 6s*dw in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal + b8mi .hmtbl0 mv(u .e+8tc:mfn8djlplane act as rails to support a light metal rod of mass mtjfcvhm8m u8nmd8.:(l0ei.b +t bl+ 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 maximum d jt : z-j1+,wl2bwogpaeflection of the electron beam near the center of a TV screen due to the Earth’slbw+- j, g wa1op2tzj: $5.0\times10^{-5}\mathrm{~T}$ 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. Be) wfdzfa 7l:)yo/hdr0 low) is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbityffa)7 o)lw d hd:zr0/s 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 squayray 5hs3th/tk0x4fk ./ c,z ere of side l, carry e,f /rzshh35ty kc.0kay4 e/txqual 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 accelerqp7+b kw.of4mk zn*2x bea90 iators 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 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 ofb7fkzqi42 apn*0b wxk+m 9o.e 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*p +/c*yi-dw vtg+hac a circular coil of wire carrying a current I (as in Fig. Below) icc+yg/ai*-wtd +h *vps
$B=\frac{\mu_{0} N I}{2 r},$
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 ij8 c0j3;hbjfy5cl4 x ps 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 thewjaw9j(pnwgh. t+;+k magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m aboven k.(hjgajw; p+ w+w9t 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 field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic f *2zkc+ 4q4qxg*vi7atmj h q/nield would make a beam of electrons, traveling to the right at a si+ qc am 2xgq*h*44/ 7kvtqzjnpeed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0.010 T, perfw/*mzpb) h+7g / gtkupendicular 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, respectively. Calculate the change in the kinetic energy of tbu /+)tmw*7pzhg/gk fhe proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm ibe2y7aig,-ioviobodw y9 py6j*172s n diameter, is to produce a 0.30-T magnetic field at its center. If theobi j6 y ,71oe-ypi7g2bo9*2wi sdayv maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the sam 3lynweccp5c - j81kf:k/tm (re current but in opposite directions. They are suspended by 0.50-kcw3 nlfc1c5m(et/yp:j rk-8m-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 magneticqbvyidw u7y6;;t1 z ,u 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$