A compass needle is not always balanced parallel to the Earth’s surfacg,+ebyewdh1pw7b,- ;kxb 1 tpe, but one et p;xdwg1e,kyh1p-e ,+bwb7bnd may dip downward. Explain.

Draw the magnetic field lines around a straight section of wire carrying 8as:q .) j2e b)cpuj6bce+oww a current horieawe)s8:bq 6w p jjc2+cub )o.zontally to the left.

In what direction are the magnetic field lines surrounding a straight wire carrl-rxm 9/as.wb 7hd+hbying a current that is moving direcsh /b ah.wx-mr7d9lb+tly away from you?

A horseshoe magnet is held vertically with hnvi 1td d xvp- i8y6y70s95dkthe north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is y1s tikv9-vd06i xnd 8p yd5h7the force on the wire?

Will a magnet attract any metallic object, or only those mt3y0kcdj.3 fs , v/etz vol5,pade of iron? (Try it and /,cvto35 pj3zk 0vyel s.tfd,see.) Why is this so?

Two iron bars attract each other no matter which ends are plac7h6y1salfe 60y ng (bced close together. Are both magnets? Explaih(7 eya60n bg f6sc1lyn.

The magnetic field due to current in wires in your home can affect a co,g9d ih* wge:umpass. Discuss the effect in terms of currents, includ*u e9dgg ,iwh:ing if they are ac or dc.

If a negatively chargh: xz/a/fez 2zed particle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the pazh x2//zz ae:frticle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charggx8 .ge ca+i,sed particles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the paa.cg8, sg xie+rticle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic f0n2b q 9v4ed; qrefwj6lq9t6a ield as shown in Fig. 20–46. What can you say about the charge on each lv6j09qadwq 9efb;e6 t4 qr2nparticle?

A positively charged particle in a nonuniform magnetic field followl .+lyx6eq(kly rux4, s the trajector,qe4 yl+ll6x.uyx (kry shown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attraj4 8g:e)pw9kmy x(fol ct a magnet? Can a magnet attract an iron rod? What must you consider to answer these questions?k4)pe y l(ojwm :9fg8x

Explain why a strong magnet held near a CRT ( vspek 42hsv+television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by tryin4vkvhs (s+pe2 g this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rodcmtsxsl7j g)j 8ewm* ,4;)zqms, two of which are magnetized but the third is not. 8)7jm;ltje g )mc mq,zss4x *wHow would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? W8x oe:cw ;qwt*/ m+getith an electric field? E;t:e ww tmqgo+e*8x/ cxplain.

A charged particle is moving in a circle under the influence of a uniform magnetdn7x p7ea+l7wrle . .oic field. If an electric field that points in the same direction as the magnetic field is turned on, describe thenw7edx rp +. ea.o7ll7 path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromagnetic /azx/ ) amjj*;alaaf7pumping. 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 jx jaa7l z/m*aaf)/;a. 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 ca xkbs 8,z6xsb:hvi40grrying a current from lefvgi:4b8 sxs 0 bzkhx,6t to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric charger*76h(aix mw 1uubo -v.m7bu(r- uh 6*axowi1v

A charged particle moves in a straight line through a pm-l l(s 6fbftm.v6b d1articular region of space. Couldbvf s6lf mtd 1.(lb6-m there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways i88 ixwz zen (9x(s.yhln some region of space, can we conclude, for cert(h z9xyz e8s( i8nl.xwain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fiv6x.bkr3+k(z vhkmv6 r.v tu.eld $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain region of saqcy )bn(m rb -5yvw(x y70:ixpace are being deflected by an electric field or by a mnx05b(yc-b7 i vqrya:ywx )( magnetic field (or by both)?

How can you make a co, usse 7rarj- .n.i-/+gmk vtl4fs l*kmpass without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles .l/h*he( dqhhj ,mku1 to each other, but hemq(h .*lk,hu/d1h jdon’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitih:ktr i7pf p/kh c38z ad07w;z 9kvqm(2*pf hational field, is suspended directly above a seco2*h8fak qkk;wzt:9fi d7h rvp3 cz0( ihpm7p/ nd, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract ;dni/h eb:k6gok6s; wan unmagnetized piece of iron?

An unmagnetized nail will not f /n 6tv(vfwnr;cahcxh0(-; i49oiuoattract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the otherait ivhwr;6cvu n;f(-fohoxnc0 49/( end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and 4 x.xf/pzldr :nsa+amcq ;o4 0the other is doubly ionized. How will their positions on the z40.anrl +s pxm;4/a foxd:cq film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenozl:uqjlq. .j3.qhz oo ,i57sl id 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)luws2o xl2, s a relay . A relay is an electromagnet (the iron rod inside the coil d2 ), u2olsslxwoes 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 current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magn)oed(-rog3 wo itude of the force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform merog(doow )-3 agnetic 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 w7oweb11a j,k2f9x kjcire1k, c ej 9w1kfj7ao2bx stretched between two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic forc8i a+4p4vhxime on a 160-m length of straight wire stretched pi44xi8hmva + between two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long if the maxi3o8glj 2gg i8-n+u ctqmum force on it is g +n8l8- co g23gqiutj0.750 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is orient z0yrl)6slvmma.m/fp 0*o.a ced horizontally. At that point on the Earth’s surface, the dol) am0cf.mzsyr .*m6v/ lp0aip 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 carrv v4-bdycd26jying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the d b4 jc2-v6vydpole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter zn.zs .ox xvik9*a*(qon a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximu*szv9kz(no. xa *xi.qm, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is oc16 od. dczj4a 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- jeb z)zt5(kf:veuw a-.b, ob wire could just “float” horizontally in air because of the fob)ejzfv -(-b owba: 5eu,zkt.rce 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 chargea hxa:ud;phu: 7qf+v+ $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the fo.tm e6h.ef*bg rce 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 djn:7ul2 c n6 x0yw0xgniagram shown in (Fx0j07x6n:ucl2nyn wg ig. 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 directm(7r d)j.qbl m +kgoiucv: p9,ion 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 :vt1k2j j exslws 7c1j0ruaff v97/l +vertically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton y7dm 3ltiu .l4g.xb5wenters a 0.20-T field, in a plane perpendicula345gb7ty.mxid. uw ll r to the field. What is the radius of its path?    m

  An electron experiences the greatest force ha *9izvc,z m ffana 3:yi,x:;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 elecro0lgalt+p0w0i3 z )w*y8df05g h w fstrons that go undeflected when passing through perpendicular el0 0a3 5ypilos0ghwtfdgwfrl * w+)z0 8ectric 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 j6vr fd/tnw3 +whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge q moving with d x( l3vcv bjs;: 0ca2ezm3lwhuv3q70constant speed vs2vzd0lqw(l3 b 7;:mv0 ejc 33c hxvua 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 a circular path of raddmml(47 7/zdd*to +oqq b w+tpius r in a uniform magnetic field B. Show that its momentum++ do(lmzq qt 4dto*dpw/77m b is p = qBr .

A particle of mass m and charge q moves4 dgo vqy7mxl4szi8 wqr- ,-*g in a circular path in a magnetic field B. S4o w*q7r, igvml-yd-g4xz 8sq how that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular moment r4sj0jp4tpwg,1jjn1*mek p:um 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 b8p e-xxy *2umr+x4mklhl 1e)to the Earth’s magnetic field bh e1mxel +)2l*x8k -ryu pmx4of $5.00\times10^{-5}\mathrm{~T}$, 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 equop;j. np8 h1p*rw,f5t wu0e paator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with xtu6knrspq vq4 vz1) h0rj, :+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 b( m*aibnx vqlrhw9 5tg-95j c+q6gr;stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Eal arjrmb 9 (6*w-tcihggq5;5nqbx+9vrth’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 v)yh3*u hlih, produce a magnetic field no larger than that of the Earuhli*hy3 v )h,th $(0.55\times10^{-4}\mathrm{~Т})$ 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 towa5kl ..q ru6xasrd you. Indicate, with appropriate arrows, a.sqk.5lr6 u xthe 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 2b k2fvym :1,u.iuxp1ge0okp +4-A current exerts an attractive force per unit lgf20uix:+ epm, u .k1ykovb1p ength 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 betw)fsou/y7s) j ween two parallel wires 35 m lon /7w s)ofjuy)sg and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being car/*u krcb+0 .b umc(iekried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is eb.kmku+0i*c(u r/bcto be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high pol , x1w0ink h z+c-a;8r0 g)ccjkzj)arxes. What is the magnitude of the magnetic field produced by this wire at the ground? H aaw)k n01,zgc xx)c-hkic8jr r0+jz;ow 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 ioj0*c:t8ns b q j0blx,n the same direction. Determine the majls:*,xq0 c 8jbob n0tgnetic field 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 f3xoj9.pp0 ecu4y )v (kvkqx7placed 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at vypo e. ukxx7c qp 3)(4kfv09jthis location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due north. Wh;pyn v6xz70wl,hj p8 tat is the net magnetic fiewh7 l6nvtyj ,px; 08pzld 20.0 cm due west 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 point in spac:tqqw-l o6i xe.jnk,75ko5 hse 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 long straight wiresqo xdzt u 4x1gm1x)p m:u30y3u 2.0 cm apart in terms of the current I in one when the other umy o0xx:4 3gmzup3dtu1 q1x )carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, an i9)q+ r a3 dhdiea43qmanstrument. If the q4a 3 93)admdraeiqh +insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plaq;t rnu/2ad) zne of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to ;)qarn 2du/zt 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 23nhadz vanqkl.1a3 r05as/..t$^{\circ}\,$ 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 straightm8gsnx2u df9z0q /:ey wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the9m :xde uy2 z/f0nsqg8 loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carrigjhyc79 jw7w/ v-6mez0 ) qslces 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 magnetically 15 cm below (Fig7-)6hgjq9 wwlj7cevsym zc0 /. 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:(/l *smnjk aayd7yg2 that they are perpendicular 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 (dslgay*kn my:j/7a2 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 w 0ylf:c;n;i odires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in ti:dyf;0 on ;lche 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 onrcvp s(in4d w5xs+-b1 fvu;7se another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit bp;1d-vvrx 74uss i5fwc+s(nlength 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 k*3o ith 5i:aygyo5)pand direction of the magnetic field at the midpoino* p5i aoyth)5kgiy3 :t 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 currents I iv6 jt:b,*uz z1kf, zoqn the same direction. One wire is at x = 0, the other is at x = dqf, z,:tkjob*zv u6z1 , (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 o ab,mqmjd 7 bk2yqb17h4.gzkkwv)+ d(f 420 turns of wire and carries a current of 2.0 A. Calculatzb v 2b1 dhj(a7 bkqkm.dwgq4y,)k7+me 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 T a52u xb q7j:avw l xh-ef6y6+d4p ,qzkkt its center. How much current should the solenoid carry if it has 975 turns of thew5j 6p+7 62yk , -fdqvzaeb qk:4lxhxu wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long s,rwyv4 n9l3mit :bf+ ptraight wire cuts through the center of the solenoid, along a diameter. This wire carries a 2wf p4,vlyn r3ti+ mb:92-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that9y ok)o*nv97g4tgjw za l8e 3p produces the greatest possible magnetic field for a given voltage. Should you make your copper wire9oln*zvgy3 j4geo)ka9 w8p t7 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. Belc, cism ,w5v2uow). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic fieldsv,,m2uw5 cic
(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 thun-p y-llfe.*70pku8: l nplo at the magnetic field between the conductors of a coaxial cable (Fig. Belowlu kf n0p.7le8l-*p y-nu lp:o) 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 its face parallu vd ah-m.a 13u*: zppuuw5p0btu3ef8 el to the mu wdu :favmebp* za08t3up .p-5uh1u3agnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflect1j,uj rdax4s 2s full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometerr ge6uu7s( k+d weakens by 25% over the years, what current will give full-scale deflection if it origd(u6gkr u+7se inally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output to4 nebq9yhn4(.qmc*g prque change?9pn(c*.4q4nyqhm g be

Show that the magnetic dipole moment M ofrj0v x+x:rzf,k-. g;dy dgea 8mjo66x an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angulerddzj:8o x 6 axg+vxk.y-mfj;06 ,grar momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loopsd(pyo1f9s n9x(d 4s;lr:h syy lies flat on the ground. The Earth’s magnetic fields9y:1 fhnr( slysp (y4x9o d;d at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radiu9ik8ljwr /hw)s 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction must kw9)8i r lhj/wit point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium a9ebeyp x(c+*cseq93rkp. w o)toms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 c3oqk+ rb.*(w9 sc9pecx)eyp em. 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 pla 5 hv jgd0pqe g6-/f:71pinzjftes in the mass spectrometer o1q- pzfp6fd5g/gj7h i0:venj f (Fig. 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 being used to monitor air polluteammvb; hv.bn (52ws5ants. It is difficult, however, to separ2e a5v.b (vmbsmh;nw5ate molecules 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 acceleratescug+) klp a+l9qu zn)) ions by a voltage V before they enter a magnetic field B. The ions are assumed to start fu+cn)9lkq+)augl pz) rom 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 o si, ajjygl zr.f6554ef wire per meter, and a 25-A current flows through the wire. If the permeability of the iagref5si , y4jj. zl65ron 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, zi2c6 -1p :cvloin:wxand has 640 turns of wire. The magnetic fi:6niwoc z:pilv- 1x2celd 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 /8f h0etn7 fgy$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 updq/gqxuhi 4* -on entering a region of constant magnetic field. What is the ratio of the radii of thq4u/qh- ix* dgeir circular paths?   

  The power cable for an electric troln(3 fvg *p,octley (Fig. Below) carries a horizontal current of 330 A toward the east. The Eart,v 3p*ft(goc nh’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 whh89c6wi s4 ag5zj nf,bich has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almosth::q v r8lm+pqpx j8+sj0mv)f horizontally to the north and ha: h0m mpl8xq r+fq8)v:sj+pjvs 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 i tt1 :6ttxeja-y-czqzrx7t..s $6.6\times10^{-27}\mathrm{~kg},$ 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). e zolhqm bla,/1r.7w9 A large current moves in a closed loop composed of fixed rails, a power supply, and a very b1hqm7l9./or zla e,wlight, 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?
   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 0xvz k,2r+xich*3ik r5juq v; suspended in air due*r+xhv2qk3 xuvj0,; k5icriz 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 flow in the suspended wire.    A

Two stiff parallel wires a distansb ar .+k+,xgu ijcjszq9 1v20ce l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below).k + 0arjq ,zus9 1.xjc+g2sbvi 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 epkkprj*ex +;a7k8j g(lectron beam near the center of a TV screen due to the Eart+7x8kjek j;a*gpk r p(h’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementary :goh 02/cutc8pf ids4particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an el4/i08t uccofs gh2 :pdectric 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 thn5+ pl8tlrf1 sk r,m3fe corners of a square of side l, carry elsn m3lr,1+ 5k tfrpf8qual currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beawvi 9zj.nv)j v8:h6uzb)d+sbm steering”; that is, the magnetic fields can be used to change the beam’s direction without altering vwjdjznshb6 )+vv8 z:.9 bi)u its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrying a7 2 *a0-x6uoryeqthk j current I (as in Fig. Bel6tj kexauoq20-y7 hr *ow) 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 magnqny 7i:7(a .p7kaxd+ tsiv(k fetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic 9s4l .6zwq psv-wfim9 fields produced by overhead power lines. You estimate that the two wires are eap mqf9 -6svwz9. liws4ch 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 field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a bmi l,pf 8srdcmv4o5d 9m8d3-wnkc c.;jg (m g7eam of electrons, traveling to the right at a sp.3;dg8sfw574 cm8p ,don(g-c9mvrjc mmd ikleed 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 0mrrrx+ + mf18i.010 T, perpendicular to the plane of the spiraxrri +m1mfr +8l, 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 solenoipy z(y 1nnlmmc9 l 36i6y.zsw;d, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum c9 l;w innmsym6c.ylpz6y13( zurrent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires k 2bomn4sq2r8, each of diameter 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 make an angle of 48n2 2 mqkosbr3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a unifog fcaa6tl+:g 1d/x) cfrm 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$