A compass needle is not b3b+9c:ffsxwo6fc / bdmd,-y always balanced parallel to the Earth’s surface, but one end may dd fbcm+9c/y,d: w-ffo6xb 3s bip downward. Explain.

Draw the magnetic field lines around a straight section of wire carjss*c6go* yuxt3 0tetpmz;x8 d ;3/hlrying a current horizontale*su jy0sx8 o;/*tt3cxl t 6;hd3zmgp ly to the left.

In what direction are the magnetic field lines surroundingugifm x2cs8b + 76ty-e a straight wire carrying a current that is moving directugsf8-7i+ b2cmx 6teyly away from you?

A horseshoe magnet is held vjg sqr2go0j) m fnm 520wn a5s*6)c oj6ybfg,jertically with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from tsgg r)2q0y,n2j jcag5j6 56*wfm0fn)sm joobhem, 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 made of iron?la4t ,yyc22 c;hd ;2 mii(ug-ykf6tzl (Try it andlmc2ytyt-2 kz ;i,2g4 c;fd6ay (lihu see.) Why is this so?

Two iron bars attract eachjh/m w.aj4ekbwi8+x*x-f. ot other no matter which ends are placed close together. Are both magnetxom4tb 8h .wfj+kj/e iwax-*.s? Explain.

The magnetic field due to current in wires in your home can affect a compass. Dve888t;2c wht9p cagafbr; y3gva:.viscuss the effect in terms of currents, including if ag8pwtc8vyr;8 g9 2b v. ;cehfva3:ta they are ac or dc.

If a negatively charged particle enters a region of o4 x0 5axxz/s 1zt8ls ydvh20vuniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Exaohv4/05x8 ss yt1 d2xzz0l vxplain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-carrying wilp n8gp+o mfe1;)3pjure. For each charged particle, the arrow indicates the direction of motion of the partic 8jnogf)mel+13p; upple, 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 field as shown in Fig. 20–46. Who aqea(( wh9v-at can yow-haa( 9(e vqou say about the charge on each particle?

A positively charged particle 8b-lvg,79ybe*-xkbyn6(zf ys w5i xt in a nonuniform magnetic field follows the trajectory shown in n8w,v5yfg7yl9te (kyz -xibb6 bsx * -
(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? k3s8tjw3d x 1s0,xrskv84sl p Can a magnet attract an iron rod? What must you consider to answersdlk84s0sw x1xp,33r8jkt v s these questions?

Explain why a strong magnet held near a CRT television scryyq)) toq) ;xr3vxv t-een (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongey )x)v ;)3 xy-qtqrtovst. [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 r)s7ld v-m0kmrods, two of which are magnetized but the third is no- 7kdm 0sm)vlrt. How would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic fielt8a s ggqe:n 06(*unvw1ym/gi d? With an electric u gqg80ia6gm1*:y/n w(s tvnefield? Explain.

A charged particle is moving in a circle under i(;+xpif4(di et-/c it ttp9-lyb6ncthe influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic fieli-t(pdye;t- i6lc/tnpfbxi(t +9ci 4d is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic/ 3(buppvan b7 field is the idea behind electromagnetic pumping. 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 tovp7/3bun (ba p move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a current fropqob7ld rj ih6b lh-)e9;8 )3ff9f jqdm left to rio9 7h 8rff ddf)-l9bq3)i;lepj6hjqbght
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetij qqn673f. lirc fields that surround a moving electric charge. jnir.l76q 3fq

A charged particle moves in a straight vfpuk** ) 3m x3-ynm1acyhn5uline through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situ5m- k3xf)nay vunhp m*31cy u*ations.

If a moving charged particle is defle9ef nx+ a(6y )mq9sun ccw:mi:d( zd5ected sideways in some region of space, can we coz( d(c 9cyw f m+xs:9 n:)qdienu5ame6nclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform is; w6mv*x i(xmagnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electro cb,vt2 .jwdl/ns in a certain region of space are being deflected blb v,.c/wt2 djy an electric field or by a magnetic field (or by both)?

How can you make a compass without u efqc55 iqc2sn;bn +x2sing iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to eac::: vtrz+jdp7+qrn c obt,c+7btb do-h other, but don’t quite touch. Describe the magnetic force one exerts on +oo-q,rvbttbdr:++::tc7n pzc7 dbj the other.

A horizontal current-carrying wire, free to move in Ea hj3 t q5 +rvtitg(q+yyajb)14m/,bu vrth’s gravitational field, is suspended directly above a second, parallel, current-t4j(yqbit at3hj5+ v1 qmru,b yvg+)/carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized piecblbl99a;n 3m2 j; fuzge of iron?

An unmagnetized nail will not attrsjvx 0 02wl(tdact an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the o wj2d0(0stxvl ther end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other b n qdxi cr50*p.og5/bis doubly ionized. How willd5 x.* pio5/rg0qbcnb their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid i; ;dlaguvo;0 vf
(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 gi q5y( /dp3lyrelay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activatedld/5y( pgi3yq, 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 magnitude of thstxn (ai m( 2u+u)*emue force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field? tu(+eu2 xs( m* mu)ani   N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic forceoior9lpp+f c79 5h8 vb on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s map 9o7i8+ cf5vhpbr9ol gnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitudckbn-/. 6 zg io/grh+ge of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Ea /6og+ ib/ngk.gz rch-rth’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 ma.kq r eyz64da-*ws,xtximum force on it is 0..e *atz6rw syxd4q,- k750 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current ist6bln. u:rcs : oriented horizontally. At that point on the Earth’s surface, the dip ang6b ::c.s ulrntle 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 cardy +yl:l3 br)grying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field? br:)ydlg y+l3    T

  The magnetic force per mbztdf( 8 (*llreter on a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field ifbt llrf*(8(dz the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire 4 ikjdno)r2;w1)5 (p 0b wix* ccjxoljis 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” horizontally ee 4a8(0b-7l 2pdlhk+qn lojdin air because of thaj2dllhe 7n+ ol8 -4(qkpde 0be 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 c)kyp(0ue8qvg3xl js *harge $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the force on a sh6id 5yu:yi4qk i(.on 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 dian 1zjzcoq)hd e5q ,i50gram shown in (Fig. Below), where 5qqj1)ech zo, z0di5n $\vec{v}$ (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 nrpy08+ )z, p*lrm-cphcw6 7ifib f :lof $\vec{B}$ 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 verticapze-/ bqr8sjiub,5a:w i 23e qlly 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 e2d3zts mzd. )qnters a 0.20-T field, in a plane perpendicular to the f z2.tdqz)smd3ield. What is the radius of its path?    m

  An electron experiences the greatb fs y,y4r:u7kest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when passingm)24 z fj-p s3 (l4tem k*,dtcfjydsf, through perpendicular electric and magnetic fieltyj4,d, - cftesm)lf mk43pz2d*fj (sds 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 helihu4c6 u nzpi5)um atom whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge qj pcd:-4j vts1i c2b2v moving with constant speed v to make one circular revoc ivd:sjjcvp 12-b2t4lution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q mj9t7o etu,-13hcvncf oves in a circular path of radius r in a uniform magnetic fiecvt 9fht73j,cue -on1ld B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a b:2 rkcr;y6 d y01cws 35xlvdlcircular path in a magnetic field B. Show thatyw5 3vd:r;1lbyxs6crd 0lk2c its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Proble tu;jnzc2-t; im 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed)ykmv m4w7 a9m of 160 m/s perpendicular to the Earth’s magnetic field 9m4wymm k7v) aof $5.00\times10^{-5}\mathrm{~T}$, 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;mfzmk+a)g3(g 8co w41bti yz7k*ttk 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 spf3 qi4, :buuupeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehicleg ogvf83kaojl .3s;0k carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compara v s.o;gk glf3kj380oe to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no largerw d;k03z zlsr9 than that of the k zdr0l zsw;39Earth $(0.55\times10^{-4}\mathrm{~Т})$ 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 k npq jr:nt n3(pa:*t+r:m8tvtoward you. Indicate, with appropriate a pm k pv3:rnn(8jt+tta:qnr:*rrows, 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 attractiv+mb;aqc +to5nw8 4 hy:jvtq .oe fortn:b v.ow 85;ycm4+ato qj +hqce per unit length of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnituut)(2xoxq my ;de and direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carryinomy(tq) ;xu x2g 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earh:wzgl 9. 0;uhtoz3 ieth’s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowz; uleg03: o.ztw hh9iable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the topsh0y)8ry bhv w*9d f0*h,duuc q of 8.5-m-high poles. What is the magnitudy9*d huqd8bfw)u0*, hr0cy v he of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apa io y ll/ p7ts,+tw5t-5kto6rkrt 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 the7o- tk+p55k6/tislt,o lr tw y other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm(0. qsp zq/bu-d fg-rf due south from a straight vertical wire carrying a 35-A current downward. In what direction does the comp(u.pg/s dqb -0q zfr-fass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due north. s sziz.: -d7auWhat is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but-szas:7i d zu. 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 pass(+my:k2c ew6 mxx am1r51vy owes 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* zo5jls. :rzqxo(9ju m6,qk h between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these cu,h(:uq*mjx zj s .65oklz9oq rrrents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc cultzo :) kldc66kshh0gp9 -/larrent 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 their midpoint, in their plane (Flhs) doh k6/plt:gzcl06 k-9 aig. 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 jtfomz 63)m f.bk76pq(Fig. Below), parallel and just to the right. If it carrmp o6ftk)7fqb. j6m3zies 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle poi(sro 9li;j*zcnts 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 straight :bettf .l;w9bwire, 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 ott; :e w.fb9lbn the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire, madjb d9autj0kl(q/b5 c ;e of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below). 5q 0bjuja;kb(tcl9/ d
(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 perpendicb5b unuaq 9b(ktozyp.y 0x1i1 )(b4itular to each other. At their closest, they are 20.0 cm apart n x(u4tbbkiy(b0zio5) a9p tb1 qu 1.y(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 cf7gnoift*n cqt anfu.n5645 0arries 2.0 A current. Wire B’s currentqtin0.u5 afngoc 6tn*f fn754 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 dhmdxubd 3p4 , z1tlfa 4)w:b+3.8 cm from one another. (Looking along them, they are at three corners of an equilaptxh:3d4 4dbz)ubw,adm+ fl1teral 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 mayy*7zrou .boqove5c y1p222 rgnitude and direction of the magnetic field at the midpoint of the side of 1brrc. uy poz y2v2oe2*7oqy5the 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 curren*/+. qoe /taix.mlz zpts I in the same direction. One wire is at x = 0, the+p xezoi.q/tla*m /.z other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns ofhg 1j bmkqr:h:q9b :0j,w g7fa wire and carries a current of 2.0 b jj fq1g,w:h09 q7:bmhrk:agA. Calculate 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 owz:qzd e;oleeet3 p82b7sc x2r3s6a r 1v/:t wf 0.385 T at its center. How much current should the solenoid qtearp r eo3se:8wxsletb2c1 :zd 6w/;3 2zv7carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. lu8)-y mw.90shzwk5kpypdo8 The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, alony8 0 .yp98l5km hspww odk-zu)g 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 tr exjj.h:4x3 r0t1 vowant to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or somethi r4t0txo 1v:jr3 xjh.eng else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Belk 1woqpeo sgu) *1v)/s;q rhs:ow). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetisos q1hqv:)gu/sk p ;ow1re)*c 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 s3 xan gmsn3g*8xbb+ 3(k hlyj8how that the magnetic field between the conductors of a coa3*y8k8 bj xg 3slnxb3h(n+mgaxial cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is place 3:z-sbor4:vkk wi dzw )9;kzed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30zv;iz:r3b4kdw -k:e z)9k ows A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle defil p8r8n c1gb.lects full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer wea-e b/:ipe.m ub-vqqw:cmq c21 kens by 25% over the years, what cu cb.1-:ecm2 bq i-:qu/vqmpewrrent 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 output torque chq.e ltfuf)f qqs7q ;c 7wsj:79angelq7 fes;q :t)79cwjsqfqf7u. ?

Show that the magnetic dipole moment M of an electron orbiting the pl) 3okj13w9gg8b zz oc5phhyp8;z lk )roton nucleus of a hydrogen atom is related to the orbital angular momentum L of the electrook1gh3hy9 l3oz ;)5kzb8wlpp cz8gj )n by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containinkbvdbgotpadd x3jb;..j61 +wg a p-7- g nine loops lies flat on the ground. The Earth’s magnetic field tpxa- vb .7j1jpoabk bg+- d6gd.3w;dat 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 radius 5.10 cm in a 0.566-T 8 ttv6o+yh/pi magnetic field. What value of electric field could make their paths straight? In what direction mu+/8t6hypvi ot st it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radiix;;ugjobl u7w a a;.6rc79xypamm/5t of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of tau;;bxu ma9 7/yalrwc7ot xmj5;6.gphe other isotopes?

  Suppose the electric field between the electrec.k;j9/5 f3vmx2n ei0+ u7m tg aedciic plates in the mass spectrometer a/jx2e9kitvf3.0cdume;i e ngc+m5 7 of (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 pollua:,q - (twhqyx/ n7rmitants. It is difficult, however, to separate molecules with near / mxnh7,qwt(ayq-r:ily 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 accel*a2s lhsl)g+n 6do-o yysa24zerates ions by a voltage V before they enter a magnetic field )-2sad*zysalg h noyosl 4 26+B. The ions are 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 hxbhenb a*y,.-hm d*k3at8 +)9jp xccloops of wire per meter, and a 25-A current flows through the wire. If the permeability of the iron is tahmxcd8 .y* ph-+b,)ec9h*a bj3k nx$3000\mu_0$ 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 640 tshy1mn ooc( (.urns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. oh1n.ms o(cy( What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumv6q)3a l/ nptp8s7g5dm mbg ) etd:7dm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon entering a region of4c9v.:,mad2p i ojkb n constant magnetic field. What is the ratio of th.9kc vap ,j4b2:dniom e radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below3z 7q1 1iwxeb qn( sppt4op:f*) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a st*1ts zxo4q1np 3ie:7 pwqp( bfrength $5.0\times10^{-5}\mathrm{~T}$ 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 od 04p 7a/hcg;qzsu)uin an airplane 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’szec7 h0h 0fcd( magnetic field points almost horizontally to the north and has magnitude zhc70fh c d0(e$B=0.50\times10^{-4}\mathrm{~T.}$ 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 61o8n1fkr(j.6supqnk q -axv $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A large current ev.7 wnf-xqd m2/.qn 2p ,c ex3dml;gkmoves 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 ba7,dxm 2q-3cl kg q.nexd;fp n2/ vewm.r 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 co5e y99uu5za9y i(t etepper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires ie ety 9tu59eyiua5 (9zs 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apartzo(um6 gv65j k in a horizontal plane act as rails to support a light metal rod ofozk vum(65g j6 mass m (perpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflgr5d m:.ouuz zsy/ -0aection of the electron beam near the center of a TV scr:/zurd ga0.-u sz m5yoeen 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 device used to accelerate elementary particl)lvla 4(tn)bj es such as protons to high speeds. Particles starv tb(jl)n)a 4lting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the cy t0h1vzy n48mr,4hgcrl( :nrorners of a square of side l, carry equal cur8rhh4 0r:zy(tylm1nc4 v ,gnrrents $I_0$ 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 .issy-( /tjvavery 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 t(jsi .-s/yva 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 ca2 dx4 +lh)ho*o ex7cojrrying a current I (as in Fig*d7h eoj4+l2xoh) o xc. 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 tpsx2 nw-0bsn ( 9*8lu*ojzxsbhe magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields pro*y x .2 nl2zr.kleby3rduced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For a22*xel yr. l3r nbykz.n 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 magnetin* k+fab/:3 e7qy ( /wjtbsljkc field would make a beam of electrons, traveling to the rwje: sa/bkln+kb (jfq */yt37 ight 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 p wkv5qmyv8 :44ob wy +y7gj3yeath 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, respectively. Calcg y+m7w5ke4 ojv vbwyy3 yq48:ulate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnet7t1b tf (-tnviic field at its center. If the maximum current is 5.7 A, how many turf(t1 i7-bt ntvns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diamgc zcfl,.wa3xg0 ,j0ceter 0.50 mm, carry the same current but in opposite dirzc, 0fx g l,cgw.30cajections. They are suspended 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 qnxj tt*9iwj jqmj*2)9h k2gah/.h*s 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$