A compass needle is not always balanced parallel to the Eart/k/z ynted viz2(1dt1;u: j zah’s surface, but one end mezu y2/(vdjatzd;/z1tk n:i 1ay dip downward. Explain.

Draw the magnetic fi/:* ac00pw0hmkyioeveld lines around a straight section of wire carrying a current horizontallykw0 p:*ei0acy0mv/ oh to the left.

In what direction are theo*vc nj/7;q )jji-tld magnetic field lines surrounding a straight wire carrying a current that is l)n o;dq ji*t/vj7c-jmoving directly away from you?

A horseshoe magnet i8klre;ki xxpp7;u 4 c)s held vertically with the 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 the force 4 k)p klu7pr;xei;c8x on the wire?

Will a magnet attract any metallic obj;gc r.(7vnt r xmp5ib7ect, or only those made of iron? (Try it and see.) Why is thixprb m 77c5v;i( .gtrns so?

Two iron bars attract each other no matter which end6xlbbp b r48ms: e1+kes are placed close together. Al6mx1pbs bre8:ke+b 4 re both magnets? Explain.

The magnetic field due to current in wir2mxqurojalpdo-x c+*-il7y j,e 9k19 es in your home can affect a compass. Discuss the effect in terms of currents, m+dx r2oa,y1o *iulkc xp79e-ljq-j9 including if they are ac or dc.

If a negatively charged particle enters a reggpdhk;ekz* ,15; f uyln,mu3 kion of uniform magnetic field which is perpendicular to the particle’s velocilze;y1 ku *3 k5hpn;,dfk ug,mty, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particl2od6 qd9t :yjbes move in the vicinity of a current-carrying wirejd 9d2:6y tobq. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field owjobv5(v25das shown in Fig. 20–46. What can yb wov525( odjvou say about the charge on each particle?

A positively charged particle in a nonu*ru ;e :40a etoyk)hbnniform magnetic field follows the trajecto ee)nu hob*4yra0:t;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 attract a magnet? Can a magnet attract an((imc7sp4pq c iron rod? What must you consider to sp (7mqcip 4(canswer these questions?

Explain why a strong magnet held near a CRT television scvimj6,-,)uj6aq w0 w ydfiwb )reen (Section 17–10) causes the picture to becoi wi)d,uj)vaf- 6jbqw ,wmy60me distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetd wt5zsdoa9ka b)u 8/9ized but the third is not. How would you determine which two are the magnets without using any addiwb9a) 9ds ouadzk8/t 5tional objects?

Can you set a resting electron into motion with a magnetic field? With an electrs *,/ ni-k n:ecneqm7,e(r yomic field? Eym7iceen*,n -,(/kms roe :nqxplain.

A charged particle is moving in a circlc-5 .n;sw pagle under the influence of a uniform magnetic fieldsnwp.l;c a 5g-. 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 in a magnetic field is the idedi.mc j 8ud)2i-sjuu* a behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. Tu2u)is mc8 d. j-uj*idhe 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 dire qcgq, a ys9s. 2opu;oo+.0lwacted toward a horizontal wire carrying a current from left to right,la +c 2 wsqop.09u.os;oayqg
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a mo9uwsdj; s0v;jving electric charge.u0s;9vdjs jw;

A charged particle moves in a straight line through a pr *cqk8.lxrc) articular region of space. Could thc) rqkl r8.*xcere be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, carf4uga;eu(zu5l2 (l v n we conclude, folu (gua54eufr2 (; zlvr certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of spbw3dwsix 7a58 ace there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether0cv q 8ge6ou56iobfw. moving electrons in a certain region of space are being deflected by an electric field or by a magne5u.806ofe 6 vq ocgbwitic field (or by both)?

How can you make a compass without usik0fp*xnkcz qx +)sk 754roiz)ng iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to eap/ +pstw lmm ul 4::3k+wle3bjch other, but don’t quite touch. Describe the magnetic force one exerts onwbm4 p w l+p:je3lkl+/3m:tus the other.

A horizontal current-carrying wire, free to move in Earth’s gcvok 1wp2ib95 ravitational field, is suspended directly above a second, parallel, current-carrying wire.2bck51pw i o9v
(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 wn t7ktw(w4w/attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper cgm0q es0hceuvd 8 r8.,; oat1dlip. However, if one end of the nail is in contact witr;h oe0s,0a8 v 1c.qdtemugd8h a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is sin-by ans m;f*p1gly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Below) diffna s-m;y bf*1per?

What would be the effect on B inside a long solzn,hky3( vd 4henoid 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 solenoel 7qk w2i9px 0(frfs 0xj,lc6id is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a 0ei lk0,xf 7cj6f x9swrq2(lppiece 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 the force per meter of l(csytetjb;q-p): c3jya( 0aiszox+; x3n e u2ength on a straight wire carrying an 8.40-A current when perpendicular to a 0.9)ty;: e;cbt(i +c3onjqas2up yse0-3 azx(j x0-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 fof 9s0i0zqc xw6rce on a 160-m length of straight wire stretched between two tow96izq 0scfx0w ers 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 force onjf +w,+io..fnv 0+jw rwri-n. v8nncg a 160-m length of straight wire stretched between two towers carrying j.i.c+o-.jgvnn i, 8+f wvwr+ rnf0nwa 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 maximum fl;).1npqf unhorce on it is 0.750 N whenp fhn). nq1l;u placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. Att xf4yx)j6*a c that point on the Earth’s surface, cjx)4tfy* 6 xathe dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maxim)-9nr 2c9 d 7oixoh r,aprpv:4xz+chq um 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 magnetin:74p cz)rq,xpo ria ohc2 -9xrhv+9 dc field?    T

  The magnetic force pe.ed3ny :vdcyeat sm(6 t6e2(s r meter on 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 maximum, and :(aeet 3e t6s( s.dv6nmcdy2y sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire -kglw/ +u etm8lj s6e-it+7(uzt,f8qezq,xois 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” horizq2n j7/n4puiyueyh /: ontally in air because of the force due to the Earth’s magnetic fieldyepy h2ui/n 7q4: j/un $\vec{B}$, 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 ccehcx3.u e6f ;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 an electron traveling r(,d16 jwls pde61c8 qn7ie( pnol;jm$ 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 diat e8ppa3e a06ngram shown in (Fig. Belowe8ap3p 0 aet6n), where $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direction ofp5 zdnzt 8 hit/wio74l71w,d f $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward with a speed of 2vcuk 6yt:lh.hogww;+w bi4 - $1.7 \times10^{6 }\;m/s$ 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 en(ui5ldj xdg7 gu n0o*)ters a 0.20-T field, in a plane perpendicular to the field. What is the radius0x 5n g(7jl)dioud*ug of its path?    m

  An electron experiences the grea:c1q24n e9 ogokn4w mttest 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+w9r yvpzn/v . when passing through perpendicular electric and magnetnpvzv w+y9/r.ic 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 atomp/d qigf46n y1 vrs:6i.j5 x7,umuvvn 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 partic0 1*hstn:ce jhle of charge q moving with constant sp1 s0nhte: jhc*eed v 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 tnz/cos-eip b4 /kd-+:ug ac;in a circular path of radius r in a uniform magnetic field B. Show that its momentum is p c u-4sepao //-+;t:zbnc dgki= qBr .

A particle of mass m and charge q movi ix5ju 37*qgies in a circular path in a magnetic field B. Sijiu7q xg3*5i how that 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 paoem71j mya p.aq1/91g orqhpa*zq;r )rticle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves b1iaerqw8b. 0 /i(kvv b;4e bbwith a speed of 160 m/s perpendicular to the Earth’s magnetav(qi4/b.bb;ee8 i wvrbk b 10ic 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 has magnitudeysnr v76+ zsfiga ad3ev52,h4(wmw8 0 e2sksj $0.40\times10^{-4}\mathrm{~Т}$ 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 spa tfh:isryvmf /3 ys,cv3,;) feed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A current. Howq*i ab.w e/do- strong is the magnetic field 6.0 cm away from it? Compd bweo*q .-ai/are 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 a)qzd(pqubrwet:mnm / / 9...y dj7uzellowed to produce a magnetic field no larger than that o: twbuzz9 m.e)//q eyupd.(nmdr.7 qjf the Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out ofp0wsdq 5b7 y7(r* mao t,sxu6p the page toward you. Indicate, with appropriate arrows, the directioaowpdr*7 m6uy5psx,q 0 b(s t7n of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carry)h0c6uqb - 2w 2f9hcu3gahgbk q/e1 tpw h,c)ying an upward 24-A current exerts an attractive force per unit length of g bahch- h)gkphec2u/w u w36,qc 2yb fq91)t0$8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the force between two*m8 y*z8ljao +c+ rqxf parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the samezo+ q*8 jcfma*l yx+r8 direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is beinqc)ly m35w9ve zjueg0(4b jz 4he86iyg carried out 1.00 m from an electric cable. What is the maximum allowable curreeq zg y5vcjiym4 9whljb)e4(3e68u0z nt 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 tops of 8.5-m-h+l 3 mbgph6(suigh poles. What is the magnitude of the magnetic field produced by this wire atsbmgl +p u(63h 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 parallyk5ti4 (z5pfjmc3s f/ y:i 7 44ncoaadel wires 13.0 cm apart carry 25-A currents in the same direction. Determinedtp/7(myjf3i5sc4o4 acza f:5iynk 4 the magnetic 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 placed 18 cm due south from a straight vertical wir);kp :e*asnb vfj/i9hucu*vgql)r+) e carrying a ;q+npb:c* vs)hl fvjre*))9ugiu k/ a35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carri)o -)ve+qt*4/p humwsjb wx7ves 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward, /x) *-mb 4 v+tvjwho)esquw7p37$^{\circ}\,$ 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 poif+zp2(7 w2ck4bh rdo hnt 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 iirzuv 7 / wk,2d8.esbtwo long straight wires 2.0 cm apart in terms of the current I in one when the other carries 2ke uw,.b8idzrivs/7 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 instrument.t0cn7y+ 7 znmq 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 (Fig. Below)?m0tcq7+z yn7n 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 v0 w( /lmti;yg:pp j*w* 9:jpavdt2np 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 nearesp0t/jlpva gmt9n v (:y i:*dp;2j*pw wt 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 23vh6f3 niepfy/ (q *,:ofiefz -$^{\circ}\,$ 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 wire6 fexwfl1pk(n,3h eli8g) p 7i lies in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Detergei)7 13fnpxhl 8 (klipe ,f6wmine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire, mgnca jp c*l 9-u)1imx7ade of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm bea 9*inu 1)xj 7pmc-gcllow (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 orik2s d4um25 alqvq(.ho ented so 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 midway between them if the top one carries a current of 2a4lv5m2 2us.o(kd hqq0.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wihrobe/wo y6ib 8n y hj4.3j9,ore A carries 2.0 A current. Wire B’s current y.3o4ohjbw8r ojh yebin ,/9 6is 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 another. (Looking along them,n 5 alaxadr69 u1e8/yg 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 thnue/algx815 d a96 ayre 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 diqejw9tz*l sy rwxl3(/rp7l02rection of the magnetic field at the mi* lrxw3t/2qy79elz js( 0lpw rdpoint 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, arak3f 2d 2sgzo gz fqxv0/qtir5j99) : distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Deter/9 2 :dqk)iq9sga ztfrrx50oj2vg3 zfmine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has pc4/hk1r 8pddme 8e1zee +co;a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside ne8cehomk1zd 1e;dpc8 r4 /ep+e ar the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to prod+ ywmons:6 cx*brc4 (cuce a field of 0.385 T at its center. How much current should t:ocs(+c cxw6b n 4*yrmhe solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The c g3kj7 bhw.1dtx(9 ztburrent in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carriest9b1twj xh dk.3b7zg( 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 wan.-il p/bncpc,auv(x zj(x 3/ dt 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 something else? Consider other variables, such as solenoid diameter, length, and j(av.bxu/il ndxc ,zp(- p 3/cso on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’s l*tovo*r zxn3bb)w j .8aw along the circular path, shown dashed in (Fig. Below a), to determine that 3)jbxnr.obw8o *zt *v 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 magnetin,)nh3 iairvlh9 q* )sc field between the conductors of a coaxial cavi*9sihln) ar3,)nh q ble (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 kgy(;asfrsk8; k w.s,k .k4 sq22.0 cm on a side is placed with its face parallel to the magnetic field between the polekr;wkfk 8 as4 ;yqgsksk., .(s pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale for 5ij +6hxb zbsfb5*mo)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 g*c- fnn1e6j btalvanometer weakens by 25% over the years, what current will give full-scale decb1ten-* f nj6flection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output tor3)ersfyb2q( y 5euq( fque chanyqyq5sebref3f) 2u ((ge?

Show that the magnetic dipole mlytwh9 :5 w8vu7zdik-oment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentu-whi:kt 7 y uw598zldvm L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loopw czsf1nwnwbd15fd sz 6wiw3 l5*q7:7s lies flat on the ground. The Earth’s magnetic qcwlw7n75b*1dwsn3fd1:si6f wzw5z field 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 radius 5.10 cm i:-wp7 gwx:t vd7 nf9fbn a 0.566-T magnetic field. What value of electric field could make their paths straight? In what t-7g:v w wbf:p7 fn9xddirection must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal toql;mh ,t :4v6as pa)(noly*dv3cx5 ,zsi i ts; 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius c65ss doi,;tti; ch3va a *v:y 4(znsmqpl )lx,orresponds 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 mass spectrom lf8+umufm)u+9g+a w seter ofsw9 m)afm+u+ u+fgl8u (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 pollukkggh;tmo 32-pw:7;ivh yft3;ot2u +x q 6xp btants. It is difficult, however, to separate molecules with nearly equal mass v23xo3q-g2ttp hbpif;7ykh+k: ;xou 6g;w tm such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V before tfne wb gvt6t33em0,i5-b e1d khey enter a magnetic field B. The ions arfmw5k3-n6v 01ee be ibgt,td3 e assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A current flows tbk5ak*0j ;iv2f 9 nnwghrough the wirea*50nvkk 9 fw;gbnj i2. 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 64dacny 9dwnh,2wv6 w4 -0 turns of wire. The magnetic field inside the s,wad dhn6 yvc4w29 n-wolenoid 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 bf +:xx)zhol8mrtug1w 9k,z+ $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 owmy, ya9 5suf ;ms8pe*f constant magnetic field. What is the ratio of the radii of their circular pat9yu,wema; *f5ps ysm8hs?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal aey/v 5uyg2 c ;a8an0x6:neugcurrent of 330 A toward the east. The Eevcayuy5u 68g/ann:0 g; eax2arth’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 wlb o;agt3ho*6 awaf7n 4g0 bl;hich 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 almost horizontally to the3 fy/:vm-h ovpx-bxy k /r)9rnz1 spq) north and xfv-zph m1 9yn//yo) q)vrk3bp:sr -x has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helh: xn k-/kb l9a4)jgkup.c0osu x-t/bium atom, whose 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 lare* )rr 5bv( nvwdbmdm8/ninsma4 )y71 h -y7zrge current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has aby) n18e*h sdmnmvyz)v bim4rwadr75/ -nr7( 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 sutl, hex(:2gix 6mq 4ygspended in air due to the two magnetix4g:hq(2 x6 ,gietmylc 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 distance l apart in a horizontjkl:fbv *r0 q9al plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). l0vr * :qkf9bjA 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 electron btm4 (b 0 skrw(moly,;ceam near the centerolw (m y,k(;t 4cmrbs0 of a TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementappq is7 s,jnt )e*07oary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magaes) in*qsptj o0p, 77netic 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 cf7ri;/cai, h e;msw:ymg21sgh5c uu 8orners of a square of side l7g 5rym,gws;f ;hcm ciiu8 u2h:ae1 /s, carry equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very k9n* mprx (3*yjpdfxus1e ybbp:q52q i, tw))useful in particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends ovep: ybqxm2brde9) )3n,u5(wp i*ykq x1jsftp* r 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 t;sq.4 zxad v*et 6+jgcenter of a circular coil of wire carrying a current I (as in Fig. +qdsza* tj 4gt.evx6; Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic field is abouth-r0/ k m4s g-bytklt 0drfv6; 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 fienl .a+a-mq ,obvnxp 0ye or18,lq9wp9lds produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are aboqywl1pn.80+pearbn,am9vx qlo,- o 9 ut 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 beam of vo8z xvxp29 vank9d47q8jm6yelectrons, traveling to the right at a sp kmvda4jy2vn896vz7 pq8ox 9xeed 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 svxm (k3,h 4vpmagnetic field of 0.010 T, perpendicular to the plane of the spiral, as3 vkm4hxpvs (, shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid;ou5* ee e5pam, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum c5oem * peuea;5urrent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 05b8 kzat7lj5 n-d.e uc.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 st.za8ndj 7-cluetk5b 5rings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T at a 4 .upejq3t .)z:0ir4z n9rmylb5$^{\circ}\,$ 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$