A compass needle is not always balanced parallel to the za0ozykhzl(fx; t k-6y;g,1 pEarth’s surface, but one end may 0x z1a6gp ly zoy;-;zf,k(h tkdip downward. Explain.

Draw the magnetic fiey*fo-1oy7j9eu x-enx ld lines around a straight section of wire carrying a current horizontally toy-oyon 9eex7*jfu x -1 the left.

In what direction are the magnetic field lines surrounding a straight wire cawjh9 6is78lpp rryings9pp 8l6w ji7h a current that is moving directly away from you?

A horseshoe magnet is held n j3a *+ xddr8.n4efyfb n.nb.vertically with the north pole on the left and south pole on the right. A wire passing bn*n+8 3.ydfnn.r xd.fajbbe4etween the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only thosei4)gvpx gci3dg4:v b; made of iron? (Try it and see.;giivg43g cx )d4pv:b) Why is this so?

Two iron bars attract each other no mal y0xe*u9 4qd a.9x(27 muovdqsj1jxa tter which ends are placed close together. x*do49jm y9xdj0usqu 1eva. l7a2(q xAre both magnets? Explain.

The magnetic field due to current in wires in w pp,uzdek.2 )l84woo9+(mlzp*cwqv your home can affect a compass. Discuss the effect in voqpw,* wk zcm2l4w)(e8o p+l .9dupzterms of currents, including if they are ac or dc.

If a negatively charged particle en yf( y o)vuz1cg7e/sm:ters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Nec g1s )z: fmyv/(euy7oglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in thm (1mro cd-+ *1a gemwicdk8z9e vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates t+gmr(wi 91dmc zk-d*moe ca 81he 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 showr8g/ o+3xl e *jvi.leun in Fig. 20–46. What can you say about the charge on each particle? * o3 /lrixeu l8jvg+.e

A positively charged particle in a nonuniform magnetic (q d(6ff* sh):gnrqwrfield follows the trajecto6) :*(hwd(nsrrqfgfq ry 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 mva( 99)nmur+c k k kqku6uylm/ (l*7sgagnet attract an iron rod? What must you consider to an/7+q)u lcr6mknkvu9a l* 9 kusm(gk(yswer these questions?

Explain why a strong magnet held near a CRT televisi 8jzq. qj ex04gn6 n:47ievwkion screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where ne.njv 7q:j4x i4e 6 q08zigwkthe 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 wh,e , fp-akgbyfx+66qeich are magnetized but the third is not. How would you determineq,6 +- fbapg,6kye xef which two are the magnets without using any additional objects?

Can you set a resting electron into motion9ra*ig p;p8d9dxs c1v with a magnetic field? With an electric *9avp sdpcx89di ; 1rgfield? Explain.

A charged particle is moving in a circle under the influence of a unitun55:t kg j,oform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the chargej ,utkon 55g:td particle will take.

The force on a particle in a magnetic field is the idea bu(lje wh2b1q 7ehind 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 ib1lquw 27 eh(jn(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 dirf5hy/ 0oge; yeected toward a horizontal wire carrying a current from left to right ef;g/hy0 y5eo
(Fig. Below). In what direction is the beam deflected?

Describe electric and/1;kf9 hhzsk(py: o8gp rxze -9or magnetic fields that surround a moving electric charge.89y:h-;kp gz9skrpozeh1(x f

A charged particle moves in a st1;0pfz bw+p-r/ye(xqcu mp : ;yx:qqfraight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situations+ p wpxm1er0 q;x-buzpqy/: (fq y;f:c.

If a moving charged particle is deflectzn csg* v/ick 0hlgdym5-pc259 v 3.used sideways in some region of space, can we conclude, for certaivgc-zygh2snl* 530/ccpu 9 kivsd. m5 n, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic f l )c.m hjam0ag-a9a tigpe:,l.gu18gield $\vec{B}$. 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 cert;uzeg 7t;dr- dain region of space are being deflected by an electric field or by a magnetic field (or by both7urg;edz ;dt- )?

How can you make a compass without using iron or other fer rcjqnw(t6k ahm;x17 0romagnetic material?

Two long wires carrying equal currents I are at rightr0i/g;k j* rv9b2atje angles to each other, but don’t quite touch. Describe the m/ e92;ajtrr*ji vg0k bagnetic force one exerts on the other.

A horizontal current-carr- 3 cz6;cmze x,cc9x5t+no mhsying wire, free to move in Earth’s gravitational field, is suspendec, scnxcz zo; +tx9ce6m5hm3 -d directly above a second, 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 mag w/46 ; l+vjco69cif,knrbtq/ 6kd jvwnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract a fw6 jrf+qh0qpsnz 6t6z25g7tn unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the oqs j+6pg z 07hw5nt26t6frq fzther end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly aud 3vcn+jr+j51 .nrh ionized and the other is doubly ionized. How will their positions on the film of a mass specc1r 3vdhjnn ++a5u. rjtrometer (Fig. Below) differ?

What would be the effect on B inside a long(xbfxmnn9+8w qxl(-;ofi :l q solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . A relay i..k i nwbcw j,8;n38 ypqwln:as an electromagnet (the iron rod inside the coil does not move) which, when activated, attract pw.3b,n yjwn8:cn.l8k;iw qas 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 the force per meter of length5kdnb a eq4jwr-y5m-. 03hig r on a straight wire carrying an 8.40-A curre 0d4 5y brq53h- k.jrwei-nmgant when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude zzs2w/ n*lfo-oob(i.of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a .ow*o(2lsfn-/ zz boi 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 on a 160-m length of straightu+x1 timr7cj.pmkv3; wire stretched between two towers carrying a 150-A1m7x+vm;j.kc3it rup 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 k 1wcin6vwe(u0s6* jglong if the maximum force on it is 0.750 N when plac6 * wnu60ewi1kcj(g sved in a uniform 0.0800-T field?    A

  A 1.5-m length of wird(yvcwwb,,odj ,5 6 okr(xee0e carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle ofcrw d,xykjo6d5e,w0bo(, (v e 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when plrs;41q pp:s qlaced 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 fi4: srqlp1qp;seld?    T

  The magnetic force per meter on a wire is measured to be only 3)7/mdeu8c 7h . nfyyzf5% of its maximum possible value. Sketch the rech/7)8f yef mun zyd7.lationship of the wire and the field if 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 is aw 2 4tyf)grt1z 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 “fl gq )dj5q33uiono*yc4oat” horizontally in air because of the force due to the Earth’s magnetic field q o yq con)jdu53ig4*3$\vec{B}$, 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 charge /l jkjwp dw* qi,-8pt9$q\,=\,+2e$ 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 traveljbv480glw b5 + pvkrl8ing $ 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 o;xv uddvi:3bg9 e f3d1f the force on a negative charge for each diagram shown in (Fig. Below),d;u b3dd egv x1fv3:i9 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 v4. a9vpw uy2nof $\vec{B}$ 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 verticts *ms n;w*.5q6isvr xally 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 enter)ov a7am l:xe9s a 0.20-T field, in a plane perpendicular to the field. What is the radius7ao)l9: exmav of its path?    m

  An electron experiences the greatest fortjjk tk 4 g2q-yky5ut/8b/st+ce 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 undeflhlb.pxlof -d:*p ;6fx ected when passing through perpend*;fb fpdxp ol xh6.l-:icular electric 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 heliumw (.g2dopw i9o 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 particl jts(o s-hjcsl80 g 7f71utq6be of charge q moving with constant speed v to make one circular revolution in7 - jbfju68sst7got cs(q0h1 l 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 pathlrv: +qdror7ye :s):x of radius r in a uniform magnetic field B. Show that its momentum is pl7+dxys: or:v :qerr) = qBr .

A particle of mass m and charge q moves in a circular path in a mjmzcf23bio 3;n5yxw; /rz( n,pjq mf8 agnetic field B. Show that its kinetinpfj3w;iz8q jmb(cy,zx;or 5 3nf/m2c 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 hwuu6;hlnik /w,y(n/egl wz 0d9pf6q-3uwo 6Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s ma4ac+xl)p hs; ygnetic ; p)sc+y4hlax 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 fi2td bblt o0p0*eld at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with mtwtj;g,x j 61w7iz0 gspeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 65-5/ 90r9vpkf5m e(:izowph7zh gq +r gsA current. How strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field 7p9vm+q:(g0ik/esr5 z hwzpg5 o9 hfr. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is all g-i6: qzfu1e06dqhy f g/qbh 1ih5mk9owed to produce a magnetic field no larger than that of t019 /hfhzq dq mq:-e1ibk5ug6ifg yh 6he 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 wix+fgmln v5+au p(1x e2re carries current I out of the page toward you. Indicate, with appropriate arrows, the direction +p x+5(2evuf1 gmaxln 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 up)isxyuq nonu/3:-to* ward 24-A current exerts an attractive force per unit length o* u:iuy/ o)x3n- ntsoqf $8.8\times10^{-4}\mathrm{~N/m}$ 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 paralle2v87aj1rlm jf l wires 35 m long and 6.0 cm apart, each carrrvj 2m8a7ljf 1ying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is be9yzb3fz13q:l8)hr l p5(sdkee tg9ui ing carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the exper3qz:5etekhg)bzrul yi3 ps1d8(l 9 f9 iment is to be accurate to $\pm1.0\%?$    A

  A power line carries a -x j l 0go,uo:ggps:.tcurrent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of abougjg too.gp:, lu:x0s -t $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13. o2 r wv,*otf7p+a0mi c3w(tse0 cm apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Figs*( 0iva+,ttromfw opw2e37c. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wit- 5sfcml )ep6re carrying a 35-A current downward. In what direction does t)m cp5l- sft6ehe 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 carries 22.0 A of current due north. What is the 4o61w zb vzct49ct5ds net magnetic field 20.0 cm due west of the wire if 6s514 t d9ctwoz 4bcvzthe 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 po(4i-uh1*x i1kch p zcwint in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wires 02o6fv a9fjod 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currents ar0ajo f v92fdo6e
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.2.me8pgq ma)p0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are8.)q2e ma mpgp 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 tl gofg.u8(5de/rb i0l he plane of the two wires shown in (Fig. Below), parallel and just to the right. If itrb lgd5eu.lfo(gi08 / 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 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 23593 lqkvu y/h0t hq(gorheb6 9$^{\circ}\,$ 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;fd.gkdt(rzq 9eqpyr 9f/5v r) y22uf wire 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. Determine the magnitude and direction of the net force on 9df5)q9t2z (eydrgp/ uqrk ffr;yv2 .the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A ssy16oo t v6rb: lpm9q(econd wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magneticaqm6r:9 pb( soovy t16llly 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicular to4z )ias -ygsx j19zp wc*-9xea each other. At their closest, they are 20.0 cm apja) -w aipy*9 x9g zz41xc-essart (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 caa 4pkkxn 6r8f /xv4-cqrries 2.0 A current. Wire B’s current is 4fvk-p x/ 4 c6arkqn48x.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 frog5)x 2b 5y1 sgmagxjn +8hu*tem one another. (Looking along them, they are at three corners o2y8j mxn55u g*x+h1 eatbg)sgf an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and8a/h wxl) e(*uwwff;l direction of the magnetic field at the midpoint of the side of the triangle axl w*w/we l f)f8u;h(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 I2ru o5u2-1h:hhpayfp in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Deter25h2hfrhp:u y- a pu1omine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carries a codj1)*rm (ezv*1g;vehy60kgk o 7atrurrent of 2.0 A. Calculate the fieldrjgoe1zvh(d keo*;7a*k yg)6 1mr0vt inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produu tl 1fq(v wl,e0 h5,fb3emat/ce a field of 0.385 T at its center. How much current shoftluvqm e,h (f3t0/,1l5 beaw uld the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The2hi+ qrpq.h ar :k*(lj current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameterrl( a+ijk:p 2 rhq*qh.. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practic8q-x:jzqr (piaw i q8(al 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 variablexq-i(qj p8 (8awzr iq:s, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use siv5s qsp;g-;h (nx (cAmpère’s law along the circular path, shown dashed in (Fig. Below v;;igc ((x5shnq-ss p a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the majbayg332c j 3am-3ls ngnetic field between the conductors of a coaxial cable (Fig 233ybal sjca3gj3-mn. 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 pl2 b 9(n9 k-u,7h cp2vc(oy-fjxtrzroaaced with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows inorr-h,2(ft2p9xju a c7k9on cb(vz-y the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects fulga57+oj, mg1; z-etp,.cxnr m8hn l mnl 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 weakens by 25% over the years, n*6-2 r0 aw2l7u-ylu/3jdrwor i :uvb4y sm kmwhat current will give full-scale ds6aiu*mv7r4 d l/owuj nmwr22 :k-br0uy3 -lyeflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by whatije5k9a2s )o6hx 8ykg factor does the output torque ch8) 5 xa6eihg9kosy2kj ange?

Show that the magnetic diw z*lh-907lecc sksx)pole moment M of an electron orbiting the proton nucleus of hs9cxsz 7w*cl 0lke-) a hydrogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and contain8d+wv 5tmt ;lring nine loops lies flat on the ground. The Earth’s magnetic fie +vdl5;r8tmwtld 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 in a 0.566-T magnetifc), cdaike00 c field. What value of electric field could make their paths straight? In what c dca0),ik0fe direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoxxv+huxaz 10koa88 ihz (;cnw0;l m0qms have radii 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 nzx v; zq00cxl8( w +hah1aixu0ko; 8mthe other isotopes?

  Suppose the electric field between the electric plates in the mass spectrometer)pun-kb fs+4k.,rw y)s qek /c of (Fig. Ber+wy,su/bksf kcqekn )) .p4- low) 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 aj 5t.oxhkw3v 4ir pollutants. It is difficult, however, to separate molecules with nearly equa o45whxv3 jk.tl mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V before they enterbusf;; xmw2jcdrgb,l )o6 9w 9 a magnetic field B. The ions are assumed t m,bwrujo 9;2 xdgl b)f69wc;so 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 /7aii 2z l1hahloops of wire per meter, and a 25-A current flows through the wire. If the permeability of the lai a21hhz/i7 iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid i(abc+5i jpm4s k.yi8is 38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the 5(ip+aj y.b4c8ism ikpermeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentuqrr :,q 1 . sfyrdgt1cy /qn,k3jvao+3m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 adoo,c1ulixq6 (.l h g, region of constant magoh1( ,c, g.oidxl6qlu netic field. What is the ratio of the radii of their circular paths?   

  The power cable for an ef ,p9olu(jqwm o/g l0*lectric trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic fielj (g lo9ou,qlf0 pm*w/d 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 which has acquired a net charge xzl6z .+ypc b4of $1550\mu C$ 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 horiz5ivu84zwh l7 i)+xnz7.hmwnhontally to the north a.hw5vx8zmhu) n hli7z i47+wn nd 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 helium atom,t9hek 7y) lop- 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 g:j )n+kkg+o/il lu w+(Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supiog+lnkjwk+ ):g/+ ul ply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire ibe;7 jc2 p cj(4wnz;nfs 1.00-mm-diameter copper wire and is suspended in air dnfc2p bnc;4(e;j j z7wue 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 distance l apart in a horizontal plane act askmu c zg93(pbd6)ru gc27dvu ; rails to support a light metal rod of mass m (perpendicular to each rav 36z bc7gm)r(dk 2gpudu9c ;uil), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron b8fnsahi1 0b +1kwlq m 1,bito3eam near the center of a TV screen due to the Eqf3m i8i,0hsn 1 b+1ablto1wkarth’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 particle23yiq ahym;: ns 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 electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing toqmn3 :yi;hay 2 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 paralle ma)3 5t-ezvtbl wires, located at the corners of a square of side l, cartbat-3 zve5 )mry 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 use03s ub7qomhp (pep 4)bful 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 over a region 4oequs3mp hbp( 70 b)p5.0 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 a currh a +x83( iz0z+pqzakient I (as in Fig. Beloz a zaz+qp khx3i80+(iw) 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 fieldi sq qn/:2- oy4v0phwx 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 magnjrrcp z(k:(kk(d6 kx+itude of magnetic fields produced by overhead power lines. You estima( r+ dzkkkpcj6((:x rkte 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 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 oc4*oh .jjg0 j i *+9akrl(qhmkf electrons, traveling to the right at a s (r kjj9ijh 4c0aom*+.*qlhk gpeed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0.0nkdd /0oeji2t)l-d:c8h og .t 1 jesj*10 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. Cal *kdj j02ejsd. tg1ol/etohd n)i- 8c:culate 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 magnsg(cf19z4.z g jtqyg8etic field at its center. If the maximum currc yzf 8t.gzqjgs(9 41gent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminudus p3z* hdy-w2+x.h ym wires, 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 (Fi -zs* hd32.dwuxhp+ yyg. 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 uniwaq 6 fb66y*yiform 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$