A compass needle is not always balanced parallel ,y gi3)iholjqr fq k2t-( gcfc:h):2sto the Earth’s surface, but one end may dip dow,q tc lhrc:-i j:i)(k)qsf gfog 322yhnward. Explain.

Draw the magnetic field lines around a straight secti *h 80, uk-fd( +twurdo(juuxqg*dg.k on of wire carrying a current hor* kg ,htq*udgx-( o+dk0u (duj u8r.fwizontally to the left.

In what direction are the magnetic field lines surrounding a straigh x)/4dbf:1n68vy,ft4hia yi snp n6*viu3hypt wire carrying a current that is my 4:i s4)6fy* n/iviyh1ap b6nv3uxndf ,t8 phoving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left anu +d ivb7g:3s2ezi)n b/a mmo6d 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 o: n zbeiu6/av gsm+7 )o3i2mbdn the wire?

Will a magnet attract any metallic avpj71e 1tq 25zhfp a1rfg/d 6jx1s6 2vsvmx1object, or only those made of iron? (Try it and see.) Why is thi qm17511d/2 z6fjx sp1j agvx set1fhrv a6p2vs so?

Two iron bars attract each other no matte4xb0-4 xryhymr which ends are placed close together. Areb0xm 4hrxy4y- both magnets? Explain.

The magnetic field due to current in wires in your ;)k fc3ix*4nm fuiz c8home can affect a compass. Discuss the zf;mc34f8i n)xkic*ueffect in terms of currents, including if they are ac or dc.

If a negatively charged particle enterd q t-l;bxh/)g :q8nzgm ;-/ybd03qcwu0zqvns 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 /d:q-ub t0zlmqn 0n;)bc-y hw3v gdz;/q 8xqgsame? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a curre3h-- o6qpmqgf7 7woyxnt-carrying wire.fhq7gmpyw- x7o-q 6o3 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,uf3*/j a:x- dtxdlb7 x enter a magnetic field as shown in Fig. 20–46. What canxdf b7ldj x-3 x/:ua*t you say about the charge on each particle?

A positively charged particle in a nonuniform magnetic field foz h, ;8xy gzyyq6fpa d-.zpk3*llows the trajectory shown iykd*;,z .y6ah3q8yppz-zxf gn
(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 i ou0y)3 6drjfspg.3a. oihj6y-oym7w zd, r1qron rod? What must you consider to answer yjdojyq z op6ys6h.fd3- ,umg w.7rao 1 03)rithese questions?

Explain why a strong magnet;xayri/uj/iqhaq *60 held near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage tja*hr0i;x /i/6uqyqa o your TV by trying this.]

Suppose you have threo -c-a4;jkv t; .dy4dmckw7:zf 8uw 0bo9pfrde iron rods, two of which are magnetized but the third is not. How would you determine which two are the magnets without using a r9t0p-cycb7wfu f; wo-o:.k4 ;z dad84 mjdkvny additional objects?

Can you set a resting electron into motion with a magnetic field? With an el .). gy2rrsutp mx+jl3ectrl2.smjy)t+g3 r.urx p ic field? Explain.

A charged particle is moving in a cc/3osbxieg7 r8b0k5circle under the influence of a uniform magnetic field. If an electric field that points in the same direction ack8rc oebxsbg3 7 5i/0s 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 idea bx2m+t p 1idv,cxwzdr p4-z6 l4ehind 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 to move. Do p d pticmxpr dz4x62w,v-+z1l4 ositive and negative ions feel a force in the same direction?

A beam of electrons is dir.hl1piiz )e4 tm(d4vu ected toward a horizontal wire carrying a current from left to right14em)(pu4 ihv.ztl di
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electrii,amh5jhbh53uy* sk6 c charge.h5hiha5 6u*3s,y mjb k

A charged particle moves in a straight line through o( p+id28l7 owrauy15th:; +swdpsus a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possibl swd2p i:odp5rsa8 wl+;71uu t +hy(soe situations.

If a moving charged particle is deflected sideways in sb / vialhky ,bbef07f+qb2grf z9b ,t+zb9s(,ome region of space, can we conclude, for cerb/z (+7fb9f9 qaefiby,b v+k2r,, btbglhz 0stain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic field 6kf.e 6qxfk3g) z0jzj$\vec{B}$. 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 eleuc)grl166 0qz bp*d rzctrons in a certain region of space are being deflected by an electric 6zcu 0drgr6 lz)bq1p* field or by a magnetic field (or by both)?

How can you make a compass with)g+1 ouzpcm:j out using iron or other ferromagnetic material?

Two long wires carrying equal curra;8h-da va0 k,r;-xq. tlyrg wents I are at right angles to each other, but don’t quite t0ryd- w qax8-glhat,. vk;a; rouch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wih)) z.mx9 tmmlre, free to move in Earth’s gravitational field, immt9z.)m )hxls suspended 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 magnet attract an unmag1dxvoo 0d o5d.netized piece of iron?

An unmagnetized nail will not attractam:4c(b( enjz an unmagnetized paper clip. However, if one end of the nail is in contactcb4e:zmn(ja ( with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other*42mf r8zrum m4zw*do is doubly ionized. How will their positions z2 omrm8rzm4uf dw**4 on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inqy nifj0ota6d2 za :7-side a long 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 rewo14 *ip 5c9lf7yexwdlay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical 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 currc5e917w 4ixwfoydl *pent flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a str8a;uoeh-m1m6cl 4age aight wire carrying an 8.40-A current when perpenae 1 c8l6uh;m gam-e4odicular 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 of the magnetic force on a 160-m length of straight wirs( 2v2 5je*dfp f* hr-ud5cgqee stretched between two towers carrying a 150-A current. The Esc huv255rq2e fd*gpf* de(j- arth’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 sde, jp-6qe2p ytraight wire stretched between two towers carrying a 150-A currentqj6d pepe- 2,y. 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 fy+ 7j7tbx- vfin a wire 4.80 m long if the maximum force on it is 0.750 +y f7t7bfvxj -N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At th 4 xuz6gdb4rib)2z* qvat point on the Earth’s surface, the dip angle of the Earth’s magnetic fielduxgi2dbz)z qr *4bv64 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 maximum of 1.2j2no6i5g ls8w 2a6t.+f iu vls8 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, whal.2w5otj +iuv f6ial2nssg 68t is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a mn9g ve/c, 42c fqitg+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 sketch the relatf+mce/ gtc2, 4nigv 9qionship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a mhaxg1o4buca1 r o/vp,4z d9q9 aximum 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 coppew 4, ryrh qtek++amd5:9dvd 3cr wire could just “float” horizontally in ai+5d4+dry hkecdq9 rw ma:tv3,r because of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chargean*pih ,k)f9pcjh n(zaj.cb33:k m q5 $q\,=\,+2e$ 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 anhegk 81xta-05q.dwbd d direction of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negatix.9 )4soou( .opzzkw(r uad ,qve charge for each diagram shown in (Fig. Belo.xku.94zzwp)( ooo r qd(sa,uw), 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 directi*l76ceh;dk yoau0z/,y p2f jmon of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected verticall 62ggaw y*sin)etz0y8 y 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 enters a 0.20-T field, in a plane perpendicul +owgse;z * b )9kh8xm2pd1tlnar to the field. What is thk 2 nstml+1bg dxhe8wozp9;*) e radius of its path?    m

  An electron experiences the greatest force as it travels g0xmdin. z/wq9 70jrj$2.9 \times10^{6 }\;m/s$ 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 undeflected3-ugpjlf u /j3: xjsq2 when passing through pe3jju/s-pxglu3: qjf2rpendicular 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 helium atom whose masso6 n7q 4)js la xcx/k4taf,2dd is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge q x8iqk,d s2ho. g :mb(ymoving with constant speed v to make one circular revolution ii8h(bs q,kmx y:.g2do n a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circuhkoixq3t *-3b ld(.t ylar path of radius r in a uniform magnetic field B. Shl b3(q*ot h.-xktd3iyow that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetiyo e 49;d4ntx 8 tu(0it guwgvh6zu*1sc field B. xg8;4h6tue91svtgwouzin4y d 0 tu(*Show 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 particle iz6tm -ik/zvb*+r 7mwi n Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Eartvhj4i)re, p-3r+as 3qrgl8h ch’s magnetic fieldv3c q8 ,raigr hlhp)-4r +sj3e 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 fii1.c nb1:wru feld 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 g2c x6p:+e dbfz3ii.lspeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehicmnz0qu x+a98 *z7vqjyle carries a 65-A current. How strong is the magne79*y qvu+0amzx8 qznjtic field 6.0 cm away from it? Compare 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 1yk.cic ab7o.6gr05u3fdbdj7w jtn3magnetic field no larger than that of the jucdif1tw 35o6 nka3g0 d.cr7 b b7j.yEarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight5ql x+ /a1apmjoj, gp6 wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction +6xa,p/ajjl1mo gqp5of $\vec{\mathbf{B}}$ 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 a q.hkll8zf7,/ bbm k.rgdmof08 q .le9ttractive force per unit lengfb . lgbok0.he.8qq9f8rm7k/,mzd llth of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and.s)q/eshj (6 n*sraaj direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in th*(nq) ss jhejas.a6r/e same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic / glux6 (cryi*0- wf4e/ojn7kd+ gs mnfield is being carried out 1.00 m from an electric cable. 4fxkoym*i6lr/g+ (g nj- /we nuds0c7What is the maximum allowable 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 t*x mgp uzczoz.x0(va e(.b +gr2g8 4dsops of 8.5-m-high poles. What is the magnitude of the m .zo.r(g(8g d*02upmacgxsb4 v z xez+agnetic 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 wireso3dg d8p g6qi(k39zxs 13.0 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(Fig. Below).3 qikgs3d 6 zpdg89(xo
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical w te*a3rfxm,0c ire carrying a 35-A current downward. In what direction does the compass nee,* cxt0a3f mredle 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 nep(e8a+k u z.bk q.ssua 5p l26uhpnq0-t magnetic field 20.0 cm due west of the wire if the Earth’s fq0s un bp kuleakq+ z62uhsp-8.a.5p(ield there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in spacrbz+ *24imt7jcu 4otc)xx*o ie 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 yit j1. )/edh8xx/p/al.sxk mng7o.jdgc11qbetween two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume thejhmg i.xxqsk.n8adc/pl1/ o gxe7y1 j)t/1. dse currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts wpmy ivzvj8ma 40 i6hv4 bq5,)25.0 A of dc current to, and from, an instrument. If the insulated wivj0b zwpvqmhai,4 5 )mi4yv86res are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fi.j7agbrfg,/ nm n 5mc +n*puu1g. Below), parallel and just to the ri*1bnnumfcng 5+./ a,rpmj 7 ugght. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle poiq,1r9ae(7ibtqz (zav 8f :: vsdrrh 5ints 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 wire, as shnn3n (u8z-ipj)s 2) l1 ,jvvfxzkmfab7mr 64down in (Fig. Below). There is a current of 2.5 A in both wires. Determine the j,f(1 f4x) z) dnv2mn -pi br ns8jmv37aukzl6magnitude 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, made of 2o j2m+a*t9yuurq*om. x2n g n..5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically *qauorm9u.j.nn2tog* xy2 m+ 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 perpe1 c;pkt)cgk3 zndicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). t1ck3kz)pcg; 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 apa-kc4aee do /cme53 fe7rt. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in them5-af3ekc eo /7ec4de 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 wirt; 0de-yqf(lv x eac80es are 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in ex8efc( lva -y 0t;0edqach wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and directil lj+bnww40 :mxd)iz:1f+fwjk m :nh/on of the magnetic field at the midpoint of the side of the triangle 0 4:j j1f kn ixnw+wz:w/hb+:m)lmfldbetween wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a d7ry)m:4e(wljpyd7w .ztiqb 0istance d apart, carry equal currents I in the same direction. One wire is at x = 0, te rm07 zlwyi 4.jdb7: typq()whe 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 totale5vnjcgm9 6 y+ of 420 turns of wire and carries a current of 2.0 A. C5y6vjmnc 9g +ealculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a fie708.4 :snlda/yyxmww cte p -pld of 0.385 T at its center. Howx: yt cne.-mplp 04 sa8/yw7wd much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 rg4/ ,q8ptk:xyeu+spgy) u :jA. A 3.0-cm-long straight wire cuts through the center of the solenoid, along 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 th) p:,:u r4qg+eytuxjgs k/yp8e solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that producesqv gfhyt6fbd/+5dz qq)0,lr( the greay)dqhq,5vqfz rgdb6/ ( tl0f+test 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 so on.

A toroid is a solenoid in the shape of a circle (Figsot.pih7a6n)mk bl: / ursw3.. Below). Use Ampère’s law along the circular path, shown dashed in rs.p ab/ n3 lohu6.m7):k sitw(Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the conductors offhd(1dp* fox2 a coaxial cable (Fig. Belo2ffxohd d 1*(pw) 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 5dmv7,sf: n9gno8m vqa side is placed with its face parallel to the magnetic field between the pole piecem,fdg qv:monn9s7v 5 8s 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 s:d0rf5a wpso 11f(t,8zr ya dhu5ke, qcale 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% ov x.xxgoq/3p7ea+ob t .er the years, what current will give full-scale deflection if it originallyo q/b.xt.ga pe +3ox7x required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor doet qed .6dfzv r2,(1jdws the output torque ch jdv,qdfz(6t.2e r dw1ange?

Show that the magnetic dipole moment M of an electron orbiting t d0chu93ofu)k 6/fuviy it* p-he proton nucleus of a hyduycf )ti hfi0 9ukvo*ud/3- 6progen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lib -oma7e:v+ phes flat on the ground. The Earth’s magnetic fie7p hmb-: ea+vold 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 magrgjwza fwhf)x1ump59s e 4(+)f- g)jinetic field. What value of electric field could make theirs() f9)jj reufg mz1)g+-ifa 4px 5hww paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atg8u8 wv0 i t26) 7mqmbtl2llu1y;xdhv oms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest rav 8whg 2xqvt6miud;1l7 l l2b)0t u8mydius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectrometer5)jh acau5* au of (Fig. Beluaj c)5a5ah*uow) 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 us3n3py/vi/a ib )gf pf8ed to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such ig)yp av 83/3fn ip/fbas 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 voltagei07q cm +acp:h V before they enter a magnetic field B. The ions are assumed to qpm h7 ciac+:0start 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 h2 *.a4sumxp ise u+3g u87damfas 430 loops of wire per meter, and a 25-A current flows through the wire. If the permeability of the iropfiu2.ma 7deux*a43gms 8su+ n is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is p:o s.yvwv p(n+ i17jl nu;s)kj .n4vt38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field o.yj. vnv sk:p(uvpnt)l4 1+snw ;ij 7inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum wmyiyyu*; euhe/8. 3 n$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kinetezyz0kmfq p901d ,zh5ic energy upon entering a region of constant,k emf0z9zpzq h501y d magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric t:wp3srrap()8g cm)x orolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s mp8r g3 :o p()cwasrx)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 a8 2ntf73(a 4sjl raw bc(n9cp5idr7eo n 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’s magnetic field points almost horizontally to txwrn:pedkw n*3d.:,e oo ,dx6he north and has magnitude :*we6,,.:koo3w dp ndrxe ndx $B=0.50\times10^{-4}\mathrm{~T.}$ 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, whosex g+c-ao qvs4l,6y,4s 2bramn 8b drb2 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 largeh vkf/;+,x9 he4uzlqi 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 a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constan;i/ 9 h, zkvlux+qhfe4t 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 copp2job 9 vqno.eg 97-rc( zcrwp.er wire and is suspended in air due to the two mag-qw. 9(czg 9 p.rre7oo2 nvcbjnetic 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 fe7r4apl2o (vl apart in a horizontal plane act as rails to support a l fprl7e(v4ao2 ight metal rod of 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 deflection of the electron beam near the centp/l(n--ge+k)zbow n ls rb pv+qf*+ z01 0mvjcer of a TV screen due- +rlv qg+0we(z*bm blsfnj +v 0pk/c-nop)z 1 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 ozk:urw 1st(h/i / 0crf8s :aia device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial s1wriuh/ as:tz(8 k:r/i f co0velocity 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 phv2m*.tex* c7:x oyvtarallel wires, located at the corners of a square of side l, c 7ht: o*x2*eyvtvx cm.arry 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 useful in particle accelerators for “beam steering”; w7vn6(b +x g41xr+d-u)rd jnxmx3p+, zjpadrthat is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). 16x+pabvmx)jr z7+wrj np -, unrdgxd(+d34 xShow how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circulaulerb l7h3 9l+r coil of wire carrying a current I (as in Fig. Below) isl3h l7 +rlu9eb
$B=\frac{\mu_{0} N I}{2 r},$
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 about 1G( mmy;nbm)+b1 lvgn/w,$ 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 idei:we11- ym(jcmfruxyk/ p/i z1e 9fz;rbnq 6 8a of the magnitude of magnetic fields produced by overhead power lines. You estima:6e/cwrun(i / yem;p x8 jy19m1fkqzbizf- r 1te 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 woyn4k zae;/fxhr 46+imimt y.;uld make a beam of electrons, traveling to the right y+; yr 6infixte4;mz h4mak./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 path through a gas in a maiga; t s(cbpd4u2(i 42j zj6chw5ak(ignetic field of 0.010 T, perpendicular to the plane of the spiral, as4 js agapitu2 (((wjz;bc54cidhk2i6 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, 1.8 cn.8njg9j3fu s y 5vbd)cak(+ym in diameter, is to produce a 0.30-T magnetic field at its center.b.)u9+ynf(kc83ys j 5a nvd gj If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the same currehqw,(qy f g+ ;hz9m5e:av t4jmnt but in opposite directions. Tq(ah q,f9h5mt+:jegw v z4ym;hey 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 magnetic field B = 0.23 T at j. ioqw :5fdtu 50gg0wa 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$