A compass needle is not always balanced parallel toq+ ,6cm yat),sodl2ve the Earth’s surface, but one 2acsye ,v , +lq6to)dmend may dip downward. Explain.

Draw the magnetic field lh*absw: uq7(m8y rul 5ro5f7zhqrex3(ui q5 1ines around a straight section of wire carrying a current horizontally to the le7(qxrsr a uu1oy rq:mhbu*eq(hl5fi55wz83 7ft.

In what direction are the magnetic field lines surrounding a stra;.hxvlzz b(y+f- h3bcight wire carryincz; lyh3xz+(v -bhf. bg a current that is moving directly away from you?

A horseshoe magnet is held vertically with the nortcw 9+es9 elz/5d+ 85biummywqh 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 f8b9/weu li+y 9m+qds5cze 5mw orce on the wire?

Will a magnet attract any metallic object, or only those made of im r yw:.w(dm/rpo so,,ron? (Try it and sewomo (w/dm :,,rysr.p e.) Why is this so?

Two iron bars attract each other no matter which endsmku yz,cue b9.b 2 tem3v5,p8j are placed close together. Are bot t.,mp2kjby9emuvb3c 8u, ez5h magnets? Explain.

The magnetic field due to current in wirpyd;o(xsto5 oi2r h v55xm* 9aes in your home can affect a compass. Discuss the effect in terms of currents, includinvp5t *ox55;(os ry92iax doh mg if they are ac or dc.

If a negatively charged particle enters a region of uniform v/5cbopa-/z4 z ji mq*gc4 i:hmagnetic field whichzpoi 4:mbchi4/*vag zcqj -/5 is perpendicular to the particle’s velocity, 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 particles move in the vicx4 e-g03trblcrl3y9 vinity of a current-carrying wire. For each charged particle, the arrow indicates the levr- bgx4y03crt 3l9direction 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 as sh 11) cyuy46nw go fwf1a9k/hbxaql4-qown in Fig. 20–46. What can you say about theg)xw 9-hk1bqf1ycyawu/f1 n4 6 q4alo charge on each particle?

A positively charged particle in a nonuniform magnetic field follows bv 5, d6ngpbp 3x42hhets wcxat 6r+,0the trajectory +d anhp0b v, b6g2exs3 tt5,cpwrh x46shown 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 attju2;5aa up1 f,/h+1z1kv sg-ur0 ukrod nnr i9ract an iron rod? What must you consider to answer these questvr9huni1ano ;2z +pgusu 105dku af,r 1-rjk/ions?

Explain why a strong magnet held near a CRT television scree e.b 7xh-ax,oen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes -.bh7xaox, eecompletely 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 magnetized but the thiilc /4,qqzg r;mqa+ 2ord is not. How would you determine which two are the magnets without using any a4i l,gm 2a qz/qc+q;ordditional objects?

Can you set a resting electron into motion with a magnetic cy1q:2 ;puo :ue0p (zs4zo4r)zyqa2h+bv j iqfield? With an electric field? Exprqu0q1;i2jo () hp:2e4zcy qa oypsbv+:zz4 u lain.

A charged particle is moving in a cir,b7k/-p 5io hoj/ownrbc/)zacle under the influence of a uniform magnetic field. If an electric field tha5k7b/c iaj hzpb-)/onow/ ro,t 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 magn 4o7v a o-1kmkwtji+r:etic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in atooj1w7-:m+r4 k vik 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 positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a z:n,wqe*dr hdz:4 xc9 horizontal wire carrying a current from left : h:xq*dezz,w9dn 4crto right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electu/vyd0)/ rcqsv3p-* kpb zl9 gric charge. bv s/q*r9-kd cpvgl03zuy)/p

A charged particle moves in a straight line thr4w 7 fm *xzg.koje-xi7ough a particular region of space. Could there be a nonzero magnetic field in this regiokx fw*7-.jz7 i4mgxe on? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, p37z3k5dsg o/o rxhzqx :8bc 0can we conclude, for certain, tbc 3xd xkz/z3rhs87o:p 05o gqhat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is uq x0zy qs5kmeu.( /ig390xg qa 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 whether moving electrons in a certain region of space are beiv+b*n q+2moc lng deflected by an electric field or by a mavl2cm+ nqob *+gnetic field (or by both)?

How can you make a compass withzgy 0lh s+ uo,cr9x+2vout using iron or other ferromagnetic material?

Two long wires carrying r9 rcq-o0r+2zmu (2.yildugk equal currents I are at right angles to each other, but don’t quite touch. Describe the magnetic forc lk rg rq2omy2.ud0-+ur c(iz9e one exerts on the other.

A horizontal current-carrying wire, free8, j: dvejz71 2dx0lvkmx(d ad to move in Earth’s gravitational field, is suspended directly above a second, parallel, current-carryind0vka(8 zxd 72d, djx1mlve:jg wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized piez)luju ,a/fhu oz8. w4ce of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if onnoz hnkx589l(.t-d qpe end of the nail is in contact with ahnl(zq.pxd 5t -okn9 8 magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one isge; x66,jf(b0oo b fsw singly ionized and the other is doubly ionized. How will their po(6g obw s;o ,je0fxbf6sitions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B insidsv z8yh*9q jek*3)foue 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 z;ac, afq5kuzt18gd2yrnxv 6m8 p .;wrelay . 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 current flowing through the main switch. For example, the startp6zak t d;1y 8c5xv8un f,qz.m w2;rgaer 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 m4rk +vgsm,t r;eter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic k;vr,+mtrs 4gfield?    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 :kmxy* pd o(-hlength of straight wire stretched between two towers carrying k(dx*hmoy -p: 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*pu 61zz,.) ymzad rnqe 7(xn jxb/t5l on a 160-m length of straight wire stretched betwe6 5,j*m1(ne7nzbxzu p xtza.dr /) qylen two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long if the maximum force on it is rxab*oe,rv/ uw)2k) q 0.750 N when placed in a or) a,vu/k* )rbeqxw2uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying ( aj4 b-aj92kishnxkl10 z2j) kfp9rh4.5 A of current is oriented horizontally. At th0zx)1fj2nj(pj-hh9 k rla24sk a ib9kat point on the Earth’s surface, the 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 carryi7(betn, avx0mca(p :v ng 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 c0a,(( 7t eaxnc:pbvmvm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of its mac+x )ffok0-0 . oeuj,i;gpdmbx :syj+ximum possible value. Sketch the relationship of the wire andxfojdf,ge ymoiu:j-p bsc+k0;. + x)0 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 a maximmr n/+h.o yt+dxyq,, tum 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-diasep kpz;etki6 e5(/c) meter copper wire could just “float” horizontally in air because of t6sc ke) t(e;e/5 pizpkhe 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 chat7*tnnykn. / -n+ mud43idj5o /xpmkurge $q\,=\,+2e$ 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 magnit5)xw.5z 1yt q(ndzb xrp b( 9o*x6oamiude and 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 negative charge for ex4n,y7 2cg*y zjx p6foach diagram shown in (Fig. Below),f4,xp xn oc2z*ygj6y7 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 directv* 3j:cjhp0rz1rhaa6 ion of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward with a 6 uygl/e:q 3)9adqk3a t)eeds 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 entersmr5-gd9fp4emvr p i:* a 0.20-T field, in a plane perpendicular to the field. What is the radius of its pmevm-rgp5:9i d p*r 4fath?    m

  An electron experiences the gre qt1+pv8h fob9sgbo/ 1atest 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 undefv+-:b1d9 m f qjem1 wsnv8j(ae,1stea lected when passing through-aj191wdebqsv tmjv +fm:se 81,a e(n perpendicular 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 whw8zfx5o wc. h;ose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle oz,8(8*ptxll +-ii wvn yj:hnlr gj8)hf charge q moving with constant speed v to make one circular revolution in a uniform magnetici il jv88yx8t hpz- ll,+nwn :h)*g(rj field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uniforljj 5a+qs.k,/w7ddcnm magnetic field B. Show thatq.n +, l5/wjd7kscjad its momentum is p = qBr .

A particle of mass m and charge q moves( 3 +ym3x n -z+8g6(pi vnvuyg0ob(d dcktkdb9 in a circular path in a magnetic field B. Show that its kinetic eneryn bi+38vddgk3 (v nyt-c opb90dk(xgzu(m+6gy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Pr:haiij - pyk.6*5h htvoblem 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 Eolxu07 p0yba rf0m... lyy0 caarth’s magnetic field 00r0c ya m.yfa7o0p..yllu bxof $5.00\times10^{-5}\mathrm{~T}$, 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 37k2paxog ffy;djxby95 xss+w3l ;5 l 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 speedknm s cq/q-ue52 6/.sf/nvqtj $\nu=2.0\times10^5\mathrm{~m/s}$ 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 ca1qykg-)s /u.cw*7exvozr t -l rries a 65-A current. How strong is the magg/-lexru-w zy1ocs) k qvt. *7netic 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 produceg4j( 3vhnou1*khg /und, /oaa a magnetic field no larger than that of tknh4 ov* o agd3 /gjua/,1unh(he 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 of the page toward 3+.wx/op pusw you. Indicate, with appropriate arrows, the direction of 3p.o w/w+ pusx$\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying anle b39s4 gpqum 1sql-4 upward 24-A current exerts an attractive force per unit length olm qqpsel91 b3g -4su4f $8.8\times10^{-4}\mathrm{~N/m}$ 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 parj0vucf d3d ;:8c)rwem allel wires 35 m long and 6.ed cw3v8mju :)dcr0f; 0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’,j q4n7 6o +mez3aia8bbi 8 rb;mb(vips magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in thei;zq4(bi bm,a a+r8j6 b38n7iebm pvo 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-high poleomf lmb(f67 5as. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compm5 (bla m6ffo7are with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents in thevz33 jp0-of o ooj0xk0 same direction. Determine the magnetkfj0j03po 3v0 o ox-zoic 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 strai*,)pfjdumnx:vpk n 5 4dax 06hght vertical wire carrying a 35-A current downward. Innpa ) vx, fhp4 5jk0*n:mu6xdd 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 carrirk +y:m ld*6dfes 22.0 A of current due north. What is the net magnetic field 20.0 cm drdy:6k f+mdl* ue west of the wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a rate ra9lbja 8*q 9eof $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straig(gnpxh p2l)s uc-27 fqht wires 2.0 cm apart in terms of the current I in one when the otuhfpl)qn 22c- gxsp7( her carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and fr 6 7,lqgz.tdweom, an instrument. If te wl67.,qdg zthe insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the ne k)ajx t:g6++tx(by plane of the two wires shown in (Fig. Below), parallel and juse+ta t( y+xbxg)nj6:kt to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to 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 2xfff r3j3rt() 3$^{\circ}\,$ 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 lie.ezdb6 rsam1 5s 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 thebred61 .z as5m loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wir ,gav,zh6a4ofe, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magneticallaa6, v4, hzgofy 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 tendv/ ;1wt;*wqk qu 7 +z *l*b8beocodhey are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magneto z 1 qcb*b otwel e7u;8+*dd*w;k/vnqic 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 carries 2.0 A current. .k7 h( n2h bmxdp+26brmadv;rhf0: jdWire B’s ;.rkvr6hmn0dd :fh(+2b 2xb7pm adhjcurrent is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking along them, pic;xzh /l3 9wx ms*(othey are at three corners of an equilateral triangle.) The cur* clpx3i/ x(z;s9m wohrent 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 and direction re1ye z52qrk +of the magnetic field at the midpoint of the side of the triangle betwer52+eryz e1q ken wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires64khdu ;jx +7tr(fyhg , a distance d apart, carry equal currents I in the same direction. One wire is axdj4h tu g76h+kr(;fy t x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total ofypttlpa (fc7 gz uso9xa ,//3; 420 turns of wire and carries a current of 2poca9al7sg z/p y, txt3/u ;(f.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25l2h 5y-cdg;xew16c zh cm in diameter is to produce a field of 0.385 T at its center. How much curxz;6hw e2 1c ygchd-l5rent 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 35 ovwcrp-i3 5. 6vgxsn-eh ye83 A. 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 3 re5-5ywpn iesvvh- 68x goc.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 . vxv( hpbu5c0hg3 hx9to make a practical solenoid that produces the greatest possible magnetic fih.5b xvg0(cupvhh93x eld 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 (Fig. Below). Use Amp;gbkz y81yy vosf bm/ f0*1-hmère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic;/sfk*om mbg0b8- fy1hz1vyy 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 condu6hthcn8r );bt6h7evr hn el3-ctors of a coaxial cablt 37-lb6r;h8hehv) crtnn6hee (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed with its face pag /u1 sr-bvcf rnk0**rrallel to the magnetic field between the pole pieces ofu1r*rn c-g*k vrbfs0/ 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 vd0o /m tev .tv(va..rscale 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 thec+ukyk r 1;nh3 years, what cu+y;1hr unkck 3rrent will give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drof zv18a ;dhlbi f 7-5s/9tgfrhps by 12%, by what factor does the output torque change gthrh-isb;f 95l fav/8dzf17?

Show that the magnetic dipole moment M of an ele23qmmae h:neh2 i9h2yctron orbiting the proton nucleus of ahmyen2 e2 2q9h :3imah 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 containing nine loops lies flat f(y0cno wo(irg6 wv* 1on the ground. The Earth’s magnetic field at this locatio(o(n 0 vf1oyc *6wwrign 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 circp zj*j6)aji/rle of radius 5.10 cm in a 0.566-T magnetic field. What value of electrijaj6*i z/jpr)c field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal em2y0 d9+sv d tj3 w,i0hnlbrjpxb4./to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radiusv ,0b 2d3bs l eh/ijtw pj4my.dxrn9+0 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 masvq8u0j.1f yyupmp92 x.eexan;f+gz-s spectrometer of (Fifxeg0a; p8ze 9 unj.q+xy .p12v-muyfg. 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 pollutants. It is diff j9ju p)x 0yjfo)e;yhd14 w8g2o2dcq-b 6cvlhicult, however, to separate molecules with nearly equal mass such asbj 2 h8vylwyj)ec6 0hod d-o)2c9jx4 1; fugpq 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 accej(; +/z)5 l ybxzilhbg we9hz.e u96hwo.pi1nlerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to staro+hpw(; yuzl6 wbezi b9 g e zhj19h.5xni/l).t 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 pera.v*8c4r sr7 lsb8fw y meter, and a 25-A current flows through the wire. .c*s48l vwfsr8 7 baryIf 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 csfm-z lh99gw p 5 z (0y5+a2k0igtfpvzm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid i(vi 2ls5zppg+k fg5aty0h -9mzz09 fws 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 momentumm3)emgj u6wjd t7+1cz $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 ent 2rbls f(t0y:g u a:(y5nnbdh zj2/l7eering a region of constant magnetic field. Wh/22 bynt(j:u5g7l(srl hdabz :n 0fyeat is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizont:(3c o4rdm1twqzy d5 ial current of 330 A toward the east. The Earth’s magnet4 o3(izr 5qdm1tc:yd wic 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 aiz zsd1m3fvtw8aj(6g-l/pw 1krplane 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 ;q uf61 2 zvon wqk:f/ee3/l(uue)at dalmost horizontally to the north andt6eu2/k quf qeulwvf/ 3)n:1(eoza;d 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 atom1ct(14nvpt6 ;zdfrr tb- f-ilz7.p jh , 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 large cuyj ,(*aey6wh orrent moves in a closed loop composed of fixed rails, a power supply, and a very light, alm e(h,yjawy6*o ost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and is suspendedgd8:/lt:i h fp 9wmt1n in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottomtl 8mgtwf:hn:9/ 1 pdi 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 horizont+fqf l w,m t+3u/,zodgal plane act as rails tt /wuo, m3qz+,f ldgf+o support a light 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 electroqmc4-42 u fqgyn beam near the center of a TV screen m -qgqf24 uyc4due 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. 4 pmmvzmk:yptdcc2+7 0k.p(wBelow) is a device used to accelerate elementary particles 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 to an ac voltagedc(kpv pw7 m.t:+k 04yz2 pmcm $V=V_0\sin2\pi ft,$ 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 lu,q9y* -naglk( 4b7f -pkykb the corners of a square of side l, carry equal c llf,a7ukgkp- 4y q( kbbyn*9-urrents $I_0$ 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 inv -wo9sk(u2 tk s*5qbx 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 witxk*u-s 9bt( o s25wqkvh the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil o49qpx24 ebscyv 1a ot mx 17toc:*n1vvf wire carrying a current I (as in Fig. Below) isx*m7tn1v4 oq yvast 2vc4: px19 o1bce
$B=\frac{\mu_{0} N I}{2 r},$
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 aboutp+,ac*p 6z2qqnp9k .nu w;wviq2(zi p 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produced by o /jywoxob,r ox:ee 98u um :cqnjf8 nk8*t4j18verhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, andj8f88kw9 8no:nj1o mo,y urqxex :*4 euj/bct 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 electrons, travelke;o4bx9 yrvr3kqz iwo 6.7,g ing to the ri3z9wro vy47 .ker;bqgki,o x6ght 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 magnetic field of 0.010 T, p7f,j8a pzy q7werpendicular to the plane of the spiral, as s zw7faqy7 j,8phown 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 cm in diameter, is to produce a 0.30-T magnetis:1ws/ru+r)hltxo :w (i3hc yc field at its center. If the maximum current is 5.7 A, how many turns must the soleno h1slxc:(r/sy ow+ : iut)3hrwid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wirebu/ -8iwkx)klcz6m *us, each of diameter 0.50 mm, carry the same current but in m8u x*z ub/6kic- kl)wopposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field*gvsm) .9 *lw/bpggfip (qmjz rji5:8k: (ef s 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$