A compass needle is n4ympr3o ; tipoj as94/ot always balanced parallel to the Earth’s surface, but one end may dip downward. Exp oatj/i4 osp3m4;p 9rylain.

Draw the magnetic field lines around a straight *5oc e:x84q zwapq/-) ufu bjrsection of wire carrying a current horizo*u-w8q :ea /)qz5orcx4 fbjpu ntally to the left.

In what direction are the magnetic field lines surrounding ls if4;d51gg0dmak/ ga straight wire carrying a current that is moviagig /g;l415s0d kmfdng directly away from you?

A horseshoe magnet is held verticall.dn6*pepgm7 )vg :jqsy with the north pole on the left and south pole on the right. A wireps) jg7g6 *pdn:. vqem passing between 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 those made of iron? vm m6t-1 ac+vi(Try it and see.) Whyvt1m+iavc- m 6 is this so?

Two iron bars attract each other no matter which ends a5r( (h6tc/mh( qhcu boiye/2 tre placed close together. Are both magnets? Expl 5t(c rhh e26t/cq(iob/u( hmyain.

The magnetic field due to current in wires in your home ca1fva - hba d+t*jj cjg0pz+.m*n affect a compass. Discuss the effect in terms of currents, including if the **g pb-d1 fmjv0jcjaa+.z+thy are ac or dc.

If a negatively charged particle enters a region of uniform magnetic fiuup,mt/2dc rbp* /h 6eeld which is perpendicular to the particle’s velocity, will tpbthupd//r*euc 2m, 6 he 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 *xgye-*jhl tda;n g u46gqtf*x56 6wivksz57vicinity of a current-carrying wire. 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 prtj5 w*n ;5g 6t* x4 *7xedu fy6gsah-izgkqvl6oduced by the wire.

Three particles, a, b, and c, enter a magnemj tg 5gppr w*7ub4gyr vv(,8a7uv3v6itt)f:tic field as shown in Fig. 20–46. What can you say about the cha *j t:wvfymptu65)a(ur7rvv87 pi4bggv,3 tgrge on each particle?

A positively charged particle i,jjlibmeqqv )7p7x-, n a nonuniform magnetic field follows the trajectory )b,vex ,p7j qj7qi-l mshown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron vr:us 6.n2e5rqc1ym5 tl8w td rod? What must you consiet51r 5cd28nlswv:6 myq.turder to answer these questions?

Explain why a strong magnet held near a CRT tely+x7 r6st3 umsevision screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field xr+3 m 7ussyt6is 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 butwq;l-iz upsp 3s +l7 6z5:ga4khqdl(k the third is not. k6z4hsp; -ld qs3(qilp gza+kw l7 u5:How would you determine which two are the magnets without using any additional objects?

Can you set a resting electron inthj d.j(.5k bo5j uwym .b1as(xo motion with a magnetic field? With an electric fis5jabu(k b.(1 wj.ho5y.dm xjeld? Explain.

A charged particle is moving in a circle und5mfe o+0ktoyt+)v6 cler the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the pathm+y5oc e )+vkotftl06 the charged particle will take.

The force on a particle in a magnetic field is,yxz nbthq9+ya(fj 2) the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ionnqa)+ byt( ,29j hzxyfs feel a force in the same direction?

A beam of electrons is directed toward a hors.nfzn.nb5xwa* f 9- qizontal wire carrying a current from left nz.*w9qnf bx f-5ans.to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving elec g/6n)3/56fd*vnn favyw m nfetric charge.yavgn /dmfw3/f6nen 56f*v) n

A charged particle moves in a straight line through a particular0 o qzp;ta-h(z region of space. Could there be a nono tp;(0a zh-zqzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sidewaym:dvw*2r f3r mk,6qios in some region of space, can we conclude, for certain, that i6wmd*r:fmvqk2 3o, r$\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of spav*,odve47qiwav1a wvu2 oe5d ut7:i6 ce there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain re qwvh4cr.vhxv6c1 vwb29i1o4gion of space are being deflected by an electric field or by a magnetic field (or b wcv xvc1iqb.4v4r h 19ohv6w2y both)?

How can you make a compass without ussug8bg0mhs o0b.+w 5j:tb (x 7q (zmhging iron or other ferromagnetic material?

Two long wires carrying equal currents I.zdi56 n4p xag are at right angles to each other, but don’t 4xz6p5 n .diagquite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, fregda, 2o(cm nd--hx*are to move in Earth’s gravitational field, is suspended directly above a second, parallel, current-car-m, 2(oa*adcnd-x grhrying 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 mvqflq nr/;ed( 99i+igagnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an ,ae5 ;aa7wah* m;en6 nvh,n wdunmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end *wnn7,h a hmwdv;ae a,;an 65ewill attract a paper clip. Explain.

Two ions have the same mass, but one isz bzf2/h mocdt1 ss9 sf.(:rc8 singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Bel:zzdsb8 s f.m s9(fcr/ht c1o2ow) differ?

What would be the effect on B inside a long solenoid izan,coc ;3+6osic/ va f
(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 is an elec5awt:pue t caag0ezb*i2-. 6ztromagnet (the i g-z2z*tc6e.tu0w5ap i :a aebron 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 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 magnituzsf.)f .pl1 cpq1/z0x8t udb bde of the force per meter of length on a straight wire carryi.l s p 8fb b./01zqxpuz1dcf)tng an 8.40-A current 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 of the magnetic force on a 160-m length of straight yxy5elm,ny)m(m6kfc u6 2d kr+9a ohbe.(/dywire y rafkhnd cdb+m.( mly)yx /kmy5, e9e 6ou(62stretched between 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

  Calculate the magnitude of the0ft;iq*h4m l9r tf,n +buf wl1:zml q( magnetic force on a 160-m length of straight wire stretched between two t htmlwlq :b1n( zilfuqf ,r0*m49tf ;+owers 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 flowin kh i+ u++7nttaqcb7i0g in a wire 4.80 m long if the maximum force on it is 0.750 N when plb7 +tatinq +kc0uh7i+aced in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of cur zf)niz/1cbkhe47 u b(rent is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes 7/(u i)n hzzbkceb1 f4an 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 1.28 N when placed betweei9s/xym:htj03r nz4 ;sjtm z8n the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what isn ys;/:z jihx z98tr34mj0m ts the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire0bhxp /5umk/bvlg ap )f3p96 i11zrgz 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 relationship as it actually is, calcul1a53kv/hi1xulgb p6r9 mz bppgf0)z /ating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximu +-tkjslslp 18r: ;kfqm 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-diam40ul lajomsyf5/qq7 3eter copper wire could just “float” horizontally in air because of the force due to the Earth’s magnetic fie uys q5mloj0/ q3afl47ld $\vec{B}$, 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 charufg1tfo r:nv(d i4a91ge $q\,=\,+2e$ 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 travejwcr0(qwm:z p mhwpr-1 2zkqz4(2 g8f g uo26fling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for each diagraif4t0 -m( ati+kcuds,m shown in (Fig. Be mtu fa-tkc,id(s4 +i0low), 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 . wgzd/(k1 ehtof $\vec{B}$ 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 f v5nhi pp.*m9e sc*2p-vtk+yupward 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.h1jg sl,iimk/ fna0fll3e-h8x 6)i p-20-T field, in a plane perpendicular to the field. What is the radiukx-ll /-glhi s8faj f3)61mhin0,ei ps of its path?    m

  An electron experiences the greatest force as it travels :rvq8f9jgda ,gmao* b 50h3ws$2.9 \times10^{6 }\;m/s$ 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 o +.hf7 7yqaapzf electrons that go undeflected when passing througz +ah7f7p.qy ah 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 whose tbee2zl4f:21dz) f3 f ,tha.tspbp:q 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 15ya1im-aq)h gmdsmt /kwy0 - required for a particle of charge q moving with constant speed v to make one circular revolution in a uniform magn0dg- ktq1asay )1 w-mm5iyh/metic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q mi4s +39t3a1xxwl vgr boves in a circular path of radius r in a uniform magnetic field B. Show that its 9 i tsgr3x vb+a4l3wx1momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a,7f ygkvutdv7 i8tr *) magnetic field B. Show that its kinetic energy is propork ,)rit 7tfu dvg78vy*tional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem 21 is o2xf;jkp 6, rk$L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s magne+gf 3 ykp5d8dx r)2bbptic fieldp5dgbrd )f2p+ ykx38 b of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at f;4g kgrj*oo9v upxs3/jnku(8(b mn/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 speed zlj8y d si0rk+ z909dk$\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A current. How str f:vc/dv8u; .jmqkzxrtc5;3 a ong is thea;xk zru 3;jc8cv:f5q. /mtvd magnetic 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,ere3x/uv+j nnr kxj16b p79fi*5xqm magnetic field no larger than that of the Eartu6kn,1qxn*epfem xbvir 37xj/9 jr+5h $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long strai 9irf. ee8od6vght wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction 6od.fee8r9i vof $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upwq1gv3qr; )qhz /u-vx*p5t:s,sf q ppa ard 24-A current exerts an attractive force per unit lenv):3 f,5;a -qz rqvqqp*/xt 1gu pphssgth 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 direction of qanbmd 4 )so.-the force between two parallel wires 35 m longd4soq )-n.amb and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m fnh n14:hk)rpurom an electric cable. What is the maximum allowable pku 4:)n rnhh1current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a cpn7p* op 0/dciue+r,iurrent 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 th*i ,oe cpr 0ipn7/pdu+e 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 parallebjc h9up4 *tbg;osc8*l wires 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 fromctb ;h*8*p csguo4jb9 the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from(5;geu*po p at a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume theug* ;e5 topap( 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 glpw*yz,d ; h+north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there pointsgzd* ,h ;pl+wy 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 pa7f*m chlfe(w4zkkya h z1a)36sses a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wires 2.0 cm apav5 h 6qx6)o)mju6 qornrt in terms of the current I in one when the other carries 15 A. Assume these currentsmr5h6 o vjx)uo)6q6 qn are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, ang.yqhlzk2:s kbg: 2zxg* e.v: instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm frg:vkl :2yb: ..s*q2gz ekx zghom 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 u hyhxnq.5;r( 7re*fhin the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it* hh; rnf(.qy hxue57r 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 poin:kl4 bc ,t:wqots 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 shqd;il g ;/ aenq9xqlybvp)t2i. d+1(nown in (Fig. Below). There is a current of 2.5 A in both wires. Deg ;q;niqtl.v p(qae iy 2db)+x/ld1n9termine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire, made of 2j)2qwbd j9a l-.5-mm-diameter copper wire and parallel to the first, is kept in suspension 9-j)alqw 2bd jmagnetically 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 pe.. mxebhlby( ggxf2x77o :r x5rpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bom.xx(gfxg x.57oeb :72rby lhttom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight paf- (.tsakg i2:ptiwm*y 7ex ,jtq) h;jrallel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same diakmijt-t*x,:fjp t(e7g s 2y.;q)hiwrection.
(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 3jm6 n2hnow c,z;xw/ 8k.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic f8 ,xknwn / jc;hz2mw6oorce 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 direction3zt7za-a/jm )jwix f6w 2b*p u of the magnetic field at the midpoint of the side of the triangle between wire M and)wwu/pjza -j fta32 im*6bz7x wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I in the sn1o:of5kl hjtf8 6bm 3u6 sf7tame direction. One wire is at x = 0, the otheh ofnu3b6mjott :5s6 lf718k fr is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and cw6,-uf)cvh zzj) ax. yarries a current of 2.0 A. Calculate the field inside near the center jfwa)- )hzu.6xvyz,c.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0. mb)3hkbr gbtfr8dnyh7)0- t:385 T at its center. How much current should the solenoid carry if it has 975 turns of the wirf:d3gbrb )- t8h rymk07 n)tbhe?    A

  A 550-turn solenoid is 15 cm long. The current in i7yb5p med(0 p6xtig n*t is 33 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 concern us). What is the force on this wire assuming the solenoid’s field points due east? (7ypp d0gmxne*t5 ib 6   N

You have 1.0 kg of copper and want to make a practical solenoid that produc5p*-u9yrh /wl 7 mcn2ieb3wmjes the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fatmwebi7/wh2 plj3u- n*5 myc9r, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circgsz 9 yb3pl)xl5 .,i)eul3:qq wbao1 dle (Fig. Below). Use Ampère’s law along the circ )bdslq 315: l3qugyze plib9,).oxw aular path, shown dashed in (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 fieldkcl9ub.t9at afa; 4 o05qmo1m between the conductors of a coa0aot .1l9mbo 9c;m5auqat 4f kxial cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 2g39pcq f +gae;rn w3+j2.0 cm on a side is placed with its face parallel to the magnetqfp e3j;w3g+n +9cra gic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle del ej 0tohn5zh:3ng 0*86xs w/wos a(tnflects full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanomete 3c:9:r*)9/zc qxbr jd 6ehf:qmxsbfg r weakens by 25% over the years, what current will give full-scale deflectif xbb9xq:/*c6ezcg3qhf ::r rdm)j 9son if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output ta,/ ,w ;bapcusorque cha,;wau , bcsa/pnge?

Show that the magnetic dipole moment M of an electron orbiting t/ 8 ccbp+t1zdzj- (rvehe proton nucleus of a hydrogen atom is related to the orbital angular momentum L pe8vbz(cj+1/-dc rztof the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and coz ::w jc4ua -rbr+qt-jntaining nine loops lies flat on the ground. The Eartar-4jqz+ btuw ::-rcjh’s magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic field. What v.z qcv.*8 j firvhu xfct8)2;halue of electric field could make their paths straight? In what direction must it point? crv2ffx8i).h. tj 8 ; vzu*qhc   $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equalo,i ervxi/)o0 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 a0 r),o/vxieoi re the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectrometer3ir9(t7ou*r2zg h ,*r7gd xtatut96 fypx b o3 *t7ah6zgtrbu yu d o* xt,97 ior 93(rgpx32tfof (Fig. Below) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being ustr 0+k ks24rkied to monitor air pollutants. It is difficult, however, to separate molecules with nearly etr02k4 rs+kk iqual 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 acceleraten6zq3hz0ae m 2s ions by a voltage V before they enter a magnetic f3hnz 0ae6 2mzqield B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops ofxc7*)et ft9 gc wire per meter, and a 25-A current flows through the wire. If tg*t)9fc te7cx he permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8)w ) nz7g63 i0k mdfc3w5rwfoy.a p2yb cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 0)ywargp k ifw3z.mfw3n d6 y7c) 52bo2.2 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 momentu.l.x,8t (: z l,rmdgv*rtrfbom $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kine *p hw4d4 cddj0hy9p/*jv ai;btic energy upon entering a region of constanthh *;wy0bdp pja44ji/dv 9dc * magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) cao,.xbr/bcn4gu,2pw 21xf wbp rries a horizontal current of 330 A toward the east. The Ear g2/rbp4u .xn,pf2bc,x 1bwowth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acoje64pw a c+xfj.m.,vquired 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 mg 9d d3ebr-jv.agnetic field points almost horizontally to the north and has .re3jbddv g9-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 i7ltvb4 mwanf :j7+ n.v8pf6 hatom, 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 “projectilnkiw(fg8 s / lvzul0.3e launcher” is shown in (Fig. Below). A large 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 constant current floll v 8(.ig3z/0fnksu ww 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 h fw*fne0h+uxivb5* (is 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the susw ef + nhux*5fib(0h*vpended wire.    A

Two stiff parallel wires a distance l apar f*20wm9c-w f+.mpdepf5n gtv++ gluns .m n0tt in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (F* . 5+9nn l-fpwpsnv+0fue 0d.m2tmtg+cmgw 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 approximatc)wecyu qw1* z3kn:i2c8oc )fe maximum deflection of the electron beam near the center of c)ywuf*o:czni)wk12 qe8 c3c a TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to acbkcxm f28rg,l,viwj8;9)-hou4 ugk/y iwm -j celerate 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 tl8ji b- gkmwh8)f,r -ci4;/j ,9uvymou 2wgx khere is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners ozwwxi69 imr2fc6,o2hn36a ze:u8im z 5go uz.f a square of side l, carry equal currentsz :ix.6wz 2miz5z 6a g,riew 6uoh3 fuconm829 $I_0$ 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”r 00x)4fb 8rqcuy, co.ny)rknt(p ev2; 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 magnetiy0.rk u2tqr0en(b x r ,pno4c)) ycf8vc field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of w u a*u/9/2(wnza h0n-cvlq gok ab;.qiire carrying a current I (as in Figa /0 2k/*iwb. unqa(;9o-uhlncavqz g. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magdb5bq l-l tqy+q+(h g.netic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude d;m -pp4ld4elo)eym cd;6ls(9g2a gkwjl, s,of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate theg oee69g pwadjl2dy k4ldsl,c;)s4 ;mm lp-,( maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of electrons,5zm4emr g-v rs*((y;puvl q q +nay9y9 traveling to the rv q4erqmzy9(asv py +9m r-u5(;yln*gight 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 0.0 vx64 .m tr.oy7hxrghh/caa0 :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 10.0rh x:.r 0/g4 hachxyoa.tmv67 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 magnetic m 2n3ovn1ecz/field at its center. If the maximum current is 2mczvo/ 1e n3n5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight alua tl pv lqwuuav5(jf76(g :t58minum 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 (Fig. Below). If the a5ujtw t (: a87pvf5vll( g6uqsuspension 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 a 4m-)opbbs2f 3cgb pfg;t m-3 ,r5$^{\circ}\,$ 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$