A compass needle is not always balanced parallel to the Earth’s surddatd ;g1 4kw(face, but one end may dip downward. Exwd4gd ;da1(tkplain.

Draw the magnetic field lines around a straig 49u**3qkpox b( u8cd-nlagdlht section of wire carrying a curreul3a-9ddxck8n4p*ol u*bg q ( nt horizontally to the left.

In what direction are the magnetic field lines surrounding a straight wire vyrm1. *a9oq rcarrying a currerv9* o 1yma.qrnt that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left a;dw9lzwq*r ,6yhc p t+nd south pole on the right. A wz,6wwy qp*t+crd9lh ;ire 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, orsq tt(6wdg3 )0j(elt7 euux6 p only those made of iron? (Try it and60tsgx6 3)ude w7tt jpqe(lu( see.) Why is this so?

Two iron bars attract each otheycmtmp q /6 -8q n*ibi.- 0iq-7gvgwknr no matter which ends are placed close together. Are both magnets? Explain. qwpv-imm*n6q0niq.g7gb 8- -c ti/ yk

The magnetic field due to current in wires in your home can hu y436j bbl,dsn3aw.affect a compass. Discuss the effect in terms of currents, including if they are acn4s hbjy aw,ld6.33 ub or dc.

If a negatively charged particle enters a region of unps5c:dpf p6 r-iform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain yds-:pr5p 6pf cour answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicini)y sw2 cusc3h.dec:q9 ty 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 fo w).cy qeh:cc u93s2sdrce due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 20–ecu4ps1 7z.l lb2* keyj d(y9q46. What can you sa9yzl c4kjb ( *.les e7d1pyu2qy about the charge on each particle?

A positively charged particle in a nonuniform magnetic field bonxb4 hdmd09z09ip4follows the trajectory showzd9 mbh00bdo4ni9 p4xn 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 1yekl ykdo4ugk- 3+ k6a4br/zan iron rod? What must you cons1br/a4kk oyly4 kgzd -3e u+k6ider to answer these questions?

Explain why a strong magnet held near a CRT g kwsl cz2w6lnr,h02 8vu-t5v:j nm x6television 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 riwv6 v8h 2lz5t k,m2x:cnj-lugr 6sn0w sk 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 tke h 9e7zt19hm4ze5tvhe third is not. How would you determine which two are the magnete71z 4ht he9v5 mez9kts without using any additional objects?

Can you set a resting electron intvb oosr;8h7i 2o motion with a magnetic field? With an electric fib ohs87;rivo2eld? Explain.

A charged particle is moving in a circle under the influence oa6 bm)4/acozv i4- kmjf a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, da oj-i /m4a46mk)zvc bescribe the path the charged particle will take.

The force on a particle in a magnetic 53.iut2 xs 5xlcb*/((xphim9rcfd nifield is 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 negascfc /(rxti dnxx5mil9u i*b2p3. (5htive ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a uo +k6da iut2,current from ia+t2 ku u,6doleft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magn6ij b s0i7u090dfwt nmetic fields that surround a moving electric charge. fnb mtui6ds90i7j00 w

A charged particle molgfz .ku9.+ m(-pynoi ves in a straight line through a particular region of space. Could there be a nonzero magnetic fiel z+y (-gkmop9fn u.i.ld in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, casf/m;sty -d il 1i:/vqn qmfv l1ssi/:dt ;y-i/we conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular regionj5r sr2yid )(k )zrpvcv v9e8. of space 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 ibyx:4 ng p-reet0ww 8 .ddv8,48eqaafn a certain region of space are being deflected by an elect b pq8:r-xg.80f 8dwey, wentavade44ric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other femefq +m ;lh(5 x2ss(a+q5 acgop ;c:rod4oc(rrromagnetic material?

Two long wires carrying equal currents I are at righto+hkfl-ex-y 51z .pti wo6 zy* angles to each other, but don’t quite touch. Describe the ot -.+ 5lpo y1-fwhx6ezyk iz*magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move tir+e025x blu(jmz( fin Earth’s gravitational field, is suspended dit2l0+b i((5fjz er xmurectly 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 mwg5b;ep.wu ( ako/ j,magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if 6(w p f(zig:m4h6 cx5z8intd rone end of the nail is in contact with a magnez(6:ir5w8 pht6mdn(if x zc4g t, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionizedqm+iu,6+wx ir and the other is doubly ionized. How will thei +wir ,x+6uqmir positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long 1y;3brpl-kno 9jz9vy 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 solenk8wf6q m1zn 0zoid is a relay . 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 thrwz 6fmn0kz1 q8ough 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 straight wirr3ei v.8 za*q t ;tyws2iy2f;ze carryinget i8s tyy32i2*ar;vzw;.zq f 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 magnu/ nljq62d. mh tc.0ueetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fie lchtu. 2mudq.en60j/ld 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 straight 1ewhlqj.9awpq326p c u/db f. wire strea.p wl 6ef93db.h 1/2qqjcuwptched 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

  How much current is flowing in a wire 4.80 m long if the maximum force on it i):niws q(yu(y*y b :2aamc:vu s 0.750 N when placed in a uniform 0.0800-T nw((qu)ci:ys* av:auy b 2my: field?    A

  A 1.5-m length of wire carrying 4.5 A of;hmcb54/i, euk9l+v9x9d 1jlyeo xqg current is oriented horizontally. At that point on the Earth’s surface, the5x 94e9kq ,hd +1vm/;ibelguoc yjx9 l dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8:j 8btm78+-e hcwhjbp8jw9io4 qpkc3.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approx k8wpco8 ci9e 4 wmjh 3hq+t8pbbj:j-7imate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measure yz0(2/i8 ghe3c2vnt w7z wnlmd to be only 35% of its maximum possible value. Sketch the relationship of the wire and thy g/ t83mwczh7 0wn2inv (zle2e 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 maximum of vj - i 0dn:;6mohk5mbn$ 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/q5 sysnmz3w0iitmsfm/s* 3i*w 9 +k p copper wire could just “float” horizontally in air because of the force due to the Emi53z/ pks0 miy*ts3n+swf * s9imqw/arth’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 charge 9ya 5 /uc vj,pi9n0+wl2albcv offv8,$q\,=\,+2e$ 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 dire) 4b/b1elrsktnr8 iad73( a edction 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 eachp iq4 qm0ojldb5x;49wrd p9 rlvt 30b5 diagram shown in (Fig. Below), wheri0v 5xm4403q59o ldj9tbwrb dpr p;qle $\vec{v}$ (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 i7 enc. -(caokof $\vec{B}$ 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 speedvai+:juu7v:il 4( awp 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 e/s21 y *mgxcgplane perpendicular to the field. What is the radius og1y/*ex m2gsc f its path?    m

  An electron experiences the greatest force as it t-yei 7znh- f(vz 1o;xoravels $2.9 \times10^{6 }\;m/s$ 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 gokdpqp r6*o qr-: 3evp2 undeflected when passing through perpendicular electric q- rk rq*3o2dvpp:ep6and 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 mass is c2nwj w2uf0 bvlllkwf0c. t)/gw48;u $6.6 \times10^{-27 }\;kg$ 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 pa.a bsdn9/ 8oh ldti1,drticle of charge q moving with constant speed v to make one circular revolution in a uniform magnetic 8db.1idh9la,o nds /tfield $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path ofs+y(g l b ;l89y-drunf radius r in a uniform magnetic field B. Syulf;- ld rbys9gn( +8how that its momentum is p = qBr .

A particle of mass m anvqq0 5/ 8r do7nl9 eto2y d f(5p913mlrxjtvxvd charge q moves in a circular path in a magnetic field B/1 (o 5qpd95vo vfxv8rqt ljl9enr7dm yt02 3x. 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 in Problem 21 9+u yo9-bplp8 nov/ xu,wm +ayis $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves wimo13z v*s zj3yth a speed of 160 m/s perpendicular to the Earth’s magneti 1oms3jvzz* y3c field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equatowkzo 3**hu*5uq/nmn or 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 ab72n:fx y +b.kqt*xp speed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 stardnlct k; +7z3 pl5v,*yapgbv)t a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? C) z,vtblp5n 7l3ky+;d*g a pvcompare 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 magnetic field no larger than mvbd7q.;taq 7fs w7p):z fwq/that of the Earth fq :)v7/7m7dwqtb fa q wpsz.;$(0.55\times10^{-4}\mathrm{~Т})$ 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 :aow-,r8ozqo bj zb : l0 yjdk:8lam(4out of the page toward you. Indicate, with appropriate arrowbmb jo :y-a:lql(oja 8oz0dk w:rz8,4s, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight ty8kk.kup 2s -x-c v)uwire carrying an upward 24-A current exerts an attractive force per unit length of xckuu-psyk8- )vt . k2$8.8\times10^{-4}\mathrm{~N/m}$ 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 parallel wires 35au.oi drz4.c:3gs9 qyo)ux6 v m long and 6.0 cm apart, oou.rz .:ac )v49 xi6udsqgy3 each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field i0d:p9:hnz:hhd24g .zja kxvi s being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment iak :vz4h20i:dng.d :zj hxh9ps to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along theu( t)n) tyt2ds tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of ant)d 2ts(y)u tbout $\frac{1}{2}G$?    $ \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 the y6 95kw)cdqofsame direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from 9fywd5) o6qc kthe other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straighd;z/.m kyxpcs3l i ::rt vertical wire carrying a 35-A current downward. In what direction doe:ym3kd /xcl.s i;zr:p s 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 carries 22.0 A of current due north. What is the net mob(++kcht.d6wm a 8 ezagnetic field 20.0 cm due west of the wire if the Earth’c8. ew ht(oabz++k6m ds 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 protonxp m7f.lyw fc qlz831cfa v89;s passes 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 bd ;3lq: 3 tqq+(tbplestraight wires 2.0 cm apart in terms of the current I in one when the otheebqbqt (;l33:q pdl+tr 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 from, an ixerljtl3 * 16ynstrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the *l y1j 3lterx6magnetic 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 showd0upbb +t wyzt5x1gy ilv0dfj5: 2-q6n in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it ipbg+6j :5dditzf10 u ytq02v wx5 -byls 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 pointg ))(bxdrp8 zis 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 pl b764i2h 5syckvu67pyg-vr gn )rqi 3lane 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 n hbg5 civpvy2rnql 76-gu 63riy)s74k et 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 seco8x)5 lum peiz3nd wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Bl z8x5pi)e3um elow).
(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 oriev r(ot6 8i8hgunted so that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the botto8voh i(tg6u8 rm one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight paralltgn.bv8 0xi9ee u 4nmwc6lqigo/b1z d. c+2 -oel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in thm bo c e4n.0ebizg q2+oi9t -n/lvu8gcd.16xwe 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 anotbnzq647 0s.dlh2cj fzher. (Looking along them, they are at three corners of an equilateral triangle.) The current in eac cz4d0znjqh7l f2 b.6sh 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 of thwnoy .d0:3sde0t) fwo e magnetic field at the midpoint of the side of the triangleto swwndd:3).0efoy 0 between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carryc kfsv y(j*l24 equal currents I in the same direction. One wire is at x = 0, the othkv*lf2 cj4 (yser 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 to pxcxemg;tfjf mx. y,5g6,;+-ks :x jotal of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside ne5, m- jey 6xm;c., t+:xkjogps xx;gffar the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to q)n thpkh+g51 produce a field of 0.385 T at its center. How much current should the sole qpk)+tnh 51ghnoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cms 62i4*q(sprg 2p tsya-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (aa2*irqs(6s 4ptg2 s ypnd is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to mv/ dpu zewhawfjx m(,9-+n: m0ake a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, ada x: /+u z0(9wp jw-enm,mfvhnd so on.

A toroid is a solenoid in the shape of aa/(a+yv gxov 58bw; -v yi8akz circle (Fig. Below). Use Ampère’s law along the circular path, shown dasheda(g8o;avy x+akv v5- yz8/wi b 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 field betweejx9y5j5 wdmd4o* i nt6n the conductors of a coaxial 95j 6dm i*oj5 txw4dnycable (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 isr(ob1)kdtf t85c;aqa0p l l(c58 xpew placed with its face parallel xot(5lw0r (; 8pc ce )kqalbtaf851pdto the magnetic 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 deflects full scale fh9,v9k t 4qajjayf+ :sor 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 galvans r t,*g1vpmq.ometer weakens by 25% over the years, what current will give full-scale deflectiosqmtv.1 rpg, *n if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the ogvwxo v odj;ow fd7yc3us8: 92nd4; e+utput torque cha:edw vgn; o74uo3jdy 9ofs x2vw;+8cdnge?

Show that the magnetic dipole moment M of an electron orbiting tql 2gb. s/i+ *)li xusn8*ddfghe proton nucleus of a hydrogen atom is related to the orbital angular moment2bds)/.*ilggui fx8 ns * q+dlum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and conta8//hk z y8ffo5pgdm:xining nine loops lies flat on the ground. The Earth’s magnetic field at this location has magnitude : 8dmxz8k/ofy5p hg /f$5.50\times10^{-5}\mathrm{~Т}$ 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 0ig ufkr0fb8b( :mwo7nfw*3d cm in a 0.566-T magnetic field. What value of electric field could make their paths stm0 d :bbigfku8*f wnwr730fo(raight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal to 21.0, 2j0dh8/k1t wnc wap 8.e1.6, 21.9, 22.2, and 22.8 cm. The largest radwh k8p0./n 1jct8w aedius 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 spectrometer b3:ysfh4ywost /kzo.ev 7tx98 .v n8 tof (Fig. Belbhs.47xe9nozto38f kyv .8 s/t t w:vyow) 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 diffic( sg2hb( pf3flult, however, to separate molecules with nearly equal mass (lphffgb s (32such 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 spectrometl 80-bpdgo fx,sd;z5j xxy8j9er accelerates ions by a voltage V before they enter a magnetic field B. The ionss5-xxg dyo d8zbj 0xp, fl9;j8 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 of wir)er7rg0 1vtu-oxnl1(nfxy wbg k00f3e per meter, and a 25-A current flows through the wire. 3un- t f1b y(f70kvw)0go0xrg l1rxe nIf 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 lah j) ;3w9a:e3c/)pfx igu n3sqawz. +hqc*rcm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permlpr a gwaec)s*f)93i;q:+33z q. xu hh/wancjeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum252rtoc(tt 6 w) slg,fay8sfvu*e al 5 $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon entering:ew)xe5 znb 3b/dmrxovo )x).j rdp l5q3s(r/ a region of constant magnetic field.e)bon mxz :)rdovs5qd )rxlp.b/wxe3 ( 53jr/ What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. , u,jiyyxl80p-k3ogb Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic fi y i,xo-p38 bg0uk,ljyeld has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a oxv)9yl3 n+o dgid) z3net 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 po.fcuu 7h, dnuc6 tq4djz+l-erba12 + ay(o7idints almost horizontally to the no fuhe7- nujq(6u + da2.cbzddy7+ toi,14rcl arth and 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 aty yzh :4x/z5zjmw v6 )3sew8*t0oexb bom, 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 c* uoo;6kze)ncm 8fkv:urrent 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 barm nu*:fo)z6 voc 8ke;k 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 wirequ zb2w65p. wi is 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottopiq56. zw u2wbm 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 distancw x8bsqe h 1n;d6pu00.owv:lqe l apart in a horizontal plane act as rails to support a light metal rod of mass m (perl e 6s;0: un.p vxh8qwob1qdw0pendicular 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 approxiwbm6n ,zkdry /pv2zql+ 25ra;mate maximum deflection of the electron beam near the center of a TV sc rl6avbqz2wk+ 5m,yr;/ dzp2 nreen 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 m0ghm mtdp+ d: fl425cused 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 eachf42h:5pdm d0ml+ t cgm time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of a square of siz,l*g0 oj ( alh,n(dt7hovx +kde l, (n,*kold,x o(vjtzg70 hlh+a carry equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in;5tqlt7c1m ky lh(4fs particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extehy;sqt74(l m l5ft1k cnds 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 wirrgt)d4;ojk1ihhqw j+l ar4a3 bl*8 :he carrying a current I 4l)h4kw r+ihj d:aj8o tbg*;rl q31h a(as in Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic field 7hh m;r8y0pua-aebc7m0u.krc.ya f,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 magn3r3sg:0d pn twnom,o9-c /upeitude 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 the maximum magnetic fie eo9n3sw,3pr-/ mogd0 ut:npcld 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, travel-esm e8;v jiv)ing to the right at a speed of ) ij;8-sveevm$4.8 \times10^{ 6}\;m/s$ 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 ganhp, )k.hqz7qm o07yl s in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the ra khnh q7z.,0)7plo qmydii 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 epp sh8.14d .odu9xk;ttly3 ,n uf8ylproduce a 0.30-T magnetic field at its center. If the max; 49l1 .dupt8h,plkedt3ynxf.s y 8o uimum 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, k +osr;fwcv0 xd5 4fbh)r+ ra1carry the same current but in opposite directions. They are suspended by 0.5 1fb+rsfv05c4x w+o kad h;rr)0-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 fie,:-dl:pih 6nwp fkwu4ld 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$