A compass needle is not aljo/,l4bkz/tuy,qa4 ;v* tzrz ways balanced parallel to the Earth’s surface, but one end may dip downward. Explain,4azr */ubztzy q;ko/ltv,j 4.

Draw the magnetic field lines around a straight secsxd0b2 to .ktdm:-fg;tion of wire carrying a current horizonfm.tt-o bg xsdk2 d0;:tally to the left.

In what direction are the magnetic field lines surrounding a st) zkp ux/.o6imraight wire carrying a current that is movin. 6/ouikmzxp)g directly away from you?

A horseshoe magnet is held vertically with the north pole on the lef*5n uft6 )baixt and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you6fb)*it5un xa . In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those made of iron? (Try iti o,a:y7u08 p hq3 9f6yr rlxquy;dg8i and see.)7goyp;93i:lq6ur80,a d rux8 y hyif q Why is this so?

Two iron bars attract each jm** lja 7vft t/9yea63e c7mfother no matter which ends are placed close together. Are both magnets? Explain.9j 6ala f c m7t/*3yv*jftmee7

The magnetic field due to curr di+3vi.m jc .y5p4qgbent in wires in your home can affect a compass. Discuss the effect in terms of currents, inc g dyv3i 5jm+4q..bpciluding if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field which dch7,*vp;5a v3u zmx7xidy0j is perpendicular to the particle’s velocity, will the kinetic energypa yjd0vdim 5, uvx7 x7zh;*c3 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 vici9ua6 *d9;jvmdfhfzw 0ms8:iynity of a current-carrying wire. For each charged particle, the arrow; 0dyvi *fa9h:w 9sj8z f6mdmu indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 2n,hk6 0ki oma40–46. What can you say about the charge on each particleki,4onha0k6 m?

A positively charged particlq/xk/ m.:1e) krq jclke in a nonuniform magnetic field follows the trajectory . qkk xekq//m1 cjl):rshown 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 rod? What must yh) gjge 0d 1phhbm(2q1ou consider to answer thegqb2phj1hm( )0g deh1se questions?

Explain why a strong magnet held nyc 7 ++(u+b7ogox iqctear a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your Tq+tg c(+b7 oo i+7uyxcV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetizef bdrq v/ajl3(7 g2fp2o+:cv vd but the third is not. How wou/b3q7 jfdc a+o(r 2lp: v2vfgvld you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an electj(xrp s:l000lb tt2 ju 6eqsr3ricl003jb2 t(r6l0s j:xeqsru tp field? Explain.

A charged particle is moving in a circle under the influence of a uniform jav( w) ,hl hdh/h1+kvmagnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will takejhh a kvvl/d(1hw+,) h.

The force on a particle in a magnetic field is the idjfer oj+q(v8 / qid(b8 8a8bpeea 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 areo/i(bfrp88e bevadq+j8( jq8 caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a current u y1/ 6x5kuaqdss/yg4from left to right //ygx5 1 su yaqsd6uk4
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving gkr4 g5n43ls9jvx n1 velectric charge.gsln4vvg k5j 3r9x 41n

A charged particle moves in a straight line through a particular region of space (o6shlc60 zwgt,n fj,r gn5yupp90 i7. Could there be a nonzero magnetic field in this region? If so, 7jo( gp sgyi6wh0 n69uz, ,tnrl0p5f cgive two possible situations.

If a moving charged particle is deflected sideways in some rebbepq ( ,+bsrk*: 0idogion of space, can we concbs,0eb qr*+id(ob:k plude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space ub qmf .xz0sm 4y56p)4sb,jpy6rg4aithere 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 mo:7ds:s9; mw01: lfsrjbhb;-nsr ko j kving electrons in a certain region of space are being deflected by an electric field or1-r:bms7r;n; :s h:lbskw0jdsk9f o j by a magnetic field (or by both)?

How can you make a cz m2,cb1n 3fueompass without using iron or other ferromagnetic material?

Two long wires carryig.)1swhk/yo b ng equal currents I are at right angles to each other, but don’t quite touch. Describ.1/hb sywgk)o e the magnetic force one exerts on the other.

A horizontal current-n fqrtyjt0- s . 0/gaem79nhr:carrying wire, free to move in Earth’s gravitational field, is suspended directly above a second, n /mhqrn0:rf tat .j-ge7s90y parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized pmdhqy d2:yv80a;bg r566 kmkviece of iron?

An unmagnetized nail will not attract an wy;v joxr63;z unmagnetized paper clip. However, if one end of the nail is in contact with a magnetzv r;x 6wo3yj;, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is d ja ,bxc.spkmlsc5). ;oubly ionized. How will their positionskb l, s)xmccjaps.5;. on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B insidep/ i2 9n1deyqe*:ay dikd9j. w 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 swi0e8v8 ( ch5jn5f:nk pc2sr- hilk jm.itch similar to a solenoid 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 rrp:-eh5.mk( jfk j85h0n2 8 lcv iscnielay 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 magnit7tv5t /q lyf6kude of the force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform m tf v57kq/l6tyagnetic 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 le ivz v8g cpm8x2o.k/ 7nwb75flngth of straight wire stretched between two towers carrying a 150-8.iz7 k/g flvmv 2n8b7 p5ocwxA current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160h(/-q j*erslhu02 vr y-m length of straight wire stretched between two towers carrying a rrvl h/* yqs-e0 u(hj2150-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 flowom8(zt ta(5ff5uqw0 ring in a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T ftmf((8tz5f5u a or qw0ield?    A

  A 1.5-m length of wire carrying 4.5 A nrmyw ;rt4.be5 rr)d+of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic rmwr e trb.d; rn+)45yfield makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when placed betx*u6j6 kzjdp nyj)3 u.ween the pole faces of a magnety)z ju 6jk6xnp3 jd.u*. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be onshew- lz6 4x*sly 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 actusl4 e6 -ws*zxhally is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum of t 8t*li(opkn1e)0 ykv/o d ,s0tilns3$ 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-uc;yoa+h(z ;( emcm0 qmm-diameter copper wire could just “float” horizontally in air because of the force dumo;h m;eaccy+u( (z0 qe 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 charge ;opzk7boe :o7 $q\,=\,+2e$ 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 9 8 ,poum g(g2pp-4i.gdp qeafa,e4xo 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 )z; 6d se pw55hup; f61fznlmaon a negative charge for each diagram shown in (Fig. Belownlems)p65zd 6;w1h5f;fzuap ), 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 o: hihs9rr gg/vq+, ne72:ykmu f $\vec{B}$ 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 upwardwu4dalr 1 .sh. with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, k3h 5zgfob p1*,:qxkb in a plane perpendicular to the field. ,:kpfx5go h z*b1q kb3What is the radius of its path?    m

  An electron experiences the greatest force as it travelsneg2jf 2dg( d70tjh swqt* z jdkr,.-0:1kcnt $2.9 \times10^{6 }\;m/s$ 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 electr d5*jym;-kpp xons that go undeflected when passing through perpendicular electric and magnetic fields ox *k-;pmdjy p5f 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 heliumkjmdb;9 3 o41wit kl.i atom whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T reoej3uq0bznd; ,7j 0 yzquired for a particle of charge q moving with constant speed v to make one circular revolution in a uniform jjdnyz0oe,7zb3;0q u magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves itbo1 i,j v2e o0z wxf6+a8)*)j iphnben a circular path of radius r in a uniform magnetic field B. Show that its momentum i*) ,e 8 hz)ifvbpbx0t1 ja2einow6jo+s p = qBr .

A particle of mass m and chargeub sm;0w-eke9yvo/ iuja:f 6 ) q moves in a circular path in a magnetic field B. Sh:b-f/v ueui ea6y; jw9s)o0kmow 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 ,fwzk5ob j-nr1w cx(,is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s p ud zf*m; g9qkaqrgk0mk3 f (gao8)60xerpendicular to the Earth’s magneti3 k zuqq xak)g*;dm96(ao0f08r fk ggmc 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 equator has magn,/(uig ddl zu kcb 89sms1.kkb dp/w/.itude $0.40\times10^{-4}\mathrm{~Т}$ 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 spe0 o67dtzfk;bee*iec8 ed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 u gzxbsy4.7w06pqn l(carries a 65-A current. How strong is the magnetic field 6.0 cm away from it 7wu4sz nqbg.(6pxy0l? 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 all2*kvaeu6lu 4 zs8x y xu4sh(kx7d*u4q owed to produce a magnetic field no larger than that of 2*kuudxk4sx(4*yl4asqx uz7v6 8e uh the 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 carriesrpr1h v/usw ;2 current I out of the page toward you. Indicate, with appropriate arrows, the direction ou ;vh p2r1rws/f $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A cczp ;kvk,(itz)cd1l9 dzs4 7aurrent exerts an attractive force per unkd;4az ,1kcvpl)9szc i( dz7tit length 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 uixn1a.irs k:j 6( h3z1il6yk the force between two parallel wires 35 m long and 6.0 cm a3y k 6x.h: usa6z1krilii1(n jpart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic fie z/sq o0gx2r6or :hm-gld is being carried out 1.00 m from an electri qzomg-:0g r 2h6rsox/c cable. What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high pol+.3qrs((oiqj 1 aiawoes. What is the magnitude of the magnetic field produced by this io+(.3rqoiq( a1js aw wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apartrlssc d9i vg cv(1-z00 carry 25-A currents in the same direction. De iv0d( srczvcgl01- s9termine the magnetic 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 frm t)cu,y;wqv8 om a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this locatioqyv)m; c,ut8 wn? 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 c2dt(5-4rxy9sk o0,-vyve fun-n aaxhurrent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points -t ureny5s, hx042 ya 9vvdn-xok fa-(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 po6byfng)8 8ap/h9b kmkint 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 hte g8mh q8 t.no03zl.straight wires 2.0 cm apart intne o3.hg.hqz m l08t8 terms of the current I in one when the other 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 toq:3 ow17*afnd 2 rmzoi, and from, an instrument. If the 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*3r onaf7owiq:1mz 2d 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 .x8fcv0 hlj:bkd3w5gx ) iu,ba.a gpsqv3i., 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 exert on each of the5iwc j0sv .g.lgpx8:afq h ,3,)uxivba .kd3b 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 poi w-1xlkuysul0 t.u6q (nts 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 samel6q8yh )be ppv ;jrdwy(u j,;sh)9w )c plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Deterd9e w)u6b jhr)p yqy);wc,l hj;(p8vsmine 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 ok697dq v*x1ti.u 9ooljzg m k7f 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 1uizk.67xkv 1*oglo mt j7 9dq95 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicular to each -7el)gll, w svlqf2 - g/3fnw3srz/iqother. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnet/wi w)v-l2- nffsl3/ q3g ls,qrg7ezlic 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 ikh h j5i8lj+d5lfoak;+7m 7y2.0 A current. Wire B’s current is 4.0 A in the same direction.+hkoly+la8 fih7mk ;7dji 5j5
(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 f grro7-0utkxm )w,i +orom one another. (Looking along them, they are at three corners of an equilateral triangle.) The curr) rr o,iu0 +wk-gm7xotent 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), determineaw0 p+j qwgn99 the magnitude and direction of the magnetic field at the midpoint of the+w w90j9pnqga side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I inb *8f)-2xg 7fkav3hxjpk+i db the same direction. One wire is at x = 0, the othe7-va)gbf i * h38+fb kpx2dkjxr 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 turn8 3da (i0-i)7 nq ogni0znvq9ref ;ngls of wire and carries a current of 2.0 A. Calculate o3ef an0)(ng0 7ili; -qz9qnd8 rngiv the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoidg(r t- -0 il/ hbrlv9r,)gqm(nadm 4td 1.25 cm in diameter is to produce a field of 0.385 T at its center. How much current should tg0qr-v() 4t,(rli/hg d ltmad9 br-nm he solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid ir;o.2swch l; cs 15 cm long. The current in it 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 wios.whcr ;l; c2re assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoinz0*duxsap -1d that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, orasd-1xzn*0 up something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a soleno eq 1vmdt +3jscbgydk+r:9-;yts2z( u id in the shape of a circle (Fig. Below). Use Ampère’s law along the circular path, qb 9kdsv(- t+j 1dzcyst32u +g:; mreyshown 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 field between the conductors of lq o3abw s)vrs2o,ej u76i;j8 a coaxs j7)32iajb;oqs l6eowuv 8r, ial 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 22.0 cm on a side is placed.( bjaeyw *dj3 with its face parallel to the magnetic field between the pole pay j.d bjw3e(*ieces 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 deflectsjm ,m(adwg 2ka0 iu7-w 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 galvanometeh(jts w,-y ;wer weakens by 25% over the years, what current will g,;(ewhw- tsjyive full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops bwmm(2u6 n 2zdmc s91ely 12%, by what factor does the output torque change?d9 c2zmms 26emu (l1wn

Show that the magnetic dipole moment M of an electron orbd8a-8 xiic * e2br(zjrs5(-rwb. ffohiting the proton nucleus of a hydrogen atom is related to the orbital angul2d ez- fb*(xs ib.arwjr5or8- fc(ih8ar momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flae: fdla;ys* 2ct on the ground. The Earth’s magnetic field at this location has magnitude 2fldsa*c; e: y$5.50\times10^{-5}\mathrm{~Т}$ 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( sr4koy3bji 7 field. What value of electric field could make their pathos3(4ykibr j7s straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms nigri ,+ )8ipc6- bfxhhave radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. Thb,gi ni8)f+ 6crxip h-e largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the ele q lxg tsq34p4 bl*51ax-uv,cactric plates in the mass spectrometer ofl a1x g43 a-b4tqxulvs*p,c 5q (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 used to monitor air pollutants. It ism bfv8q tm8,a6 ba.t3h difficult, however, to separate molecules with nearly equal mass such as CO (28.0106 u) andh m88, tb.6vq3ta bmfa $N_2(28.0134u)$. 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 spect2m; fpxg52)f dbb ohk6k(e hk5rometer accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start fr (k2ebhod2kp h;5b f 56)xgfkmom 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 ha:qqo0tbz)7vnj pcm2i1k k+z9s 430 loops of wire per meter, and a 25-A current flows through the wire. If the permeabilit kjbp+ qz7:9qit0)m1v kn2czoy 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 cm in diameter, h4f2: y3+alzsy khamcbr44w) and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the l:kr y bahh44sf4mc)2a wyz+3wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentuydb ls/z.) 5 n59tvxtf6kd ;rem $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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(:expjqk(r: w entering a region of constant magnetic :xe:j(p(q kwr field. What is the ratio of the radii of their circular paths?   

  The power cable for ann)o s: 3xji 8h95i,sm2pyfqer electric trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a strength i)8irhsp:q ,m x93ej5 s n2oyf$5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a net charge ooe mpuk43 +kz of caxr/;f84+qf $1550\mu C$ 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 Ear6rh oo (zk/ct7r1)zqx th’s magnetic field points almost horizontally to the north and tr(o )xzrkh1c 7/6qzo has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mamg -pf -8+ttu3o b6oylt(wqi9ss 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). Av* zd+tqgkwa.p8g 0: iksk(7 r large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frica+vrk d. tg 7g*zk8:iskp(q 0wtionless 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 5egd24n (w 4fbdmf8r pfz6rh6 wire 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 inpg864(4heb w 6mr2ff zr5dfn d each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apa6 d/e zqivd+ntk-25q brt in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rat bvkd6ed+-q 2 n/ziq5il), (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 o9v r9k-2of o82mze ya77lvl mmf the electron beam near the center9 or7moem alf- 2 289ymvzvl7k of 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 accelerate elementarydqs;jsm3ikpw * )zb/.fq3 0y 4k6ethi6xied7 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 hol0s.isw j/ 6zm7kxife* 3kpbi d34td ;)qhy6qelow 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 wires9cr hx0+qyrt4n6 ox-;*uq opj, located at the corners of a square of side l, carry equa;9u + o xyno-6jtchr4p*x qrq0l 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 particqcl+*22otw yj le 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 magn2oclt+2wy jq *etic 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 Bi+h xu(7u*xt: ox o1lb at the center of a circular coil of wire carrying a current I (as in x:o (xo*7bih uul1+ xtFig. 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 magnetiz9ppgyj5lx+o a1w*de)dqs; cr (w9 v;c 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 of magnetic c ltjg 6jm9wm9r t4(/gfields 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. Estima94j6g t9/l(r twmgc jmte the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic fiel0swk :4jsguae 8g:k f:fb2-g hd would make a beam of electrons, traveling to the rig4::kgffjb0k sesgu2wh8g- a: ht 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 6 jt/tqwmp,9karo( y *T, perpendicular to the plane of the spiral, as shown in (Fig. Btam/w( tq, 96 ko*jrpyelow). 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 solenoidz9zw.k4j 32 wc rbp6yd, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns musp9wy3z kr2j.c4dz6 wbt the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the samo ex4v hbn02t7v f*+kq3 itae6e current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. f 0v+e2tna73te *bqvok 4ix6hBelow). 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 7zho on4b s2z5uniform magnetic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$