A compass needle is not always balanced parallel ; agm daql;98pto the Earth’s surface, but one end may dip downwarqam 9pd;g8 ;ald. Explain.

Draw the magnetic field lc6x4op/n2c )rb i oi11u oy(yuines around a straight section of wire carrying a current horizontally to the lecuy/ x 4uo)(r oipiyc1bn16o2ft.

In what direction ar.1ujheu0f .qf 3 i*yade the magnetic field lines surrounding a straight wire carrying a current that is movi1quaf * h.euf03idy.j ng directly away from you?

A horseshoe magnet is held verticalz ak:9,dzcwhe/qg/. x ly with the north pole on the left and south pole on the right. A wire passing between the dz z.qw/h/k a:gxc 9,epoles, 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 o;+mgph)wkz ru9rl-pdh .gn)tmv l407bject, or only those made of iron? (Try it and see.) 74wzlpu-;g)hmv rnr .dg t 9p0)k+lmhWhy is this so?

Two iron bars attractftm k6eo 2-g)roo; yi1wt yn:. each other no matter which ends are placed close together. Are both magneow2ryo6-kt ig1 te;fy n) mo.:ts? Explain.

The magnetic field due to current in wires in yo1 q*0:qszq ,gv )ygjyzur home can affect a compass. Discuss the effect injq:y 0sq zv gy)*,zgq1 terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic fielzl m, rk8q4m /sj51dbod which is perpendicular to the particle’s velocity,5od8msj 4br1/ zlk qm, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged pafzr: fy+l9l* a17jax articles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of thej:a7ar1alzy l9x+*ff 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 inq1 q * ad8,cgd-2romzh Fig. 20–46. What can you sayq8dmz2dg -q 1oc*,r ha about the charge on each particle?

A positively charged particle in a nonuniform magnetic field followsdediiid f y5yp:og+ 8j0)i 44 clxdri/4av -l, the trajectory shown ii,)c 4yir4i dyfldv a gl :i50 /doixep+j-48dn
(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 mv5fa2e/xl bm .agnet? Can a magnet attract an iron rod? What must you consider to answer these quest f/bla5m.xe2vions?

Explain why a strong magnet *ts:pksi fv 5pj6o7x5held near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t rtsp*k6fxsi:7 j 55 pvoisk damage to your TV by trying this.]

Suppose you have thrmx dbmrk/bts 8; 6*x)7bp(emy4cc ge2ee iron rods, two of which are magnetized but the third is not. How would you determxb6 c*rcee 7 8/mys4kbpxmt2(bg);dmine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a ma6;; 4uo*nv0d faf2 et wsutsg*gnetic field? With an electric field? Expla*s* 6;ffgttd;swuo e u240nvain.

A charged particle is moving in a circle unducy0b- ( /. pf;ktt6 5cqmjiober the influence of a uniform magnetic field. If an electric field that points in thq5tbci c0/y.mtb;f( o kp -j6ue same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the id rm(dmx4;:s3 wfg1dqhea 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 md( 4: gwr13q hdfmx;sapplied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontawf lkq y2bh:5:l wire carrying a current from left to right 5q:bf 2hy klw:
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving ewbos v0jp)x; a)ob- .qlectric charge.j bq) wo0xap;-bos. v)

A charged particle moves in a 974a4e fgq kmwstraight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possiblekweq4g 7mf 4a9 situations.

If a moving charged particle is deflected sideways in some 0at8k4at0a giregion of space, can we conclude, for 8t00g4ai t aakcertain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular regiwhfcdfhb7m32 p2+ s0von 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 in a certain ra m u6lvqz/:i9egion of space are being deflected by an elecl9 ai:zqu6vm/tric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic maog,0dt5 . ;mifxprqs -rd2wu5terial?

Two long wires carrying .zy-ro.hefbz1,sr 4 hrms ,g- equal currents I are at right angles to each other, but don’t qhs-gr1sm h.z4fr,bry-z,.eouite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’sdw2uiui6ynbtq32 .v :qzhknf4 h+2w) gravitational field, is suspended directly above a second, parallel6b)uwh w fiudkvnh2n.i 2q3qt: z +2y4, 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 m f n* yzw9g2;v866dutbzxnl3attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetif0eu .)1s8il rz hbo+ezed paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper clip. Explain zis )+0h8oer .1uebfl.

Two ions have the same mass, but one is singly ionized (gcwlw ts*yfyk.2z 7; and the other is doubly ionized. How will their positions on the filzy(y 2s *w.;wcktf7 lgm of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside8zkclije:f3 (5/ e xcd a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . A relay is an ea80ml u.3y xuma6; vzzlectromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the ma60muzam.;8uyvalxz 3 in 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 straoc- xjj 6atq;:0+ y;s4tt 6fhadtfsl0ight wire carrying an 8.40-A current w s+t jf4sa:a lty th6-; 6jt0fx0odq;chen 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 lenee9 r,ty. 1ppqgth of straight wire stretched between two towers carrying a 150-A current. Tre1 t .yp,ep9qhe 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 160-m hg*ns )8oo4er length of straight wire stretched between two towr*8 hen4gs o)oers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long if the maximum force on it is mi))eb 3gya84zd5c)wjp xyh4 0.750 N when placed in a uniform 0.h3 5z )y epd4y))w4bjm8 agcix0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. A:ig drvg9c(ih0w k.zinb:eg / v ;0f-lt that point on the Earth’s surface, the dip angle of the Earth’s fi;(:0 :cvkwdgvi - n /0geblz9hirg. 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 8.75 A is a maximum of 1.28 zj:8+ 7znoekw N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximoke7+ :8zz njwate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measurebfi00q rpn1 xe9lpns11du y ,;d 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, calculating the angle between the wire and the magnefn;pr0dil q1y,sex 11 0bup9ntic field.    $^{\circ}\,$

  The force on a wire is a maximum of y,wy i+.b4g+cdt x 0/kxon pe($ 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 copper wire could just “float” q /rac qqxb(0 q)zx*:zd5br4ahorizontally in air because of the force due to the Earth’s magnetic field xz :bqrxq4 b a/d*q0q(c arz5)$\vec{B}$, 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 charglbzdiyh+ f 13/pb 23.gik.wzv e $q\,=\,+2e$ 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 o2(8w7yamu ylzf 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 fsz kyt6 0(ic alo-61hsjfk)4jorce on a negative charge for each diagram shown in ( -s4y(z0ft hokkji66 a)csj1 lFig. Below), 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 directiogja4w :tc;:cr n of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected verticalbwu c 4ue)r9y//4uld aly upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) protor b rrxl6a:p)w36i1san enters a 0.20-T field, in a plane perpendicular to the field. What is tl: s1 )6ar6xar3iwr pbhe radius of its path?    m

  An electron experiences the greatest4af xp (w5bsp f gp5y+a-nc5/w(7 nqso force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go s9z4 u5e2tpjwq8b *euuqu/w9undeflected when passing through perpendicular electric and magnetic fields of eq p2uu4zq/w958ust 9w ebju*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 -tl9e: li dbv2,wrw8o1bb;w patom 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 r6il5 sgxc6kb6 equired for a particle of charge q moving with constant speed v to make one circular revolutxg56skic6lb6 ion in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge fs6t h+nrd +7q-xrix o)7pi)eq moves in a circular path of radius r in a uniform magnetic field B. Show that its momentum isfrnti )+-pe7+ dx6orq ih)s7x p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetic fid p*p ew9/7rpmeld B. Show tem p*9 p/r7pwdhat 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 particlej qck9yb)f.ejy1) s+9g un o6q in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a sp + ( l 4tyw*o;1bevgio9i;*tiubh) kmteed of 160 m/s perpendicular to the Earth’s magnetic mlit(b;+w 9t )ih4y;i b *e1*gtvuk oofield 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 maft948u ba 1ykn* l*q l7vwey6jgnetic field at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with speqy1b-um5y7dh)e60m .biry w fed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 carriuz+bge qhy. 3c.db0n*es a 65-A current. How strong is the magn30hbzg e q*y..bu nc+detic 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 magnetic field no larger than thg),x( oh iyubjce,3,1d n8imzat of the Eartxm, gu(8)ijzb,ce3 no 1hdiy,h $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carr )) tfrtlq57moies current I out of the page toward you. Indicate, with appropriate arrows, the direcf mtl r)7o5t)qtion of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A curren1hlyqg *k zp,)t exerts an attractive force per unit le1y*)lqz h gp,kngth 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 direcm)tao9gbh; y-fac 9,9ty :il r5hj+crtion of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A inb5lc cm ,yh-rj ai;9gat:)thof9 y 9r+ the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00,e8bk(3 .8 v7cjxg vyfo0cc ws m from an electric cable. What is the maximum allowable current in the ca0 3.v, yb8j(g vswe8co7kfcxcble 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 pogr) afxd,4jpp:wv j7 x2k4ysrg+7v9 eles. What is the magnitude of the magnetic field produced by this wire at the ground? H arpyr+pjx 4 2)7sd:wgj xg7fe,v49vkow 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 apart carry 25-A dya,*r*fhitfr:q .vt4k 19j n currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 54qn* jaff ,r9.1tr* y:kih dvt.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm dud s.)wyno2: / mgxcxp -klvd6)e south from a straight vertical wire carrying a 35-A current downc wddso).vgm6n:) xly p-/2kxward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of z8(gulxnrll, j9nuf8 +ws4 3p current due north. What is the net magnetic field 20.0 c(z,8 34fnslljrulw g89u+pxnm due west of the wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes azhg tj+ 232 71n bd1aazjffp/t 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 fieldo+bmmq yfu*d/fg2(m + midway between two long straight wires 2.0 cm apart in terms of the current (fbgf m om qdmy*+u/2+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 ne:l8 d,xi uo5current to, 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 te:d xn5i8,u olheir plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. nkhdr 1i6m wj*7-*hegBelow), 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 is 2.8 mm from the nearest wire, ce ej1k g-*6whrmhd7i*nnter to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points 2omh2e,v t 5otyb*s /w33$^{\circ}\,$ 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 showpb+ 8o hfp-lkim,.sd3 n in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitpd ,bspi3o lm8+f-hk .ude 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, v2a8(k kx8ovn made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magneticaax82v k( kvno8lly 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 perpendicular to iw(1sq ok)-sceach 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 iok(- 1c qsswi)f the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.0 A curren+tkahen ;35vh t. Wire B’s current is 4.0 A in the same d5+k ;hnv e3htairection.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Lookiuez9gd3d21jc;hl* 6fuyi0 sing 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 oppos hd1su z *g2 ci903flideyuj6;ite 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 directionhsa*e- ym v:p0:fq4 lr of the magnetic field at the midpoint of the side of the triangle between wire M and wire N. :s: qh -ye4a*v0flrmp
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal curr,c8 9j79lvi7vp i.y dp2;ujxzkl ci-d ents I in the same direction. One wirelx- ;.pjji7vp2 i8 7kid clv9,z9dc yu is at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carries )y4wq dpbhugyqz;5 z76qpt20a current of 2.0 A. Calculate the field inside near 4bp2qw d0 ;t)ypqyhg 567uz qzthe center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diamettl6j. u59u sbi./qmn ler is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the w9 u/6 5mj tqbln.sliu.ire?    A

  A 550-turn solenoid is 15 cm long. The current in it isn r3ji)-d5 vjs 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 thvn)5jjd-r3 is e force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that produces thm7 *f 1zhi/h v3lilbur()ovs 4e 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, and sshiib)uv3 (4 rz fvlm*7/ho1l o on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Usr,a e,0w mg 7it7 f;kd sf;2kdiv(/mlue Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magk 2ti;ldm7u/7 g0w , v;rf(f,akesdminetic 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 3zxp+*wg : wm tr5tlnv*re9g: conductors of a coaxial cable (Fig. Below) ispng :t+r5m*grez lw3*v9xw :t $B=\mu_0I/2\pi r$ 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 wireros-llee-wp234ao ei x2(vh2 x2*n lo 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is 2o3lwri-l 4vse-22enx(oeo ph*2lax $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects fulpxhfz )y.mm5 59:g,4vmm vrohl 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 galvanometer weakens by 25% over the yearsraubj :va1 (:5yoc/knp :1bi ey/xm i-, what current will give full-scaimr:aebjpanybxv:c 1/ i o/u:k1y( -5 le deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the ohh8. 1his1cydutput torque change1 c. dhhyh18si?

Show that the magnetic dipole moment M of an electron orbiting the proton nuo l cexzpo3o+11xjd5. cleus of a hydrogen atom is related to the orboxjd3ec 1 +.5pl1zxooital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flat on tg0t1+4qgu9 w0o ry fblhe ground. The Earth’s magnetic field at this locau0 f botgg9+1q4wr y0ltion 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 g 4bljjuo*m/; 0.566-T magnetic field. What value of electric field could make their path/ u lgmo;b4jj*s straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature vrcyzag)05 qhm-t3: ac+ : eusequal to 21.0, 21.6, 21.9, 22.2, and 22.8 cu:mac )c vsa: h5 -etz30rqg+ym. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field bexc2bcupql wjpk-c0f15h/.p , tween the electric plates in the mass spectrometer of (Fig. Below) .c1x/ qwj pp,p bcf0hlc -u52kis $2.48\times10^4\mathrm{~V/m}$ 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 tofjw(a 8tmnz-y)r19(7jre2 lhp,ijb d monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass suctp ,7 yr1dj9j)mjl wf8b-eh (ir(2anzh 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 accelerates ions by a voltage c9kt g kj7o34lV before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an kl 4gj9 7otc3kion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire perc *9bd.yl c0uyvvy*dl/nxf 5j 4:gu,u meter, and a 25-A current flows through the wire. If the permeability of thy*y0guunl4y b,cv l * ju5v9.fdcxd: /e 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, and has 640 turne3o.uncgz m o6x0fa fhu06d 67s of wire. Thegfe36zodof.6ah0xu m7c 0n u6 magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentums*(g 0mls5k;8 jvnpix c ,r6lt $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 enteringckdioe*7nbu * j 27.wb a region of constant magnetic field. What is the rin7bd2e u ow**cbj7k.atio of the radii of their circular paths?   

  The power cable for an electric trolley :.tm qs( ope0f(Fig. Below) carries a horizontal current of 330 A toward(eqp t os:.mf0 the east. The Earth’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 o b0, qht et.3u3qa0kaairplane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic fics3p*oq w+1hxj ( 8ucemjt-*d fc:s f7eld points almost horizontally to the north and has fwc8jusch-c *x:+ 7 *fpqt1 sedj3mo(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 mass isgrz 5rxmkdm6 4,t1gp6 $6.6\times10^{-27}\mathrm{~kg},$ 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 currentjwk* b/89r -jtck : e/on9cdcd 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 flow is needed to accelerate the bar from rest to 28m/s in a distance of brcn89w dk:tj9/ked*c / c-j o1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire (g*r u4bf:)(kzgur vq 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 vugqz:(gru4kf r() b *suspended wire.    A

Two stiff parallel wiref6uh, 1hhf ysw*wd,/lu(o k j7s a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnewu1,fh*f 7okl(y, ju/hsh 6 wdtic 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 maximu cj(xxm b)r.dox50+mjm deflection of the electron beam near the center of a TV screen due rj(0+) ox mxjbmc5 .dxto 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 deviexkko,k; be6.ce used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time tk;o.e6kkx,be hey 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 atlh rbf 9thl2z+qht74x0;x id3 the corners of a square of sidelh x4brf ;xtt3dh20q7 zhi9l+ l, 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 usef0hleom w3+80ugj9vw;z (pwf wsmw 3 n2ul in 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 f 8ww( zp0e9whwmj2wlv0+nm3 s 3og;uextends 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 wire caynr rp t 6yzq.z*7h1:eq,i8barrying a current I (as in Fig. hy1q.zn*b rz: r8 i 76pety,aqBelow) 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 poles7 96ozyswj (ei the magnetic 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 fields pmn3bs4zp h* x)roduced 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 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 fiel) hp4z3xsmn b*d will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a besou5r6g c/ktwt/a .k-am of electrons, traveling to the right at a sprtk.a6s o wt-5 cuk/g/eed 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 spirc l z ztb0i+p,,lgzc04al path through a gas 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 radii arei lbpc0 cg,40 +t,zlzz 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a c5jy1 lc6;t hp0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns mt;p h6 yljc51cust the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.5mf gwrnr/gj7cl6:7d8anh 4 ; hqlb,-y0 mm, carry the same current but in opposite directions. They are susp :f,76 jn 7 hmnl8c/ lwragbyh-;4grqdended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magneti/ 4p+3c s (d4ifzsryzgqzh w.6oh(cc(c 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$