A compass needle is not alw f ugh:7 g.bybg)bc9a8ays balanced parallel to the Earth’s surface, but one end may dy78ghcb.9a u)g gbb:fip downward. Explain.

Draw the magnetic field lines around a straight secy1:c;+jdxrtrv5:aju 2; fome tion of wire carrying a current horizonyrj+or2c 1;txumf:e 5:daj;v tally to the left.

In what direction are the magnetic field lines surrounding a sf6-hag6ltg*c (fl w :straight wire carrying a current that is moving directlyl6 hfg acg6l:wf -t*(s away from you?

A horseshoe magnet is held verticalja gx5htve;fmzi eg6* ;6nz52ly with the north pole on the left and south pole on the right. A wire passing between the poles, equida f;;2gzveh5xzm 6giet5n *j6istant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallicvpkn)(-r 0tx 31vrjbe object, or only those made of iron? (Try it and see.) Whx t 0vbr1evpk(rn) j3-y is this so?

Two iron bars attract each other no matter which enj6il 7ueyh*o *ds are placed close together.eio*y6l 7j hu* Are both magnets? Explain.

The magnetic field due to current in wires iz1) j yfm(yd j:d1x9bhn your home can affect a compass. Discuss the effect in terms of currents,jm1zjhd(b91 y f)xd: y including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field w9xej/z sxdyq2+/4nkord gy4( hich is perpendicular to the particle’s velocity, will the n9xrd/y + gxdzqs4 (ojey24k/ kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vi*;/ ao:;0tyizh: fjl* deddercinity 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 partio:fjh;y*t/le d d*0ei ;drz: acles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a maga-; oav6;dsp +i5tzjjnetic field as shown in Fig. 20–46. What can you say about the charge on each particleojtpz ad6av;5j i+s;-?

A positively charged particle in a nonuniform magnetic field foll37o1s y*s dcx)ef jx :n/sx:hmows the trajectory : :xm7dh3j *x/f1 csy)sson exshown 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 attra/g)n2be c:qmvhmvib9s + .q9 pgxq16hct a magnet? Can a magnet attract an iron rod? What must you consider to answer gqqh :/pg69ns2vv1emqx hm)c9+.bb ithese questions?

Explain why a strong magnet held near a CRT television screenm1 b/hn:n-:dbr1nna z/nd,uo r7 ar+q (Section 17–10) causes the picture 1- nd7 /:ou/r:b m d1 nnnnhazqar,+brto 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 risk damage to your TV by trying this.]

Suppose you have three iron rods,yi5qr*q1edv dz.4x d4 two of which are magnetized but the third is nv5dq4d*1i rz yeq4.dx ot. How would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motioz: +a-ni x4qpbn with a magnetic field? With an electric field:x4 izqabp+ -n? Explain.

A charged particle is moving in a circle undetrr u)x oshu6 ,2w+nd/r the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic ,nwt +srhd/ou6xr u)2 field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic fielii- oohi4e , t;l*1iefd is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump bloo fi1 o*,e4liio-;i ethd in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a currere.4k rhr* a2e4p8if qnt from left r rrai8ehkp44f2e. * qto right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a movim cymni(dt6)h(t 1o+j:) sldx ng electric charge.txm 6:dl+y i1(hto) ds)(mnjc

A charged particle moves in a straight li.u r+s(c9q k,zq.hlnmne through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situzk squ +n m.qc.l9h(r,ations.

If a moving charged particle is deflected sideways in some regik9i5bmedej3lh;yi hl82z; ;h.jy0 gton of space, can we conclude, for93j ;kiiehb.dmlthg80;j ezh25 y y;l certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of s9t:erekjk.5 p- sqxj0pace 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 region of space are b(d. u771 ci bo:5hp3thag onnjeing deflectedojhcn pt17o h7 (b35ud gi.an: by an electric field or by a magnetic field (or by both)?

How can you make a compass wib 4-mc6y)nepy8 u6hdithout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to eachof * +j)m0kg)r dyidj; other, but don’t 0jr+mj ;gd*kofi)) dy quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-c/*.0dsbblmq w arrying wire, free to move in Earth’s gravitational field, is suspended directly above a second, parallel, currentldms.0bq*b /w-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 unm4ui* 9q ltar+jagnetized piece of iron?

An unmagnetized nail will not attract an unmagdkm)sc:t g; y0netized paper clip. However, if one end mc:tsd; )0gk yof the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubln32xhnes v9x7y ionized. How will their positions on the film of 7ns3nv h2xxe 9a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoyguq) vc+zd 1dw7 r2 l(u,lp1qid 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 le(al*g,tq gn+nqi+qzrg9+ 2 v *he/dsimilar 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 pivgq2 ,a*tr+g/le e hvqgindz+(+ l9qn*ot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length o/( qurx ) m9gtxhrmf w4+8/okvn a straight wire carrying an 8.4)m/fh8rg+9 k x /wmuqv o4(rtx0-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of straixxx7 q4b r-8e+ix :xa5: fhgchght wire stretched between two towers carrying a 150-A current. The Earth’s magn h45q ax -rxeichx:x:7x8b+gf etic 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 length of straiz29)z imo c )k:jsw+toght wire stretched between two towers carryizocz+oji) :) 9kwt2sm ng 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 ,agiccj-75dxjc 33,r i cleep*ynwwld81o :6 if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fienl6 wcl,*dc35pe c7j-aw3x ,o ci 8jiy:rde g1ld?    A

  A 1.5-m length of wire carrying 4.5 A of currenzj j:ac) 5n;kmt is oriented horizontally. At thznc k j):am5;jat point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N wha lblb0y0m3i ,en placed between the pole faces of a magnly 30li0mbab,et. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per metior96 s p1c5m vk,. if8by-:cti lookmc (6(cver on a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating thv ,( ci.pb 65ccfvrc km6so9i-:i8o kytl1mo(e angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum o)r7d p- 7:rgg fy qzez 3pel3ke(4coi,f $ 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” horm;6 ke;,a*toavp)rve izontally in air because of the force due to the Earth’s magnetic ;a;*kvt,prv 6ao)eme 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 chargq sx zo*e5i30u7dj8 ax.m(afle $q\,=\,+2e$ 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 dirv 1xjb7o68r9rc-z6h 2yw jckwection 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 each diagram e w3;-i8himrr shown in (Fig. Below), wherer8rmeh3-;w ii $\vec{v}$ (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 obpf*cc a9h 774pv ted0;rmt5 yf $\vec{B}$ 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 upwarl6l12p hh, cnrd 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) promp+n r3ml* k6 zxq+2pqton enters a 0.20-T field, in a plane perpendicular to the fieldq6*r 2 l+xpp+zmnmkq3. What is the radius of its path?    m

  An electron experiences the greatese; /ejyy9zy 02nukkmf 3wd(,ft 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 o hqcn4(pg5dm 4j,b4 pek4y5b uf electrons that go undeflected when passing through perpue pp45 dq(g4m,ky c4hbnb4j5endicular electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom jbs,q8r()i 6f. vppdv 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 required for a particle of charge q moving wk7y* b*1.1m pluiwzu h.7nl wwith constant speed v to make one circula*.lbk*7mwup1yl . h 7ww uiz1nr revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular pathu4)) rdbcpo 0czcwt 0: of radius r in a uniform magnetic field B. Show that its momentum is p = qBrtpc cuc w00r)4 z:)bod .

A particle of mass m andvkvp4j6eh0; r charge q moves in a circular path in a magnetic field B. Show that its kinetic enr v;64pvjekh0 ergy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of tv/+bxrx)yy* qf8az7the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpubi2 slmx4v0tg5s6g +endicular to the Earth’s magne xtb5 +lu24sg0s6vmg itic 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 payf r*,8w4rivf-+eqhas 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 b0xna- dc1t.ispeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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:h2 ia.ym:twr a stalled vehicle carries a 65-A current. How strong is the mim2y :a wt:hr.agnetic 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 larg+)ke *9vb,l se gqxl.mer than that of*l x.ek g,b9eq+lsvm) 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 lon:u6*ud n:ebgj g straight wire carries current I out of the page toward you. Indinej bdu:: 6u*gcate, with appropriate arrows, the direction 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 current exerts an attq4m( k/ikv 3m3j*c:.u chq4euu y7klh ractive force per unit length o*hjquhvm4uqk y ik.me c/(: lu43 k7c3f $8.8\times10^{-4}\mathrm{~N/m}$ 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 directios1 df;gaybl6wa 7c 72tt (wn:nn of the force between two parallel wires 35 m 7f a asl6cwntn2;yd(gt1w:b 7 long and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being gx.9d 9,hozj7 vk0*k/kj5lfm ucux;lcarried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the exjx;hmg7u jl lx9fk*.5kz kd/ 0c,u9ovperiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 33gli3vpq l- dA along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced l3-vqi lp33gd by this 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 apart carry 25-A currents in the mqsybpwk.x2h/vi3,: same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below). vm:ypbx/qk,2iw 3 h s.
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wiufd2cqu9zo/lk3/m eb4u4 s 6 izv t)u2re carrying a 35-A current downward. In what direction d/)6ltu9zm/3 uebquk4svouidz4 2c f2 oes 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 carribo(;,ky-* -kgsej iv:6twy bfes 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s fvw : o-it,f6k* s-jby ;yb(kgeield 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 paudbvm g;v)u22qdjr fa8m*l51 sses 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 w5t.sxz *u4e mstraight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currents t* usz5xmw.4 eare
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current 6,cyrnf siq59jm ;5y nto, and from, an instrument. If the insulated wires are of nens rqy 56fj;n 9,5icmygligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed .v4-sp nw8woe (5sb gqin the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to ce 48.e-svo p(nqwgs 5bwnter.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points 2wuz76eeefte .,ci,-zh1 /zq(z6e qk x3$^{\circ}\,$ 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 wi 68pjai y*6lgyre lies in the same plane as a straight wire, as shown in (Fig. Below). There is a cur6 lap ig*y6yj8rent of 2.5 A in both wires. Determine 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 squ cty6y8ie ,nu8:d+t econd wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magneti8t yuu6dcyni:e t+8,qcally 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 pvou/bqfdh ; i9:3y3v aerpendicular 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 cu :oqaivv93b 3yh;/udfrrent 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 cur it7b 9ts/fa*srent. Wire B’s current is 4.0 A ini *tt/sb fs9a7 the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are picp1ja.fz u )61, mci3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on eachiazpi6,cup.f)cj 1m 1 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 the magnetic field at i0s zn.03c wwzp7y ku w8g-5stthe midpoint of the side gp7yw s z50t-n3swkc8w0iz u.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 in bhn.se.s3pw a9z) 9)lypv7kvthe same direction. One wire ishv7bzp y3p9l. 9sk s)e.vwan) 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.op:fep0e- 2.pet d dp a current of 2.0 A. Calculate the field inside near the cep ete2 . -p0eoppdd:f.nter.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to prbl vcik n;2-ijs+ if)(oduce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of(n;iv + sc2-lfj)iikb the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long sakh2f n5 j/ay*yy7v* qvp,rv ;traight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is cojfkrq 27v y *,5;pv /yvy*hanannected 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 hfm* nzq te54bya7xc4z m di2y.5qf)7make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thi5 b5hq77q4cnzefdi)mz2 x4.amy yft*n, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Uk ,or) y/vaj3sse Ampère’s law along the ciro3),/srkvj a ycular path, shown dashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the conductors oq)egecezy (g,a (*p 2af a cp c gee,e(a(y*zaq2g)oaxial 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 with it,40 4gw)ruf;j gy q o3nucsp9es face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 Acre44syjf u 0po3) wugg;nq9, 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 sca poyc*hv :7;fy ;yjgn7le 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 w+ez0 qpdp0(ki eakens by 25% over the years, what current will give full-scale deflection if itpq(p0d 0k+zi e originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the od2l 6x633kkuzu ooih* utput torque change?3z3xk lh*ku62 oi o6du

Show that the magnetic h2 +4zjem +txjr:dmk: dipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momen2m z4:rhxe ++djm tj:ktum 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 the x*1r+l+aqcx,-a,p m2m kf0vl: kqkml ground. The Earth’s kq l:v1+r+makaxxl m2 q cl0* ,mp,kf-magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circxppibqjx4 n,1a 1m4t/ le of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight?,4na1 j/ t b14pipmxxq In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, jwmv nle21fn wc7d,h 0m/)kjh5ldcy3.e2x 7a germanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 7hwm17 27)v5nec3 e yflc .2,ldkwh0/jnmjdax 6 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectromej)wm 8 cdx-js /1xje5eter of (Fig. cex w -j5/81ej)xsjmd 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 fh gxh.c q632xbeing used to monitor air pollutants. It is difficult, however, to scxh f3 2.g6qxheparate molecules with nearly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by ;rf,f njk-)le a voltage V before they enter a magnetic field B. The ions are assumed to start fromejlfr ;k,f n)- rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire pe,p9ia 8z/o5a 7 .5 tvqj(0i uzzrbqvlfr meter, and a 25-A current flows through the ,.lq5rz t7 pi z8aj(qzau /bvv io50f9wire. If 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 cm long and 1.8 cm in diameter, and has 640 turns okc2;xdj3: d :ffy.fnh f wire. The magnetic field inside the sold.:2cdh:;yf nfx3j fkenoid 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 momentum x.mc84ci(vkx7 ( swyq$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 a rv3f d:9dgq+* v4jztoo egion of constant magnetic field. What is the ratgz : 4*39qdf+d tvjovoio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carr t4p,xf/g9v b x-z/y7mx(begcies a horizontal current of 330 A xeyb/xf(,- pmcbt/ xg4v7z9 gtoward 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 airplane which has acs h 6i8py3gl/qsdw+m pd 2bx:7y 9v:aoquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almost horizontally t9ntxwb d 4*3ejo the north and has mje wx*43dnbt9agnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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,s oujvc7:paodq t :;) *0x30njd(vvcf 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 cur4xctr c (7b-vify f*/(ny lm,wrent 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 1.0 m? Icx*f(,7iwmt(/ cy-yfvl n4 brn what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire yp;(1m,fyeh2r .qmw pis 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The c w mpfe,y.q2ymhr;1p(urrent 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 distance l apart in a horizontal plane act as rai(o;. oaspt :;ecp pt*vls to support a light metal r;tpe.;pc a( svpt:oo*od of mass m (perpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflec: dlnx9clqprtb;xwc1d ). i5/tion of the electron beam near the center of a TV screen due to the Earth’scwxpq:n/db tx r )1dl5.cli9; $5.0\times10^{-5}\mathrm{~T}$ 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. gut/ljc25d e9Below) is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some /ul 9d5cgtj2e initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac 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 straigf:26a k+me6x2-zy6+l pwmr 3zhhi wuoht parallel wires, located at the corners of a square of side l, carry equal curren wzupx6+ar he :+ 23yo6z2mwi 6lh-fmkts $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators f zb-(86-g 0o frwbsjcbz(7cha4igdo) or “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 extends over a region 5.0 cm wide and8hc b0wfd- 7 zz4s-b(gc(ogi rjo6ab) 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 carryinnv0nkoa- , f)* cdim.jg a current I (as in Fig. Below) is av,fjk*idm)-cn . 0on
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic field is ab0trbozru:+ag 6 z 9scli9;c )tout 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 magnitudeasj6: 4lc z8ij 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 are:az4l68cj sji a. 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 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 electron zq*fh54up v)jqr6 d3cs, traveling to the qvrfu6zh4 pj) q3c5d*right at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0.0 0r(i2 49t;gfrfi(bu+:4wk4 g s4syv jomwhob10 T, perpendicular to the plane o4u;rjt+o4 0bg4s(9 si kfw my24hgior(v fbw:f the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diame*)8jyh 5e pofw)1f egeter, is to produce a 0.30-T magnetic field e)hoefe) 5p81 gyfw *jat its center. If the maximum 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 mmf*g, kpn*b,( t yyra(w, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below).f ngty*pk(wra ,,y *b( 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 uni/l qy4 zvkyg71form 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$