A compass needle is not a ,epf h ci-bah/a7va1/lways balanced parallel to the Earth’s surface, but one end may dip downward. fh ap/b7va ,i/-ach e1Explain.

Draw the magnetic field a+h.rpm gfx0(qt;- q ,am jm(++xuokj lines around a straight section of wire carrying a currenjmmj0rpqthg( m;q.+,-ua ax(+o kf+ x t horizontally to the left.

In what direction are the mamnm00 yw;t 5fugnetic field lines surrounding a straight wire carrying a current that is moving t0u 05myfn;wmdirectly away from you?

A horseshoe magnet is held vertically with the north pole on the left rt.i yo1y r1sy:0 5)scbf87inkck 7ofand south pole on the right. A wire passing between tff.)ik k1yscon t5rybr1 sic80 o:y77he poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those madevhkrkx 8nv7 h2)s;. mr 2h*ifs of iron? (Try it and seexvhf s h)m.*k82i7rvh;r nsk2.) Why is this so?

Two iron bars attract each other no matt po8 cx)rxm1y/er which ends are placed close together. Are both magnetsx)opmc/r y1x8 ? Explain.

The magnetic field dua1afvyo9o.+rcqg+ 8(sod7u3kg z ,s qe to current in wires in your home can affect a compass. Discuss the effect ,o7ga9q1gc3yas df +zus ( .vqk oo+8rin terms of currents, including if they are ac or dc.

If a negatively charged particle e*ft d2gs xgll 3z7+mz.nters a region of uniform magnetic field which txs+*g3 dzz7l2 gm.flis perpendicular to the particle’s velocity, 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 particles movezf in; 4fu0)pd+et(pn in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, (f+dip nz fnp)0;uet4 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 shownhrq1y9nj)wzuht+ z. ) in Fig. 20–46. What .y) z9jh uz )1wt+nqhrcan you say about the charge on each particle?

A positively charged particle in z/:ngzv :fq)e, vmmng; z-(spa nonuniform magnetic field follows the trajectory shown inq(pz/ev z-: ,gmnfsv )gmz;n:
(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 attrajwk mv-u0q -e1ct a magnet? Can a magnet attract an iron rod? What must you consider to answer thmqe 0j-uvkw1- ese questions?

Explain why a strong magnet held near a CRT television screemrdl (q6pn2 8an (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 rn6l8q ( 2pmadtrying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of whic+zan-y wi2 xlv748 jiph are magnetized but the third is not. How would you determin2jxvi pa nw-y4 izl87+e which two are the magnets without using any additional objects?

Can you set a resting electron into motion llh fo, t:*g- q c1-cdge.wkz8with a magnetic field? With an electric field? Exze ow1l*ch:f.qc,g8t -lk dg- plain.

A charged particle is moving in a circle under the influence of a uniform ma0aosx5)v. pqg8 9drp fgnetic field. If an electric field that points in the same direction as the magnetic field is turned on, descrig o8) fx. 90ap5vqdrpsbe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind e;dbndoe-0t6+.khe a ( 8fusvtlectromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump bloo0vs8e .- at ktd uh6bedo(f;n+d 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 towapq4o7yw .uel1j vn:x2 rd a horizontal wire carrying a current from left to vow1n. ejy7 4puq x:l2right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that sur2 z;eagowicq)u15b9f round a moving electric charge.9c;z2oai f)5 ug1we bq

A charged particle moves in axi:0ad4u bou9 straight line through a particular region of space. Could there be a nonzero magnetic field in t0o :b uxd9aui4his region? If so, give two possible situations.

If a moving charged particle is dear:m7.ti enz5 flected sideways in some region of space, can we conclude, for ne 5r.zi7:mta certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is l2d aic(l,7r drqbh9u29eb 3v 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 . 9rau5iody;q6+ajnb space are being defle auy6o rd.;ia bn5q9j+cted by an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferum-3lxxd2 gfs;d8xv n o9acur) *k9,gromagnetic material?

Two long wires carrying equal curr5ddozwkk;djs9x+a 5q; .eo) bents I are at right angles to each other, but don’t quite touch. Describe the magnetic bd5zj ed.9w dax;5;q+kosko )force one exerts on the other.

A horizontal current-carrying wire, free to move i0wef; jg38gwuziwv3+n Earth’s gravitational field, is suspended di ww ;3gz3j evu08g+wfirectly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either poleohbf k +k )u1r/z (t*pt)gkzt/ of a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not a 6ktxq xhm) jplpxu3ij7l55);ttract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end wjjxih7 ltqux3p;)m5lpx 5 )6kill attract a paper clip. Explain.

Two ions have the same mass, but c 5 chkwx7ns1wg -a71fone is singly ionized and the other is doubly ionized. How will their positions onw 7asc7x c1gk1whf- n5 the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B insidenrz-ta(sryzb7n 4ldy,-h0 e/by(l3d 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 9 sp8a4vt,fas x ::p,zb yhc ;e4k.dv, tcuo2ka relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needev,spv sub,cfh:4e4:aa ; o zxdyc8tp2.9k kt,d for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitudxq0jlw4-9 h8siwp,k;: gqzc;3,jx 9 jgzji twe of the force per meter of length on a straight wire carrying an 8. g xlcisxw ijw h;0,z8j49-:jg,p ztqkj3;9wq 40-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of straight w7 kn a 9pkza):8tv,cydire stretched between two towerszd)7v,p9 ayktc8:ak n carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of sq1 jr 4+y;8h*vy5 pulem(wzi ftraight wire stretched between two towers carrying a 150-A curryhiumywp8* rz l+q;f5e4 1v(jent. 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 at4 mql(znrry)wc,v7 ,qiija:2 2 z2 ub wire 4.80 m long if the maximum force on it is 0.t,w a,u y zr 2zq2rj()4cqib2m:vnl i7750 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizony*vj0 qi m++dptally. At that point on the Earth’s surface, the dip angle of the*++yj q pimvd0 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 jq)qgf aql(: *a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, wqqfl*gq)(:a jhat is the approximate strength of the magnetic field?    T

  The magnetic force per meterex4p8zy;h4 tr on a wire is measured to be only 35% of its maximum possible vaxph8;r4ey tz4lue. 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 magnetic field.    $^{\circ}\,$

  The force on a wire is a ma(db-r 4b7i ymwknbxfws *0 i7:ximum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wiruc,kx nb02 +yeiymv (,e could just “float” horizontally in air because of the force due to the Earth’ ,e0 yvy ,mku2ixbnc(+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 chcd jm3thf54 meyvo* ue8c6)q. arge $q\,=\,+2e$ 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 forc50b)dzclr y3ye 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 charw68tcvz+ 3rt1 j46aogsax 46-aywkfp ge for each diagram shown in (Fig. Below), wheret3zc6yj +s6 afwrag 8 4-kvwp4ax16ot $\vec{v}$ (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 nhjnq elmj/jq3,(291*tz zzqof $\vec{B}$ 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 ;r o*hz)j8 rvlvertically 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) proton enters a 0.20-T field, *- i3hv+c/yll/frtqk in a plane perpendicular to the fietfl/ il3y*rkcv -+q h/ld. What is the radius of its path?    m

  An electron experiences the greatest forfsf833)kw )tpnh0yng7 e6g cl*4v oaxce 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 goi437yz q6oel(bruf8;:p xa o.d jyrh5 undeflected when passing through perpendicular electric and magnetic f3ijy;(54qb:6 f8zdre. poyl7ur o axhields 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 helsn(,kwp (b sy9ium 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 requiredn vkv..f ,v9diq)j (gx for a particle of charge q moving with constant speed 9vg.(i. dkfjxv)n,q v v to make one circular 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 path os 7/kpw5lf va1f radius r in a uniform magnetic field B. Show that its momentum is 5kvfwa/7 p1 lsp = qBr .

A particle of mass m and charge q moves in a circular path in a maynn dji1,yj2 cm30izg(9st8xgnetic field B. Show that its kinetic energy is proportionalxnm19tcns28jiy, y g d0z(3ji to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in ,u2qb6 dqpkk9wf, 1vfem .fy.Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a sp/ik0h e dktf92eed of 160 m/s perpendicular to the Earth’s magnetic field of tk0 d/f2k9ieh $5.00\times10^{-5}\mathrm{~T}$, 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 magnet1ysdj0 aaz14 m/)r6y amhjsv 9ic 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 withylbbg dr;(4jv)6u;u o speed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carri zo o8 igf9 rywubb*,4a 5janw81i2a3hes a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to oii wzja4158 hy* a,bg9b2 n8fwruo3 athe 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 t-cuh5jls6tq2 ef 9. ra5phh-ohan that of the Ea hfp65herqctj52-o-9 sh al.u rth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of the page towargal3 gq d*0/nld you. Indicate, with appropriate arrows, the qa0g l/d3*nl gdirection 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 updz ;/s*b5et y z8)wwj7icb: pu,c 6dhjward 24-A current exerts an attractive force per unitcji/dy) u,b*ctws :w6; 8ezjpz 75hbd 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 the foqww8 xtz)t 9r5n;o .pfrce between two parallel wires 35 m long an9 ;tw.p8xz5otnfqw )r d 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Eg4qgk - +l/* (eknuxpbpdmgdi:d 2/ z-arth’s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accurdk+ ge2gz up:/l(*npi-q4k- / xmbgddate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of j,r0;wtl8zs 1 d:gnq m8.5-m-high poles. What is the magnitude of the magnetic field produced bl0 t1sg:8mnjdrzqw ,;y 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 s-v i;7 vrlxxc*ame direction. Dete icx*l7v-r; vxrmine 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 from a straight vefeelyx-9h3 1)ur a+iartical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontaly+3- h)ua1ile efr9ax component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due n/ w mh q:z43fzcyj:o7gorth. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downwar3:yzcg 4q:/foh7zm wjd, 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 point in space 4w )xxgfe*-ekat 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 fiel( z cc+7, c4u+ef5ca5scvoa rnd midway between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currents zo(cafc5vr45n,+c7au + cec s are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current toq z,0kqzu t1p 0bsq0l3, 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 plaq3,1u qzqzt ksb00 pl0ne (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 plzyid 3-icx 8y*ane 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 t3izc-y *dix8 ywo 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 points 2 l2,r1pvs 8oh3tq-y oi3$^{\circ}\,$ 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 plafaay. 0* xvf*5 fkik:tne as a straight wire, as shown in (Fig. Below). Thev :kff.kf a *t*yxa05ire is a current 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 second wire jw dphynlz0+-0fu0 i6, made of 2.5-mm-diameter copper wire and paral0-i0djun6h+ylw fzp 0lel to the first, is kept in suspension magnetically 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 perpendiculm qz irs-:i+x0ar 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 midw +xmsz:r0 -iqiay 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 2 fqu:g7gr +7cfz1,3muqy5jwl.0 A current. Wire B’s current is 4.0 A in the saqff7cm1+q 3u zygr:u5 jw,g7lme direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking along them, theo5 (g.v si * ) 3u;fi-sh-rwkluj6mzcby are at three corners of an equilateral triangle.) The current in each wire isiju i.-)6 -(* c z3bms uovl;r5fsgkhw 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the mady .fpndqs -/7gnetic field at the midpoint of the side of the triangle betweeys/ d-d.n7 qpfn wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distarqfw,ws9xb 1k p7v cf- j(7g3ty2a3ilnce d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below)39w 7yl,xja 1qg wsk- p (bcr2fv7ti3f. 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 ablxb; 3xjt)w4pbnc x5h /b2kh/e- +nu current of 2.0 A. Calculate the field inside near the centbx5;clkn/ /xbb3weu42hnpb h jx)+t- er.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm ibwr96eu 0qi(vp xc yc7bq5pu7mu+w : /n diameter is to produce a field of 0.385 T at its center. How much current should th6bu9w +xppmvb75ur w0(cieyu7:q q /ce solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long str pna)*l-qp2qz 1p.owo( r) ctuaight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A currenou 1 *p)ta.(qn qwpp2l)c -zrot downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practicpz s89s2 5fkcjal solenoid that produces the greatest possible magnetic fp5zsjf 2c9sk8 ield 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 so on.

A toroid is a solenoid in the shape3.siq-o h ncl* of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic fi 3on-.*sqlchield
(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 pd tw2tg+5 1+nfq-+3sesrkj ma coaxial cable (Fig. Below) iswkjd++qtmgfesnt+p125 r -3 s $B=\mu_0I/2\pi r$ 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 its face pp q+ xc57n8jxtarallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil+78n5qtc xpx j, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle defl 50i q xhk5t*49iob.gcs jq9lpects 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 galvanom 8za pcl;a+j gsk:+7j37bxtsteter weakens by 25% over the years, what current will give full-scalc tzl8s ka+tasjxg p 37+j7;:be deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the out);q 3nt hrlj;gput torque changng l3rhqt; j;)e?

Show that the magnetic dipole moment M of an electron orbiting the proh.i7lmguls .o . 5 ;s+teq0jduton nucleuidsl 7..o5 tu;.gu+ jels0qhms of a hydrogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nir7*wrxno.v a1ne loops lies flat on the ground. The Earth’s magnetic field at this location has magnit1nw7r o vx.*arude $5.50\times10^{-5}\mathrm{~Т}$ 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 fiecjp:c0xd: f4 cld. What value of electric field could make their paths straighjp:xc 4c:dfc0 t? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equdvpd2jx 9t9 g3al to 21.0, 21.6, 21.9, 22.2, and 229jvp xt93 dd2g.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field b z b6vyw0u3ll6xi *q,xetween the electric plates in the mass spectrometer of xib6ulw60l y*vz, xq3 (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 bei/t* y 9:3q n7wrmt6xtz34sglzv .lsgdng used to monitor air pollutants. It is difficult, however, to separate molecules with nearly equasst3x d*.g3z 4zn:qy6 7 wtg/vl t9rmll 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 spectro l76y g54x7 t(zoikleumeter accelerates ions by a voltage V before they enter a magnetic field(ek yix5to6 4g u77zll B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 dhbuh4b: m 9u*loops of wire per meter, and a 25-A current flows through th:*d4u9 ubmhhb e wire. 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*hh* qd7 m0w75lrd ewc cm in diameter, and has 640 turns of wire. The magnetic field inside q0mr*d5*7hc ewd7hlwthe 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 momentum4srrz6 f1q,s p $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 enterinr4u ee31 j8xbrg a region of consta4 8r rjubee1x3nt magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (m*ik we- 6f)3y rf abgtgc-;u*j8(qep Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a strengtheeg** tqyipmk()f6f 8ur;-j3w gb a-c $5.0\times10^{-5}\mathrm{~T}$ 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 acq2qj ua -emjb,isx:- 7tu3zmt5uired 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 horizn8 6y;/wsfc:er 2wnpgontally to the north and h y nc6;pngw:e2wr/ 8sfas 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 massgdjx ymeq6 59 pu*8-r37zsxoy 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 lak/fekk56 u;f frge current moves in a closed loo f;5ek/kkuff6p 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? 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 and ir3oqclc p,poz-;i;d 7s suspended in air due to the two magnetic forces from the bottom two wires. The current flow through i z orc3;op-;pld7q,cthe 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 hor r ifbqbat7 r5+xc,d+gt6)-ghizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). Ag567+ t b,idtrcgqx+-a rfhb) 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 approximayi ) ni/o. ,1r(t2.xpgynv(ie whgy7jte maximum deflection of the electron beam near the center of a TV scrjeyx iv)it y og2(1rp w,g(.niy7.nh/een 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 ela(:2fi l odc 9:g:)ddi m/qfrjementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field Bgj i9(d/f mqic)2ad :r:: ldfo. 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 straight parallel38zhwefc1 zo3 wires, located at the corners of a square of side l, carr1o3zhe83wf z cy equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beam steering”; thlz)plmh8ic 52 tb ; rwg7c(pt5at 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? I8 5tccgil plmb(7trw h z2p5;)f the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the v0u f(ux6;ap jvq08gx center of a circular coil of wire carrying a current I (as in Fig. Below) is gx u(x08vvu 0ajqp;f 6
$B=\frac{\mu_{0} N I}{2 r},$
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 f9*kzh o ta+;/kq3ujkk ield 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 magnitude0flethw) h+cz cy2x y/v73q0 dn*z,it of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to th)0cvl0y3cd t/xnq y7wh z* i,+z2f ethe 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 bea*136u0tf x6 d)ge+tgag ym mnmm of electrons, traveling to th f3gna1gmgtt*m)60uy dm +6 exe 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 ;nkjaex26ge 9 5lbey-magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two nykg 62e-9lb5 je; exasuccessive 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 diameter, is to produce a 0.o69d8ayqq5xjb5 z0t 5 vj -npy30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns mus65 -y0o8jqa jd9tv 55npzqybxt the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0zfb v p8mu5m,9nor6j 6.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strinv6rzfomj,p 5u8m96 bngs make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters aeanmyeg3 s *g*abg d-5/e,3ze uniform 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$