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习题练习:Electromagnetic Waves



 作者: 王信东Wood发布日期: 2025-06-18 10:16   总分: 66分  得分: _____________

答题人: 匿名未登录  开始时间: 06月18日 10:16  切换到: 整卷模式

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1#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The electric field in an5 8l,vk s-9k qd;,(obk+lvsu8c dprbx EM wave traveling north oscillates in an east–west plane. Describe the direction of th,pdlxbs -(cr8;k59 k ,8+vl ksbud vqoe magnetic field vector in this wave.
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2#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Is sound an electromagnetic wave? If not, what kind of wave is itq2t;-9cb(leknk w x: a?
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3#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can EM waves travel throxudn75h ao;)n tde2- gugh a perfect vacuum? Can sound waves?
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4#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
When you flip a light switch on, does the light go on immediately? Explain.g6eed zj 5mt 0f4s49syfp3w*4kwn+t z
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5#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Are the wavelengths of radio and television signals longer or shorter t bd;c8h,an2x u.g +i-uw i3xbhhan those detectable by the hn+,hchiuxd3 au bbi8;-.x w2guman eye?
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6#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
When you connect two loudsprh.v-wk8kfp**gsgtj 8 p-gn+eakers to the output of a stereo amplifier, should you be suretfhjg.g-spw- +*8 kn*p v 8gkr the lead-in wires are equal in length so that there will not be a time lag between speakers? Explain.
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7#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
In the electromagnetic spectrum, what type of EM wave would have a wavelengthncooy 4f48 sh: 5mm 2nvnwak*l ca779c of mo8cavhs:*n4acnm7n yk w4 c l75o29 f$10^3km$ 1 km? 1 m? 1 cm? 1 mm? $1\mu m$
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8#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can radio waves have the same frequencies as sound; -)mspu5 xjrbxa2dh y f5n6o+ waves (20 Hz–20,000 Hz)?
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9#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can two radio or TV stations broadcast on t - m7xnjyd,t4w+1hngzjk jsy2e; mjxdlp 64(9he same carrier frequency? Explain.
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10#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If a radio transmitter has a vertical antenna, should a receiver’s7 z ohirez* jq5krxa n+9m,e26 antenna (rod type) 9qa72m, z*rix56 k nrje ezho+be vertical or horizontal to obtain best reception?
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The carrier frequencies of FM broadcasts are much higher tha)*ajw4u8);cs wq pss wmg4ix-n for AM broadcasts. On the basis of what you lcxwi)u)ma;qgj84p w s sw-4s*earned about diffraction in Chapter 11, explain why AM signals can be detected more readily than FM signals behind low hills or buildings.
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12#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Discuss how cordless tele, h hpgi8 j7ja*ymmlg5-xr ;e)phones make use of EM waves. What about cell phones?
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13#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A lost person may signal by flashing a flashlight on and off using Md 6x.6 g5*xrnly e h6:p3spbzeorse code. This is actually a modulated EM wave. Is it AM or FM?d6ep6 e.x:*hxn zy3p lg5s6b r What is the frequency of the carrier, approximately?
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14#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At a given instant, a 1.8-A curde7ypzl. 4l x0g;3nzta 9+kchrent flows in the wires connected to a parallel-plate capacitor. What is the rate at which the electric field is chx.tkah4c+zn dp;9g03l y7 zel anging between the plates if the square plates are 1.60 cm on a side?    $\times10^{14}\mathrm{V/m} \cdot \mathrm{s}$

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15#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 1200-nF capacitor with circular parallel plates/ly/pv cz1+v s 2.0 cm in diameter is accumulating charge at the rate of 35mC/s at some instant in time. What will be the magnitude of the induced +yszpcvl v//1magnetic field 10.0 cm radially outward from the center of the plates?    $\times10^{-8}\mathrm{~T}$
What will be the magnitude of the field after the capacitor is fully charged?   

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16#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If the magnetic field in a traveling EM wave has a peak ma r/e x.p3hd(g v67su-u bknfd1gnitude of 17.5 nT at a given point, what is tufd-db1p6ueh v.rks 3n/ (7gxhe peak magnitude of the electric field?    V/m

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17#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  In an EM wave traveling west, the B field oscillates vertically and has a frzaxg n+e84 mi7equen +xa48mn i7gzecy of 80.0 kHz and an rms strength of $6.75\times10^{-9}\mathrm{~T}$. What are the frequency and rms strength of the electric field, and what is its direction? (Fig. Below)
frequency    kHz
$E_{rms}$ =    V/m
direction  



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18#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the frequency of a microwave whose wyfs+vo:05r9 djn iz i/avelength is 1.60 cm?    $ \times10^{10}\mathrm{Hz}$

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19#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the wavelength ,n k+jll.ieaq nbb4(3d;1 jt q+ vgps4of a $29.75\times10^9-Hz$ radar signal?    $ \times10^{-2}\mathrm{m}$

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20#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An EM wave has frequench0y.li1 tz c*cy $9.66\times10^{14}\mathrm{~Hz}.$ What is its wavelength, and how would we classify it?    nm

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21#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An EM wave has a wavelength of 650 nm. What is its frequency, and how would f4sjehz e m f0vo2c01.we classify it?fc0 4vz1.feomj0 2seh    $ \times10^{14}\mathrm{Hz}$  

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22#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How long does it take light t2gxwd ):3htpx/otr 73w tx2 loo reach us from the Sun, $1.50\times10^8\mathrm{~km}$ away?    min

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23#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A widely used “short-wave” radio broadcast band is ref.m 1hn/h-wzv-dnbxk4- axq m2erred to as the 49-m band. What is the frequency of a 49-m rahmmxq-k1 d w -4nzn/b- x.2vahdio signal?    $ \times10^{6}\mathrm{Hz}$

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24#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Our nearest star (other than the Sun) is 4.2 light-years away. That is, it td(;xmmko0 r,wakes 4.2 years formdx,0k;mwo (r the light it emits to reach Earth. How far away is it in meters?    $\times10^{16}\mathrm{m}$

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25#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A light-year is a measure of jj t2 70dkoe) jdsck6w9rdw52abr50bdistance (not time). How many meters does light travel in a yeawt7o j0256 s kb5)djrcdbrwka092je d r?    $ \times10^{15}\mathrm{m}$

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26#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How long would it take a message b3cvlc)q8bh)xw /xe( sent as radio waves from Earth to reach Mars
(a) when nearest Earth,    s
(b) when farthest from Earth?    s

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27#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A student wants to scale down Michelson’s light-sp6;kkq/l. ml*kqmbs 8 leed experiment to a size that will fit in one room. / 8s;mlmlbql q k6*k.kA six-sided mirror is available, and the stationary mirror can be mounted 12 m from the rotating mirror. If the arrangement is otherwise as shown in (Fig. Below), at what minimum rate must the mirror rotate?    $\times10^6\text{ revolutions/s}$


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28#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Who will hear the voice of a singer first — a person in the balcony 50+h(onr*t )gitii3( b hx(8a xv.0 m away from the stage (Fig. Below), or a person 3000 km away at home whose ea hhnxb)8+(tv rg3ai ix*to(i (r is next to the radio? How much sooner? Assume that the microphone is a few centimeters from the singer and the temperature is 20$^{\circ}\,C$.
 
   s



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29#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Pulsed lasers used in science and medicazm rd8r7;/ddr y/h. pine produce very short bursts of electromagnetic energy. If the laser light wavelength is 1062 nm (this corresponds to a Neodymium-YAG laser), and the pulse lasts for 32 rrm/h z;7yp./drad 8d picoseconds, how many wavelengths are found within the laser pulse? How short would the pulse need to be to fit only one wavelength?
N =    wavelengths
$\Delta t'$ =    fs

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30#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The $\vec E$ field in an EM wave in free space has a peak of $21.8mV/m.$ What is the average rate at which this wave carries energy across unit area per unit time?    $\times10^{-7}\mathrm{~W/m^2}$

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31#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The magnetic field in a traveling EM wave has an rms strength o 7c*9msr tuyoyx 6or7*f 28.5 nT. How long does ror7mou7yx*y6 t9*s cit take to deliver 235 J of energy to $1.00cm^2$ of a wall that it hits perpendicularly?    days

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32#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How much energy is transported acro- 4h,,p:m yg)oi 24fcb xtl7go) dldbqss a $1.00-cm^2$ area per hour by an EM wave whose E field has an rms strength of $38.6mV/m?$    $\times10^{-6}\mathrm{J/h}$

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33#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spherically spreadin p4b4* ciio:mjvh3n)b g EM wave comes from a 1200-W source. At a distance of 10.0 m, what is the average intensity, and what is the rms value of the electricp3ivjb) i b4noh :*4mc field?
S =    W/$m^2$
$E_{rms}$ =    V/m

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34#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 12.8-mW laser puts out a narrow beam 1.75 mm in dia(;ipsb ) vidv(.(g wyjmeter. What are the average (rms) values of E and B in .( y ;p)isdjv(w i(bvgthe beam?
$E_{rms}$    $\times10^3\mathrm{V/m}$
$B_{rms}$   $\times10^{-6}\mathrm{T}$

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35#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the average power output of the Sunt ece k3w2bl94, given that about $1350\mathrm{~W/m^2}$ reaches the upper atmosphere of the Earth.    $ \times10^{26}\mathrm{W}$

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36#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If the amplitude of the B field of an EM o kint c6:4ipm8x.)oxved7 v4wave is $2.5\times10^{-7}\mathrm{~Т},$
(a) what is the amplitude of the E field?    V/m
(b) What is the average power per unit area of the EM wave? $\overline{I}$ =    $W/m^2$

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37#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A high-energy pulsed laser emit)wv uag0w;, ocs a 1.0-ns-long pulse of average power $2.8\times10^{11}\mathrm{~W}.$ The beam is $2.2\times10^{-3}\mathrm{~m}$ in radius. Determine
(a) the energy delivered in each pulse,    J
(b) the rms value of the electric field. $E_{rms}$    $\times10^9\mathrm{V/m}$

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38#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the radiation pressure d crc1gx ;.ha9m/kyfj/j8 pt-uue to a 100-W bulb at a distance of 8.0 cm from the center of the bulb. Esc -jkypaxur ;f mjc//gth. 189timate the force exerted on your fingertip if you place it at this point.
P =    $\times10^{-6}\mathrm{N/m^2}$
F =    $\times10^{-10}\mathrm{N}$

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39#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the range of 9,. skk:t+,dggb qcqxwavelengths for
(a) FM radio (88 MHz to 108 MHz)    m to    m
(b) AM radio (535 kHz to 1700 kHz)?    m to    m

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40#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the wavelength for 1.9-GHz cel/cdkpd/ i6jqv tp2e12 l phone reception.    m

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41#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Compare 940 on the AM dial to 94 on the FM dia93xf lh 5 +lgah4hrvvgk*bqpk d-:s5 )l. Which has the longer wavelength, and by ga5hb fx-r d3ks5l4+h9vvl*q kh:g)p what factor is it larger?
 
$\frac{\lambda_1}{\lambda_2}$ =   

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42#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What are the wavelengths for two TV channels that broadcast at (ai;/t nlqu, k54.0 MHz (Channel 2) and 806,l ua;i(nqtk/ MHz (Channel 69)?
$\lambda_2$ =    m
$\lambda_{69}$ =    m

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43#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The variable capacitor in the tuner of an AM radio has a capacitanc0ce 3qa9eqzy 1e of 2800 pF when the radio is tuned to a station at 550 kHz. What mustze30yqq1 ea9 c the capacitance be for a station near the other end of the dial, 1610 kHz?    pF

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44#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The oscillator of a 9 :a--vo7 n j dplngebc:l/3gf:6.1-MHz FM station has an inductance of $1.8\mathrm{~}\mu\mathrm{H}.$ What value must the capacitance be?    pF

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45#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A certain FM radio tuning circuit has a fixed )mb(prr-jju / capacitor $C=840\mathrm{~pF}.$ Tuning is done by a variable inductance. What range of values must the inductance have to tune stations from 88 MHz to 108 MHz?    nH$\leq$ L $\leq$    nH

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46#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An amateur radio operator wishes to buh-na*5.cp ki5lkxf r0ild a receiver that can tune a range from 14.0 MHz to 15.0 Mnx r5-0ac ikpk.*5hf lHz. A variable capacitor has a minimum capacitance of 82 pF.
(a) What is the required value of the inductance?    $\mu H$
(b) What is the maximum capacitance used on the variable capacitor?    pF

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47#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A satellite beams microwave radiation with a power of 10 kW jdmkac96d6r0jf qw;w 2h;0k otoward the Earth’s surface, 550 km away. When the beam strikes Earth, its circular di0m6jkajf h9w0dwq rco6dk;;2ameter is about 1500 m. Find the rms electric field strength of the beam.    V/m

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48#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 1.60-m-long FM antenna is oriented parallel to tht i x1ha0xqt w7s; y2oy,5v9xue electric field of an EM wave. How large musxq0;1twxtx 9oaisyuh 7vy 52, t the electric field be to produce a 1.00-mV (rms) voltage between the ends of the antenna? What is the rate of energy transport per square meter?
$E_{rms}$ =    $\times10^{-4}\mathrm{V/m}$
S =    $\times10^{-9}\mathrm{V/m^2}$

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49#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If the Sun were to disappear or som05vz,2onqgyp ehow radically change its output, how long would it take og5, 02pz ynvqfor us on Earth to learn about it?    min

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50#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Light is emitted from/ /xmn*xer3sj-t zn(r an ordinary lightbulb filament in wave-train bursts about s/x n3n/-rxe(jmt *z r$10^{-8}\mathrm{~s}$ in duration. What is the length in space of such wave trains?    m

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51#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) How long did it take for a message sent from Earth to reach thi*f gh0h m/jal(*) r8w 9t :zpoptntl1e first astronhzl/p naomg*:ithj r*p8t)(w f 0t91lauts on the Moon?    s
(b) How long will it take for a message from Earth to reach the first astronauts who arrive on Mars; assume Mars is at its closest approach to Earth $(78\times10^6\mathrm{~km})?$   min

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52#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A radio voice signal from the Apo( q-bxn; vn wp*7: g(ruokg1pfllo crew on the Moon (Fig. Below) was beamed to a listening crowd from a radio speaker. If you were standing 25 m from the loudspeaker, what was the total kn7 pr*ug1x( :v( nb;o-fq pgwtime lag between when you heard the sound and when the sound left the Moon?    s

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53#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Cosmic microwave background radiation fills all space withr1q h(0iko8 w lggokh-7gn1/ - mfyfj, an average energy density ykh nfkh goq gw /8o(g71li1r,m--j0fof $4\times10^{-14}\mathrm{~J/m}^3.$
(a) Find the rms value of the electric field associated with this radiation.    V/m
(b) How far from a 10-kW radio transmitter emitting uniformly in all directions would you find a comparable value?    km

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54#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What are $E_0$ and $B_0$ 2.00 m from a 95-W light source? Assume the bulb emits radiation of a single frequency uniformly in all directions.
$E_0$ =    V/m
$B_0$ =    $\times10^{-7}\mathrm{T}$

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55#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the rms electric field in the sunlight tha- cbei1;9bqa mt hits Mars, knowing that the Earaqe ibm 19;-bcth receives about $1350\mathrm{~W/m^2}$ and that Mars is 1.52 times farther from the Sun (on average) than is the Earth.    V/m

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56#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At a given instant in time, a traveling EM wave is noted tzaye* q. ,6v*-krueu ko have its maximum magnetic field poikvu e*,zq. e ary-k6u*nting west and its maximum electric field pointing south. In which direction is the wave traveling? If the rate of energy flow is $560\mathrm{~W/m^2}$ what are the maximum values for the two fields?
 
$E_0$ =    V/m
$B_0$ =    $\times10^{-6}\mathrm{T}$

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57#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate how long an AM antenna would have to be if it were :uk j*ccl g0;l
(a) $\frac{1}{2}\lambda$    m
(b) $ \frac{1}{4}\lambda$ AM radio is roughly 1 MHz (530 kHz to 1.7 MHz).    m

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58#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How large an emf (rms) will be generated in an antenna that consi0psv (h hkoe/.sts of a 380-loop circular coil of wire 2.2 cm in diameter if the EM wave has a frequency of 810 kHz and is transpor0 vhs(.oh/kpe ting energy at an average rate of $1.0\times10^{-4}\mathrm{~W/m^2}$ at the antenna? [Hint: You can use Eq. 21–5 for a generator, since it could be applied to an observer moving with the coil so that the magnetic field is oscillating with the frequency $f=\omega/2\pi$]    mV

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59#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The average intensity of a particular TV station’s 3 conw w1v7l47wizgy 5signal is $1.0\times10^{-13}\mathrm{~W/m^2}$ when it arrives at a 33-cm-diameter satellite TV antenna.
(a) Calculate the total energy received by the antenna during 6.0 hours of viewing this station’s programs. U =    $\times10^{-10}\mathrm{J}$
(b) What are the amplitudes of the E and B fields of the EM wave?
$E_0$ =    $\times10^{-6}$V/m
$B_0$ =    $\times10^{-14}$ T

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60#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  15 km from a radio station’s transmitting antenna, the am,5d.zky 8cdz62k1wf y.uyzk eplitude of the electric field i, cyz z kdz .kweyyu.2dfk5861s $0.12\mathrm{~V/m}.$ What is the average power output of the radio station?    kW

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61#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The variable capacitance of a radio tuner consikp,uv ip*mhq6hz(xaat9 j-x0go8+3usts of six plates connected together placed alternately between six other plates, also connected together (Fig. Below). Each pla3k8*hhvx 9jut-i+qm6 a,agx(upp oz0 te is separated from its neighbor by 1.1 mm of air. One set of plates can move so that the area of overlap varies from $1.0cm^2$ to $9.0cm^2$.
(a) Are these capacitors connected in series or in parallel?  
(b) Determine the range of capacitance values.    pF $\leq$ C $\leq$    pF
(c) What value of inductor is needed if the radio is to tune AM stations from 550 kHz to 1600 kHz?    mH $\leq$ C $\leq$    mH



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62#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A radio station is allowed to broadcast at an average powew:/4)lcnt qvs6l9t3gb 1v 4n i xd-bger not to exceed 25 kW. If an electric field amplitude of is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to hear this st:xvinnetvtbd1 g4)36qgs49 wl/b- lcation.    km

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63#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A point source emits light energy uniformly in all directionte2eebilqha,, :kgs 4bf; d-0s at an average rate 0i:ql-t ;,fg2ee ba4eksd bh,$P_0$ with a single frequency f. Show that the peak electric field in the wave is given by
$E_0=\sqrt{\frac{\mu_0cP_0}{2\pi r^2}}.$
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64#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a 50-kW radio station emits EM waves uniformly 277hf . 2s8 og,ahxmvfqcyq ;lin all directions.
(a) How much energy per second crosses a $ 1.0-m^2$ area 100 m from the transmitting antenna?    W
(b) What is the rms magnitude of the $\vec E$ field at this point, assuming the station is operating at full power?    V/m
(c) What is the voltage induced in a 1.0-m-long vertical car antenna at this distance?    V

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65#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Repeat Problem 65 for a distanclts+3s3t2lp5 q jpnd 2e of 100 km from the station.
(a)    $\mu W$
(b)    V/m
(c)    V

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66#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the maximum powe 3pnv2b/i59 xfd+esfr n20ivnfnz;7n r level of the radio station of Problem 52 so as to avoid electrical breakdown of air at a distance of 1.0 m 3/r; v ns pn9bnxnd2ffzi520 7finv+efrom the antenna? Assume the antenna is a point source. Air breaks down in an electric field of about $3\times10^6\mathrm{~V/m}.$ [Hint: See Problem 51.]    $\times10^{11}\mathrm{W}$

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