 College Physics for AP® Courses

# Chapter 24

3.

150 kV/m

6.

(a) 33.3 cm (900 MHz) 11.7 cm (2560 MHz)

(b) The microwave oven with the smaller wavelength would produce smaller hot spots in foods, corresponding to the one with the frequency 2560 MHz.

8.

26.96 MHz

10.

$5.0×10145.0×1014$ Hz

12.

$λ = c f = 3 . 00 × 10 8 m/s 1 . 20 × 10 15 Hz = 2 . 50 × 10 – 7 m λ = c f = 3 . 00 × 10 8 m/s 1 . 20 × 10 15 Hz = 2 . 50 × 10 – 7 m size 12{λ= { {c} over {f} } = { {3 "." "00"´"10" rSup { size 8{8} } " m/s"} over {1 "." "20"´"10" rSup { size 8{"15"} } " Hz"} } = {underline {2 "." "50"´"10" rSup { size 8{ +- 7} } " m"}} } {}$

14.

0.600 m

16.

(a) $f=cλ=3.00×108 m/s1×10-10 m=3×1018 Hzf=cλ=3.00×108 m/s1×10-10 m=3×1018 Hz size 12{f= { {c} over {λ} } = { {3 "." "00"´"10" rSup { size 8{8} } " m/s"} over {1´"10" rSup { size 8{ +- "10"} } " m"} } = {underline {3´"10" rSup { size 8{"18"} } " Hz"}} } {}$

(b) X-rays

19.

(a) $6.00×106 m6.00×106 m size 12{5 "." "00" times "10" rSup { size 8{6} } " m"} {}$

(b) $4.33×10−5 T4.33×10−5 T size 12{4 "." "33" times "10" rSup { size 8{ - 5} } " T"} {}$

21.

(a) 1.50 × 10 6 Hz, AM band
(b) The resonance of currents on an antenna that is 1/4 their wavelength is analogous to the fundamental resonant mode of an air column closed at one end, since the tube also has a length equal to 1/4 the wavelength of the fundamental oscillation.

23.

(a) $1.55×1015 Hz1.55×1015 Hz size 12{1 "." "55" times "10" rSup { size 8{"15"} } " Hz"} {}$

(b) The shortest wavelength of visible light is 380 nm, so that

λ visible λ UV = 380 nm 193 nm = 1 . 97 . λ visible λ UV = 380 nm 193 nm = 1 . 97 . alignl { stack { size 12{ { {λ rSub { size 8{"visible"} } } over {λ rSub { size 8{"UV"} } } } } {} # = { {"380 nm"} over {"193 nm"} } {} # =1 "." "97" "." {} } } {}

In other words, the UV radiation is 97% more accurate than the shortest wavelength of visible light, or almost twice as accurate!

25.

$3 . 90 × 10 8 m 3 . 90 × 10 8 m size 12{3 "." "90" times "10" rSup { size 8{8} } " m"} {}$

27.

(a) $1.50×1011 m1.50×1011 m size 12{1 "." "50" times "10" rSup { size 8{"11"} } " m"} {}$

(b) $0.500 μs0.500 μs size 12{0 "." "500 "ms} {}$

(c) 66.7 ns

29.

(a) $−3.5×102 W/m2−3.5×102 W/m2 size 12{-3 "." 5´"10" rSup { size 8{2} } " W/m" rSup { size 8{2} } } {}$

(b) 88%

(c) $1.7μT1.7μT size 12{1 "." 7 mT} {}$

30.

$I = cε 0 E 0 2 2 = 3.00 × 10 8 m/s 8.85 × 10 –12 C 2 /N ⋅ m 2 1 25 V/m 2 2 = 20. 7 W/m 2 I = cε 0 E 0 2 2 = 3.00 × 10 8 m/s 8.85 × 10 –12 C 2 /N ⋅ m 2 1 25 V/m 2 2 = 20. 7 W/m 2$

32.

(a) $I=PA=Pπr2=0.250×10−3 Wπ0.500×10−3 m2=318 W/m2I=PA=Pπr2=0.250×10−3 Wπ0.500×10−3 m2=318 W/m2 size 12{I= { {P} over {A} } = { {P} over {p r rSup { size 8{2} } } } = { {0 "." "250"´"10" rSup { size 8{-3} } " W"} over {∂ left (0 "." "500"´"10" rSup { size 8{-3} } " m" right ) rSup { size 8{2} } } } ="318 W/m" rSup { size 8{2} } } {}$

(b) Iave = cB022μ0⇒B0=2μ0Ic1/2 = 24π×10−7 T⋅m/A318.3 W/m23.00×108 m/s1/2 = 1.63×10−6 T Iave = cB022μ0⇒B0=2μ0Ic1/2 = 24π×10−7 T⋅m/A318.3 W/m23.00×108 m/s1/2 = 1.63×10−6 Talignl { stack { size 12{I rSub { size 8{"ave"} } = { { ital "cB" rSub { size 8{0} rSup { size 8{2} } } } over {2m rSub { size 8{0} } } } drarrow B rSub { size 8{0} } = left ( { {2m rSub { size 8{0} } I} over {c} } right ) rSup { size 8{1/2} } } {} # = left [ { {2 left (4¶´"10" rSup { size 8{-7} } " T" cdot "m/A" right ) left ("318" "." "3 W/m" rSup { size 8{2} } right )} over {3 "." "00"´"10" rSup { size 8{8} } " m/s"} } right ] rSup { size 8{ {1} slash {2} } } {} # = {underline {1 "." "63"´"10" rSup { size 8{-6} } " T"}} {} } } {}

(c) E0 = cB0=3.00×108 m/s1.633×10−6 T = 4.90×102 V/m E0 = cB0=3.00×108 m/s1.633×10−6 T = 4.90×102 V/m alignl { stack { size 12{E rSub { size 8{0} } = ital "cB" rSub { size 8{0} } = left (3 "." "00"´"10" rSup { size 8{8} } " m/s" right ) left (1 "." "633"´"10" rSup { size 8{-6} } " T" right )} {} # = {underline {4 "." "90"´"10" rSup { size 8{2} } " V/m"}} {} } } {}

34.

(a) 89.2 cm

(b) 27.4 V/m

36.

(a) 333 T

(b) $1.33×1019W/m21.33×1019W/m2 size 12{1 "." "33"´"10" rSup { size 8{"19"} } "W/m" rSup { size 8{2} } } {}$

(c) 13.3 kJ

38.

(a) $I=PA=P4πr2∝1r2I=PA=P4πr2∝1r2 size 12{I= { {P} over {A} } = { {P} over {4π r rSup { size 8{2} } } } prop { {1} over {r rSup { size 8{2} } } } } {}$

(b) $I∝E02, B02⇒E02, B02∝1r2⇒E0,B0∝1rI∝E02, B02⇒E02, B02∝1r2⇒E0,B0∝1r$

40.

13.5 pF

42.

(a) $4.07 kW/m24.07 kW/m2 size 12{4 "." "07""kW/m" rSup { size 8{2} } } {}$

(b) 1.75 kV/m

(c) $5.84μT5.84μT size 12{5 "." "84" mT} {}$

(d) 2 min 19 s

44.

(a) $5.00×103 W/m25.00×103 W/m2 size 12{5 "." "00"´"10" rSup { size 8{3} } " W/m" rSup { size 8{2} } } {}$

(b) $3.88×10−6 N3.88×10−6 N size 12{3 "." "88" times "10" rSup { size 8{ - 6} } " N"} {}$

(c) $5.18×10−12 N5.18×10−12 N size 12{ {underline {5 "." "18" times "10" rSup { size 8{ - "12"} } " N"}} } {}$

46.

(a) $t=0t=0 size 12{t=0} {}$

(b) $7.50×10−10 s7.50×10−10 s size 12{7 "." "50" times "10" rSup { size 8{ - "10"} } " s"} {}$

(c) $1.00×10−9 s1.00×10−9 s size 12{1 "." "00" times "10" rSup { size 8{ - 9} } " s"} {}$

48.

(a) $1.01×106 W/m21.01×106 W/m2 size 12{1 "." "01" times "10" rSup { size 8{6} } " W/m" rSup { size 8{2} } } {}$

(b) Much too great for an oven.

(c) The assumed magnetic field is unreasonably large.

50.

(a) $2.53×10−20H2.53×10−20H size 12{2 "." "53" times "10" rSup { size 8{ - "20"} } H} {}$

(b) L is much too small.

(c) The wavelength is unreasonably small.

1.

(b)

3.

(a)

5.

(d)

7.

(d)

9.

(d)

11.

(a)

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