Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 22, Problem 61P

(a)

To determine

The wavelength of radio wave in air.

(a)

Expert Solution
Check Mark

Answer to Problem 61P

The wavelength of radio wave in air is 526m_.

Explanation of Solution

Write the expression for wavelength.

λ=cf (I)

Here, c is the velocity of light, f is the frequency, and λ is the wavelength of light.

Conclusion:

Substitute 3×108m/s for c, and 570×103Hz for f in equation (I).

λ=3×108m/s570×103Hz=526m

Therefore, the wavelength of radio wave in air is 526m_.

(b)

To determine

The capacitance in the tuning circuit.

(b)

Expert Solution
Check Mark

Answer to Problem 61P

The capacitance in the tuning circuit is 390pF_.

Explanation of Solution

Write the expression for the frequency in an LC circuit.

f0=12πLC (II)

Here, L is the inductance, and C is the capacitance.

Rearrange equation (I) to obtain an expression for C.

C=14π2Lf02 (III)

Conclusion:

Substitute, 0.2×103H for L, 570×103Hz for f0 in equation (III).

C=14(3.14)2(0.2×103H)(570×103Hz)=3.90×1011F=390pF

Therefore, the capacitance in the tuning circuit is 390pF_.

(b)

To determine

The maximum induced emf in the antenna.

(b)

Expert Solution
Check Mark

Answer to Problem 61P

The maximum induced emf in the antenna is 380μV_.

Explanation of Solution

Write the expression for induced emf in the coil.

|ε|=NΔΦBΔt (IV)

Here, N is the number of turns, ΔΦB is the change in magnetic flux, and Δt is the change in time.

Write the expression for the maximum magnetic flux.

ΦB=BA=Bπr2 (V)

Here, B is the magnetic field, and r is the radius of the coil.

Replace B by Bmsin(kz+ωt) in equation and find the value of ΔBΔt.

ΔBΔt=ωBmcos(kz+ωt)

The maximum value of ΔBΔt is obtained when kz+ωt become equal to 0, replace ω by 2πf in the expression of ΔBΔt.

(ΔBΔt)max=ωBm=2πfBm (VI)

Write the expression for the relationship between electric field and magnetic field.

Em=cBmBm=Emc (VII)

Rewrite equation (IV).

|ε|=Nπr2ΔBΔt=Nπr2(Δ(Bmsin(kz+ωt))Δt)max=Nπr2(2πf)Bm=Nπr2(2πf)Emc (VIII)

Conclusions:

Substitute, 50 for N, 0.016m for r, 570000Hz for f, 0.80V/m for Em, and 3×108m/s for c in equation (VIII).

|ε|=50×3.14×(0.016m)2×2×3.14×570000Hz0.80V/m3×108m/s=380μV

Therefore, the maximum induced emf in the antenna is 380μV_.

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Chapter 22 Solutions

Physics

Ch. 22.7 - Prob. 22.7PPCh. 22.7 - Prob. 22.8PPCh. 22.8 - Prob. 22.9PPCh. 22 - Prob. 1CQCh. 22 - Prob. 2CQCh. 22 - Prob. 3CQCh. 22 - Prob. 4CQCh. 22 - Prob. 5CQCh. 22 - Prob. 6CQCh. 22 - Prob. 7CQCh. 22 - Prob. 8CQCh. 22 - Prob. 9CQCh. 22 - Prob. 10CQCh. 22 - Prob. 11CQCh. 22 - Prob. 12CQCh. 22 - Prob. 13CQCh. 22 - Prob. 14CQCh. 22 - Prob. 15CQCh. 22 - Prob. 1MCQCh. 22 - Prob. 2MCQCh. 22 - Prob. 3MCQCh. 22 - Prob. 4MCQCh. 22 - 5. If the wavelength of an electromagnetic wave is...Ch. 22 - Prob. 6MCQCh. 22 - 7. A dipole radio transmitter has its rod-shaped...Ch. 22 - Prob. 8MCQCh. 22 - Prob. 9MCQCh. 22 - Prob. 10MCQCh. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - 6. What is the wavelength of the radio waves...Ch. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - Prob. 9PCh. 22 - Prob. 10PCh. 22 - Prob. 12PCh. 22 - 12. In order to study the structure of a...Ch. 22 - Prob. 13PCh. 22 - 14. When the NASA Rover Spirit successfully landed...Ch. 22 - Prob. 15PCh. 22 - 16. You and a friend are sitting in the outfield...Ch. 22 - Prob. 14PCh. 22 - Prob. 18PCh. 22 - Prob. 17PCh. 22 - Prob. 20PCh. 22 - Prob. 21PCh. 22 - Prob. 22PCh. 22 - Prob. 23PCh. 22 - Prob. 24PCh. 22 - Prob. 25PCh. 22 - Prob. 26PCh. 22 - Prob. 27PCh. 22 - Prob. 28PCh. 22 - Prob. 29PCh. 22 - 30. The intensity of the sunlight that reaches...Ch. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Prob. 33PCh. 22 - Prob. 34PCh. 22 - Prob. 35PCh. 22 - 36. The intensity of the sunlight that reaches...Ch. 22 - Prob. 37PCh. 22 - Prob. 38PCh. 22 - Prob. 39PCh. 22 - Prob. 40PCh. 22 - Prob. 41PCh. 22 - Prob. 42PCh. 22 - Prob. 43PCh. 22 - Prob. 44PCh. 22 - Prob. 45PCh. 22 - Prob. 46PCh. 22 - Prob. 47PCh. 22 - Prob. 48PCh. 22 - Prob. 49PCh. 22 - Prob. 50PCh. 22 - Prob. 51PCh. 22 - Prob. 52PCh. 22 - Prob. 53PCh. 22 - Prob. 54PCh. 22 - Prob. 55PCh. 22 - Prob. 56PCh. 22 - Prob. 57PCh. 22 - Prob. 58PCh. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 62PCh. 22 - Prob. 61PCh. 22 - Prob. 63PCh. 22 - Prob. 64PCh. 22 - Prob. 65PCh. 22 - Prob. 66PCh. 22 - Prob. 67PCh. 22 - Prob. 68PCh. 22 - Prob. 69PCh. 22 - Prob. 70PCh. 22 - Prob. 71PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 77PCh. 22 - Prob. 78PCh. 22 - Prob. 80PCh. 22 - Prob. 82PCh. 22 - Prob. 79PCh. 22 - Prob. 81PCh. 22 - Prob. 84PCh. 22 - Prob. 83PCh. 22 - Prob. 86PCh. 22 - Prob. 85P
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