Chapter 31: Q. 14 (page 901)

The magnetic field of an electromagnetic wave in a vacuum is $B_{z} = (3.00 μT) \sin [(1.00 \times 10^{7}) x - ωt]$ , where $x$ is in $m$ and $t$ is in s. What are the wave's (a) wavelength, (b) frequency, and (c) electric field amplitude?

Short Answer

Expert verified

a.Wave length of EM wave is $6.28 \times 10^{- 7} m$ .

b.Frequency of EM wave is $4.775 \times 10^{14} Hz$ .

c. Electric field amplitude of EM wave is $900 V / m$ .

Step by step solution

Calculation for Wavelength of EM waves (part a)

(a).

As it stands,

$c = 3 \times 10^{8} m / s$

$B_{z} = (3.00 μT) \sin [(1.00 \times 10^{7}) x - ωt]$

Wavelength is,

$λ = \frac{2 π}{1 \times 10^{7}} m$

$λ = 2 π \times 10^{- 7} m$

$λ \approx 6.28 \times 10^{- 7} m$

Calculation for frequency for EM waves (part b)

(b).

Frequency is,

$c = f \cdot λ$

Both should be divided bylocalid="1648798271555" $λ$ ,

$\frac{c}{λ} = \frac{f \cdot λλ}{λ}$

$f \approx \frac{c}{λ}$

$f \approx \frac{3 \times 10^{8} m / s}{2 π \times 10^{- 7} m}$

$f \approx 4.775 \times 10^{14} Hz$

Calculation for electric field amplitude of EM waves (part c)

(c).

As it stands,

$B_{z} = (3.00 μT) \sin [(1.00 \times 10^{7}) x - ωt]$

$= Bsin [(1.00 \times 10^{7}) x - ωt]$

$| E | = c | B |$

$| E | = 3 \times 10^{8} m / s \times 3 μT$

$| E | = 900 V / m$

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The magnetic field of an electromagnetic wave in a vacuum is $B_{z} = (3.00 μT) \sin [(1.00 \times 10^{7}) x - ωt]$ , where $x$ is in $m$ and $t$ is in s. What are the wave's (a) wavelength, (b) frequency, and (c) electric field amplitude?

Short Answer

Step by step solution

Calculation for Wavelength of EM waves (part a)

Calculation for frequency for EM waves (part b)

Calculation for electric field amplitude of EM waves (part c)

One App. One Place for Learning.

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The magnetic field of an electromagnetic wave in a vacuum isBz=(3.00μT)sin1.00×107x-ωt , where x is in m and t is in s. What are the wave's (a) wavelength, (b) frequency, and (c) electric field amplitude?

Short Answer

Step by step solution

Calculation for Wavelength of EM waves (part a)

Calculation for frequency for EM waves (part b)

Calculation for electric field amplitude of EM waves (part c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Radiation

Electricity and Magnetism

Electricity

Fundamentals of Physics

Physical Quantities And Units

Study anywhere. Anytime. Across all devices.

The magnetic field of an electromagnetic wave in a vacuum is $B_{z} = (3.00 μT) \sin [(1.00 \times 10^{7}) x - ωt]$ , where $x$ is in $m$ and $t$ is in s. What are the wave's (a) wavelength, (b) frequency, and (c) electric field amplitude?