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The magnetic field intensity vector of a plane wave is given by H (x, y, z, t) = 10 sin (1000t + 0.002x + 20) ay where ay denotes the unit vector in y-direction. The wave propagating with a phase velocity
- a)5 x 105 rad/s
- b)50 x 105 rad/s
- c)25 x 105 rad/s
- d)150 x 105 rad/s
Correct answer is option 'A'. Can you explain this answer?
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The magnetic field intensity vector of a plane wave is given by H (x, ...
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The magnetic field intensity vector of a plane wave is given by H (x, ...
Given Information:
The magnetic field intensity vector of a plane wave is given by H (x, y, z, t) = 10 sin (1000t - 0.002x + 20) ay.
To Find:
The phase velocity of the wave.
Solution:
The magnetic field intensity vector of a plane wave is given by H (x, y, z, t) = H0 sin (ωt - kx + φ) ay, where H0 is the amplitude of the wave, ω is the angular frequency, k is the wave number, and φ is the phase angle.
Comparing the given equation with the standard equation, we can determine the values of ω, k, and φ.
Amplitude:
The amplitude of the wave is given as H0 = 10.
Angular Frequency:
The angular frequency ω is given as 1000 rad/s.
Wave Number:
The wave number k is given as 0.002 rad/m.
Phase Angle:
The phase angle φ is given as 20 rad.
Phase Velocity:
The phase velocity v is given by the ratio of the angular frequency ω to the wave number k.
v = ω / k
Substituting the given values, we get:
v = 1000 rad/s / 0.002 rad/m = 5 x 10^5 m/s
The phase velocity of the wave is 5 x 10^5 m/s.
Final Answer:
The correct answer is option 'A', which is 5 x 10^5 rad/s.
The magnetic field intensity vector of a plane wave is given by H (x, y, z, t) = 10 sin (1000t - 0.002x + 20) ay.
To Find:
The phase velocity of the wave.
Solution:
The magnetic field intensity vector of a plane wave is given by H (x, y, z, t) = H0 sin (ωt - kx + φ) ay, where H0 is the amplitude of the wave, ω is the angular frequency, k is the wave number, and φ is the phase angle.
Comparing the given equation with the standard equation, we can determine the values of ω, k, and φ.
Amplitude:
The amplitude of the wave is given as H0 = 10.
Angular Frequency:
The angular frequency ω is given as 1000 rad/s.
Wave Number:
The wave number k is given as 0.002 rad/m.
Phase Angle:
The phase angle φ is given as 20 rad.
Phase Velocity:
The phase velocity v is given by the ratio of the angular frequency ω to the wave number k.
v = ω / k
Substituting the given values, we get:
v = 1000 rad/s / 0.002 rad/m = 5 x 10^5 m/s
The phase velocity of the wave is 5 x 10^5 m/s.
Final Answer:
The correct answer is option 'A', which is 5 x 10^5 rad/s.
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The magnetic field intensity vector of a plane wave is given by H (x, y, z, t) = 10 sin (1000t + 0.002x + 20) ay where ay denotes the unit vector in y-direction. The wave propagating with a phase velocitya)5 x 105rad/s b)50 x 105rad/sc)25 x 105rad/s d)150 x 105 rad/sCorrect answer is option 'A'. Can you explain this answer?
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