Concept explainers
The magnetic field of a wave propagating through a certain nonmagnetic material is given by
Find the following:
- (a) The direction of wave propagation.
- (b) The phase velocity.
- (c) The wavelength in the material.
- (d) The relative permittivity of the material.
- (e) The electric field phasor.
(a)
The direction of wave propagation for the given condition.
Answer to Problem 1P
The direction of wave propagation for the given condition is
Explanation of Solution
Given data:
The magnetic field intensity of the wave is
Calculation:
Write the standard expression for the magnetic field phasor of TEM wave propagating in the
Here,
In the above equation positive sign is used when the wave is travelling in the
In the given magnetic field negative sign is used so the direction of wave propagation is along the
Conclusion:
Therefore, the direction of wave propagation for the given condition is
(b)
The phase velocity for the given condition.
Answer to Problem 1P
The phase velocity for the given condition is
Explanation of Solution
Calculation:
Write the standard relation of phase velocity, wave number and angular frequency of uniform plane wave.
Here,
Compare the given magnetic field and equation (1) to calculate the value of
Substitute
Conclusion:
Therefore, the phase velocity for the given condition is
(c)
The wavelength in the material.
Answer to Problem 1P
The wavelength in the material is
Explanation of Solution
Calculation:
Write the standard relation between wavelength and wave number of plane wave.
Here,
Substitute
Conclusion:
Therefore, the wavelength in the material is
(d)
The relative permittivity of the medium.
Answer to Problem 1P
The relative permittivity
Explanation of Solution
Calculation:
Write the standard relation between relative permittivity and speed of light and phase velocity.
Here,
Substitute
Conclusion:
Therefore, the relative permittivity
(e)
The electric field phasor.
Answer to Problem 1P
The electric field phasor is
Explanation of Solution
Calculation:
Write the standard relation between electric field and magnetic field intensity.
Here,
Write the standard expression for the intrinsic impedance of the medium.
Here,
Write the standard expression for the electrical permittivity of any medium as,
Here,
Substitute
The permeability of the given non magnetic medium is,
Substitute
Substitute
Simplify the above expression.
The conversion from
So, the conversion from
Substitute
Conclusion:
Therefore, the electric field phasor is
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Chapter 7 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
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