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The velocity of a plane wave in a lossless medium having a relative permittivity of 4 and relative permeability of unity would be
- a)1.5 x 108 m/s
- b)2.5 x 108 m/s
- c)1 x 108 m/s
- d)2 x 108 m/s
Correct answer is option 'A'. Can you explain this answer?
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The velocity of a plane wave in a lossless medium having a relative pe...
For a lossless or perfect medium, velocity of plane wave is given by
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The velocity of a plane wave in a lossless medium having a relative pe...
Solution:
Given,
Relative permittivity, εr = 4
Relative permeability, μr = 1
The velocity of the plane wave in a lossless medium is given as:
v = 1/√(μr εr) x c
where c is the speed of light in vacuum, c = 3 x 10^8 m/s
Substituting the given values, we get
v = 1/√(1 x 4) x (3 x 10^8)
v = 1/2 x (3 x 10^8)
v = 1.5 x 10^8 m/s
Therefore, the velocity of the plane wave in the given lossless medium is 1.5 x 10^8 m/s, which is option A.
Explanation:
The velocity of a plane wave in a medium is determined by the properties of the medium, such as the relative permittivity and relative permeability. In a lossless medium, there is no loss of energy, and the wave propagates without attenuation. In such a medium, the velocity is given by the above formula.
In this problem, the relative permittivity is given as 4, which means that the medium has a higher capacitance than vacuum. The relative permeability is given as 1, which means that the medium has the same permeability as vacuum. Substituting these values in the formula, we get the velocity of the plane wave as 1.5 x 10^8 m/s.
This result is consistent with the fact that the velocity of a plane wave in a medium is always less than the speed of light in vacuum. In this case, the velocity is reduced by a factor of 2 due to the higher capacitance of the medium.
Given,
Relative permittivity, εr = 4
Relative permeability, μr = 1
The velocity of the plane wave in a lossless medium is given as:
v = 1/√(μr εr) x c
where c is the speed of light in vacuum, c = 3 x 10^8 m/s
Substituting the given values, we get
v = 1/√(1 x 4) x (3 x 10^8)
v = 1/2 x (3 x 10^8)
v = 1.5 x 10^8 m/s
Therefore, the velocity of the plane wave in the given lossless medium is 1.5 x 10^8 m/s, which is option A.
Explanation:
The velocity of a plane wave in a medium is determined by the properties of the medium, such as the relative permittivity and relative permeability. In a lossless medium, there is no loss of energy, and the wave propagates without attenuation. In such a medium, the velocity is given by the above formula.
In this problem, the relative permittivity is given as 4, which means that the medium has a higher capacitance than vacuum. The relative permeability is given as 1, which means that the medium has the same permeability as vacuum. Substituting these values in the formula, we get the velocity of the plane wave as 1.5 x 10^8 m/s.
This result is consistent with the fact that the velocity of a plane wave in a medium is always less than the speed of light in vacuum. In this case, the velocity is reduced by a factor of 2 due to the higher capacitance of the medium.
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