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What is the velocity of a plane wave in a lossless medium having a relative permittivity of 5 and relative permeability of unity?
- a)3 x 108 m/s
- b)1.3 x 108 m/s
- c)107 m/s
- d)2 x 108 m/s
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
Velocity of a plane wave in a lossless medium is given by:
v = 1/√(με)
where μ is the permeability of the medium and ε is the permittivity of the medium.
Given:
Relative permittivity of the medium, εr = 5
Relative permeability of the medium, μr = 1
μ = μ0μr, where μ0 = 4π x 10^-7 H/m is the permeability of free space.
ε = ε0εr, where ε0 = 8.854 x 10^-12 F/m is the permittivity of free space.
Substituting the values in the equation for velocity of a plane wave, we get:
v = 1/√(με) = 1/√(μ0μrε0εr) = 1/√(μ0ε0)√(μrεr) = 1/√(1/299792458)√(5 x 8.854 x 10^-12) = 1.3 x 10^8 m/s
Therefore, the velocity of a plane wave in a lossless medium having a relative permittivity of 5 and relative permeability of unity is 1.3 x 10^8 m/s.
Answer: Option B. 1.3 x 10^8 m/s.
Velocity of a plane wave in a lossless medium is given by:
v = 1/√(με)
where μ is the permeability of the medium and ε is the permittivity of the medium.
Given:
Relative permittivity of the medium, εr = 5
Relative permeability of the medium, μr = 1
μ = μ0μr, where μ0 = 4π x 10^-7 H/m is the permeability of free space.
ε = ε0εr, where ε0 = 8.854 x 10^-12 F/m is the permittivity of free space.
Substituting the values in the equation for velocity of a plane wave, we get:
v = 1/√(με) = 1/√(μ0μrε0εr) = 1/√(μ0ε0)√(μrεr) = 1/√(1/299792458)√(5 x 8.854 x 10^-12) = 1.3 x 10^8 m/s
Therefore, the velocity of a plane wave in a lossless medium having a relative permittivity of 5 and relative permeability of unity is 1.3 x 10^8 m/s.
Answer: Option B. 1.3 x 10^8 m/s.
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