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In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by?
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In a non-magnetic dielectric medium with dielectric constant = 4, the ...
Understanding the Plane Wave Electric Field
The plane wave given is represented as:
E = (-i + √3 j) exp[j(ωt - k·r)]
Where:
- ω = 10^8 rad/s (angular frequency)
- k = propagation vector
- r = position vector
Dielectric Constant and Speed of Light
In a non-magnetic dielectric medium with a dielectric constant (ε) of 4:
- The speed of light (c) in vacuum is approximately 3 x 10^8 m/s.
- The speed of light in the medium (v) can be calculated using the formula:
v = c / √ε
Here, v = (3 x 10^8 m/s) / √4 = 1.5 x 10^8 m/s.
Relationship Between k and ω
The propagation vector (k) is related to angular frequency (ω) and wave speed (v) by the equation:
k = ω / v.
Calculation of the Propagation Vector k
Substituting the values into the equation:
- ω = 10^8 rad/s
- v = 1.5 x 10^8 m/s
Thus:
k = (10^8 rad/s) / (1.5 x 10^8 m/s) = (2/3) rad/m.
Final Result
The propagation vector k can be expressed as:
- Magnitude: |k| = (2/3) rad/m
- Direction: The direction of k is determined by the direction of the wave propagation, which can be inferred from the electric field vector's components, here indicating a direction in the complex plane.
This analysis provides a comprehensive understanding of the propagation vector in a dielectric medium with a given dielectric constant.
The plane wave given is represented as:
E = (-i + √3 j) exp[j(ωt - k·r)]
Where:
- ω = 10^8 rad/s (angular frequency)
- k = propagation vector
- r = position vector
Dielectric Constant and Speed of Light
In a non-magnetic dielectric medium with a dielectric constant (ε) of 4:
- The speed of light (c) in vacuum is approximately 3 x 10^8 m/s.
- The speed of light in the medium (v) can be calculated using the formula:
v = c / √ε
Here, v = (3 x 10^8 m/s) / √4 = 1.5 x 10^8 m/s.
Relationship Between k and ω
The propagation vector (k) is related to angular frequency (ω) and wave speed (v) by the equation:
k = ω / v.
Calculation of the Propagation Vector k
Substituting the values into the equation:
- ω = 10^8 rad/s
- v = 1.5 x 10^8 m/s
Thus:
k = (10^8 rad/s) / (1.5 x 10^8 m/s) = (2/3) rad/m.
Final Result
The propagation vector k can be expressed as:
- Magnitude: |k| = (2/3) rad/m
- Direction: The direction of k is determined by the direction of the wave propagation, which can be inferred from the electric field vector's components, here indicating a direction in the complex plane.
This analysis provides a comprehensive understanding of the propagation vector in a dielectric medium with a given dielectric constant.
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In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by?
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In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by?.
In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by?.
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