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A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25?
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A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 nco...
Understanding Electromagnetic Waves
Electromagnetic waves consist of electric (E) and magnetic (H) fields that oscillate perpendicular to each other and the direction of wave propagation. In an isotropic dielectric medium, the relationship between these fields is governed by the material's permittivity (ε) and permeability (µ).
Given Parameters
- Magnetic Field: H = 0.5 cos(4 × 10^8 t - 2z) A/m
- Electric Field: E = 80 cos(4 × 10^8 t - 2z) V/m
Wave Propagation Relationships
In a dielectric medium, the speed of light (c) is given by:
\[ c = \frac{1}{\sqrt{\mu \epsilon}} \]
Where:
- \( \mu \) = permeability
- \( \epsilon \) = permittivity
The wave number (k) is related to the frequency (f) and the speed of light:
\[ k = \frac{\omega}{c} \]
With \( \omega = 4 × 10^8 \) rad/s, we can calculate k:
\[ k = 2 \: \text{(from the wave equation)} \]
This shows that:
\[ c = \frac{4 × 10^8}{2} = 2 × 10^8 \: \text{m/s} \]
Calculating Permeability and Permittivity
Using the speed of light in vacuum \( c_0 = 3 × 10^8 \) m/s:
\[ \frac{1}{\sqrt{\mu \epsilon}} = 2 × 10^8 \]
Squaring both sides:
\[ \mu \epsilon = \frac{1}{(2 × 10^8)^2} = 2.5 × 10^{-17} \]
The permittivity of free space \( \epsilon_0 \) is approximately \( 8.85 × 10^{-12} \) F/m.
Thus:
\[ \mu = \frac{2.5 × 10^{-17}}{8.85 × 10^{-12}} = 2.83 × 10^{-6} \: \text{H/m} \]
Using the relative permeability \( \mu_r = \frac{\mu}{\mu_0} \) with \( \mu_0 \approx 4π × 10^{-7} \):
\[ \mu_r = \frac{2.83 × 10^{-6}}{4π × 10^{-7}} \approx 2.25 \]
Conclusion
The relative permeability \( \mu_r \) of the medium is approximately **2.25**.
Electromagnetic waves consist of electric (E) and magnetic (H) fields that oscillate perpendicular to each other and the direction of wave propagation. In an isotropic dielectric medium, the relationship between these fields is governed by the material's permittivity (ε) and permeability (µ).
Given Parameters
- Magnetic Field: H = 0.5 cos(4 × 10^8 t - 2z) A/m
- Electric Field: E = 80 cos(4 × 10^8 t - 2z) V/m
Wave Propagation Relationships
In a dielectric medium, the speed of light (c) is given by:
\[ c = \frac{1}{\sqrt{\mu \epsilon}} \]
Where:
- \( \mu \) = permeability
- \( \epsilon \) = permittivity
The wave number (k) is related to the frequency (f) and the speed of light:
\[ k = \frac{\omega}{c} \]
With \( \omega = 4 × 10^8 \) rad/s, we can calculate k:
\[ k = 2 \: \text{(from the wave equation)} \]
This shows that:
\[ c = \frac{4 × 10^8}{2} = 2 × 10^8 \: \text{m/s} \]
Calculating Permeability and Permittivity
Using the speed of light in vacuum \( c_0 = 3 × 10^8 \) m/s:
\[ \frac{1}{\sqrt{\mu \epsilon}} = 2 × 10^8 \]
Squaring both sides:
\[ \mu \epsilon = \frac{1}{(2 × 10^8)^2} = 2.5 × 10^{-17} \]
The permittivity of free space \( \epsilon_0 \) is approximately \( 8.85 × 10^{-12} \) F/m.
Thus:
\[ \mu = \frac{2.5 × 10^{-17}}{8.85 × 10^{-12}} = 2.83 × 10^{-6} \: \text{H/m} \]
Using the relative permeability \( \mu_r = \frac{\mu}{\mu_0} \) with \( \mu_0 \approx 4π × 10^{-7} \):
\[ \mu_r = \frac{2.83 × 10^{-6}}{4π × 10^{-7}} \approx 2.25 \]
Conclusion
The relative permeability \( \mu_r \) of the medium is approximately **2.25**.
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A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25?
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A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25?.
A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane electromagnetic wave with H=0.5cos(4x10^8t-2z) A/m; E = 80 ncos (4×10^8t-2z) V/m travelling in an isotropic magnetic dielectric medium. The relative permeability (µ.) of medium is:2 or 2.25?.
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