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A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium is given by?
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A plane electromagnetic wave given by E = 85 course bracket 4 into 10 ...
Understanding the Electromagnetic Wave Equation
The given electromagnetic wave is described by the electric field \( E = 85 \cos(4 \times 10^8 t - 2z) \). This equation indicates a plane wave traveling in the \( z \)-direction.
Wave Characteristics
- **Angular Frequency (\( \omega \))**: From the equation, \( \omega = 4 \times 10^8 \) rad/s.
- **Wave Number (\( k \))**: The wave number is \( k = 2 \) rad/m.
Relationship Between Properties
In an isotropic magnetic dielectric medium, the relationship between the speed of light \( c \), the relative permittivity \( \varepsilon_r \), and the relative permeability \( \mu_r \) can be expressed as:
\[
c = \frac{1}{\sqrt{\varepsilon \mu}}
\]
Where \( \varepsilon = \varepsilon_0 \varepsilon_r \) and \( \mu = \mu_0 \mu_r \).
Finding the Speed of Light
The speed of the wave \( v \) can be calculated using:
\[
v = \frac{\omega}{k}
\]
Substituting the values:
\[
v = \frac{4 \times 10^8}{2} = 2 \times 10^8 \text{ m/s}
\]
Relative Permeability Calculation
The speed of light in vacuum is \( c_0 \approx 3 \times 10^8 \text{ m/s} \). The relationship between \( c \) and the medium's properties is:
\[
\frac{1}{\sqrt{\varepsilon_r \mu_r}} = v
\]
Squaring both sides:
\[
\frac{1}{\varepsilon_r \mu_r} = v^2
\]
Thus, rearranging gives:
\[
\mu_r = \frac{1}{\varepsilon_r v^2}
\]
Given that \( v \) is known, if \( \varepsilon_r \) is also known, you can easily compute \( \mu_r \).
Conclusion
To determine the relative permeability \( \mu_r \), the value of relative permittivity \( \varepsilon_r \) is essential. This relationship allows for deeper analysis of the properties of the isotropic magnetic dielectric medium in which the wave propagates.
The given electromagnetic wave is described by the electric field \( E = 85 \cos(4 \times 10^8 t - 2z) \). This equation indicates a plane wave traveling in the \( z \)-direction.
Wave Characteristics
- **Angular Frequency (\( \omega \))**: From the equation, \( \omega = 4 \times 10^8 \) rad/s.
- **Wave Number (\( k \))**: The wave number is \( k = 2 \) rad/m.
Relationship Between Properties
In an isotropic magnetic dielectric medium, the relationship between the speed of light \( c \), the relative permittivity \( \varepsilon_r \), and the relative permeability \( \mu_r \) can be expressed as:
\[
c = \frac{1}{\sqrt{\varepsilon \mu}}
\]
Where \( \varepsilon = \varepsilon_0 \varepsilon_r \) and \( \mu = \mu_0 \mu_r \).
Finding the Speed of Light
The speed of the wave \( v \) can be calculated using:
\[
v = \frac{\omega}{k}
\]
Substituting the values:
\[
v = \frac{4 \times 10^8}{2} = 2 \times 10^8 \text{ m/s}
\]
Relative Permeability Calculation
The speed of light in vacuum is \( c_0 \approx 3 \times 10^8 \text{ m/s} \). The relationship between \( c \) and the medium's properties is:
\[
\frac{1}{\sqrt{\varepsilon_r \mu_r}} = v
\]
Squaring both sides:
\[
\frac{1}{\varepsilon_r \mu_r} = v^2
\]
Thus, rearranging gives:
\[
\mu_r = \frac{1}{\varepsilon_r v^2}
\]
Given that \( v \) is known, if \( \varepsilon_r \) is also known, you can easily compute \( \mu_r \).
Conclusion
To determine the relative permeability \( \mu_r \), the value of relative permittivity \( \varepsilon_r \) is essential. This relationship allows for deeper analysis of the properties of the isotropic magnetic dielectric medium in which the wave propagates.
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A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium is given by?
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A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium 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 A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium is given by? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium is given by?.
A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium 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 A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium is given by? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane electromagnetic wave given by E = 85 course bracket 4 into 10 to the power 8 in multiplied by t - 2z travelling in an isotropic magnetic dielectric medium the relative permeability of a medium is given by?.
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