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Transcribed Image Text:### Problem Statement
A 10 GHz uniform plane wave is propagating along the +z direction, in a material such that the parameters are given as follows:
- Relative permittivity (\(\epsilon_r\)) = 81
- Relative permeability (\(\mu_r\)) = 1
- Conductivity (\(\sigma\)) = 2 mho/m
**Questions:**
a) (20 points) Find the values of \(\gamma\), \(\alpha\), and \(\beta\).
b) (10 points) Find the intrinsic impedance.
c) (20 points) Write the phasor form of electric and magnetic fields, if the amplitude of the electric field intensity is 0.5 V/m.
### Solution Steps
**a) Determine \(\gamma\), \(\alpha\), and \(\beta\):**
- \(\gamma\) is the propagation constant.
- \(\alpha\) is the attenuation constant.
- \(\beta\) is the phase constant.
**b) Calculate the intrinsic impedance (η):**
The intrinsic impedance (\(\eta\)) of the given material can be found using the following formulas and given parameters.
**c) Phasor Form of Fields:**
Write the phasor form of the electric (\(\mathbf{E}\)) and magnetic (\(\mathbf{H}\)) fields given the amplitude of the electric field intensity.
Make sure to apply the appropriate formulas and conversions for the calculations.
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