Between the top and bottom conducting plates of a parallel-plate capacitor, with a distance of d,...

 

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Between the top and bottom conducting plates of a parallel-plate capacitor, with a distance of d, the plates are maintained at potentials VO and 0, respectively. Between the plates, there is a dielectric piece with a thickness of d, length a, and width w. The dielectric constant &(y) of the material varies depending on position and is given by the following function: € (y) - [EoEr1 [€0 €r2 0≤x≤ a ; 0 ≤x≤a ; 0 ≤ y≤ 0.3d 0.3d < y ≤d Assuming edge effects are neglected, and considering the regions: 0 ≤ y ≤ 0.3d 0.3d < y ≤ d a) Draw the geometry of the problem in the Cartesian coordinate system. b) Write the boundary conditions and find the electric potential V, electric field strength E, electric flux density D, and polarization vector in each region of the dielectric. c) Calculate the capacitance of this capacitor. d) Determine the surface charge densities on the upper and lower plates. Between the top and bottom conducting plates of a parallel-plate capacitor, with a distance of d, the plates are maintained at potentials VO and 0, respectively. Between the plates, there is a dielectric piece with a thickness of d, length a, and width w. The dielectric constant &(y) of the material varies depending on position and is given by the following function: € (y) - [EoEr1 [€0 €r2 0≤x≤ a ; 0 ≤x≤a ; 0 ≤ y≤ 0.3d 0.3d < y ≤d Assuming edge effects are neglected, and considering the regions: 0 ≤ y ≤ 0.3d 0.3d < y ≤ d a) Draw the geometry of the problem in the Cartesian coordinate system. b) Write the boundary conditions and find the electric potential V, electric field strength E, electric flux density D, and polarization vector in each region of the dielectric. c) Calculate the capacitance of this capacitor. d) Determine the surface charge densities on the upper and lower plates.