Question

Answer number 2 using the given hints. Thanks

1. For the given capacitor, there are conducting plates at z = 0 and 2 = 3d. Between the plates, there are 3 layers of insulators: 2 free space regions and one dielectric with permittivity e. The electric field in Region 1 is E = - a, (V/m), where Ps is the surface charge density on the top plate ( = 30). The surface area of each plate is A. (a) What is the electric field E, in region II? The answer is an expression in terms of ps. (b) What is the capacitance of the entire structure? Area A 1 € II 2€ III € " Area A 2. For the given capacitor, there are conducting plates at z = 0 and h. There are two insulators between the plates: Region I is free space with permittivity of Eg and Region II has permittivity 2€0. Both regions have area A. A total charge of + is on the top plate and on the bottom. (a) What are the electric field vectors E, E, in Regions I and II in terms of the surface charge densities Psi and Psi, respectively? (b) Using the tangential field boundary conditions at the interface between the two regions, how are Ps, and Ps related? Your answer for this part should be something like "Psn = — Psi". (c) What fraction of the total charge + is on the plate in Region 1? (d) What is the total capacitance? Area A Area A + € II 2€0 HINTS: One approach to these problems is to use boundary conditions extensively: the normal boundary conditions (both dielectric/pec and dielectric/dielectric) and tangential (dielectric/dielectric). Assume all fields are oriented in the -a, direction and neglect fringing. Assume all surface charge densities are uniform Ps= Q = PSA. When finding V integrate from the bottom plate to the top.

Answer 1

de Q Hw (a) en : E = LEO Pogi-žio . tangential field component of electric over the surface. Continuous so. Elli = 6211 (0) Charge on Region I - sitA charge on Region I' Psa+A = 2BSITA So, Region I has PsixA Ssit A + APS* A

traction of charge = 1/2 - part of total charge would be on plate of region 1. (d) Region I - a=0 Region a - O2 = 20 REA 6 = EA = do A / using parallel combination : Ceq = Citla ETA (1+2) 2 367 38A
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