Question

3. Two dielectric materials (material 1 and 2) are combined either in series (Case A) or parallel (Case B) arrangements as shown in the figure below. The relative permittivity for material one is 10 while the relative permittivity for material two is 3000. A voltage of 100 volts is applied across the entire the top surface while the bottom is grounded (0 Volts) in both cases. The z- direction is up with z-0 representing the bottom ground. Calculate for each case the electric field Ez, the flux-density Dz, and polarization Pz in both materials for both cases. You may assume that the vertical z-dimensions of each material cube is 100 microns and you may treat this as a simple 1-D problem in the z direction Case A Case B 100 V 100 V 200 microns 1 2 2 O volt O volt N

Answer 1

E,E,Ald Case A foov nuecar Ci au A 3000 in are 2 ha0 3 In 3 0D Abo y /0o (2 (2 0.232V forom 4 301 co V299 668v 99.668 V O.33 2 O.332 toon 8-854xo IOx99.668XTO' 2 186 xIO 8-854x10 30co O.332x1o - (G-) S4RIO y 77.663 2 29179 g.8ScrAIOx O.332xIo = 88.1S7 x m

Ca se B 二100 v Jorpen E 二10V -2 8-854メ10 メ10メ0°ニ8-854XIO D E B8 54X10 C/m -8-854メ10 メ3000以10° 26.562×10た/mレ - /2- 9メ8854メ10 ×10 子9.686 メ10 2999メ8-85y 26 SS 3IO