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A parallel plate capacitor with electrodes of circular area A (radius of ro) has its upper electrode in solid dielectric (region #2) with permittivity, 82 and thickness, h. This dielectric is in series with solid dielectric (region #1) with permittivity, & and thickness, d, as shown in Figure below. The dielectrics interface has no free surface charge and & » (d + h). Given the relationship between E, and E₂ is E₁ = ₂, by assuming electric field orientation in both dielectrics is perpendicular with respect to the dielectric's boundary. d 82 €1 Area A Figure 1. Write the potential difference between the electrode plates, V. in terms of E₁. 2. Find the inner surface charge density on the lower electrode in terms of V.. 3. Write the capacitance for this structure in terms of dielectric permittivity, dielectric thickness and radius of electrode plate.

A parallel plate capacitor with electrodes of circular area A (radius of ro) has its upper electrode in solid dielectric (region #2) with permittivity, 82 and thickness, h. This dielectric is in series with solid dielectric (region #1) with permittivity, & and thickness, d, as shown in Figure below. The dielectrics interface has no free surface charge and & » (d + h). Given the relationship between E, and E₂ is E₁ = ₂, by assuming electric field orientation in both dielectrics is perpendicular with respect to the dielectric's boundary. d 82 €1 Area A Figure 1. Write the potential difference between the electrode plates, V. in terms of E₁. 2. Find the inner surface charge density on the lower electrode in terms of V.. 3. Write the capacitance for this structure in terms of dielectric permittivity, dielectric thickness and radius of electrode plate.

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A parallel plate capacitor with electrodes of circular area A (radius of r.) has its upper electrode in solid dielectric (region # 2) with permittivity, &₂ and thickness, h. This dielectric is in series with solid dielectric (region #1) with permittivity, & and thickness, d, as shown in Figure below. The dielectrics interface has no free surface charge and & » (d + h). Given the relationship between E₁ and E₂ is Ē₁ = ²₂, by assuming electric field orientation in both dielectrics is perpendicular with respect to the dielectric's boundary. E1 82 81 Area A Figure 1. Write the potential difference between the electrode plates, V. in terms of E₁. 2. Find the inner surface charge density on the lower electrode in terms of V₁. 3. Write the capacitance for this structure in terms of dielectric permittivity, dielectric thickness and radius of electrode plate.
Transcribed Image Text:A parallel plate capacitor with electrodes of circular area A (radius of r.) has its upper electrode in solid dielectric (region # 2) with permittivity, &₂ and thickness, h. This dielectric is in series with solid dielectric (region #1) with permittivity, & and thickness, d, as shown in Figure below. The dielectrics interface has no free surface charge and & » (d + h). Given the relationship between E₁ and E₂ is Ē₁ = ²₂, by assuming electric field orientation in both dielectrics is perpendicular with respect to the dielectric's boundary. E1 82 81 Area A Figure 1. Write the potential difference between the electrode plates, V. in terms of E₁. 2. Find the inner surface charge density on the lower electrode in terms of V₁. 3. Write the capacitance for this structure in terms of dielectric permittivity, dielectric thickness and radius of electrode plate.
Formula: Capacitance, C = Potential difference, VAB = -√ E. dĺ Boundary condition normal component, D₁n - D₂n = Ps Boundary condition tangential component, E₁t = Ezt
Transcribed Image Text:Formula: Capacitance, C = Potential difference, VAB = -√ E. dĺ Boundary condition normal component, D₁n - D₂n = Ps Boundary condition tangential component, E₁t = Ezt
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