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Unformatted text preview: 9 Static fields in dielectric media • Summarizing important results from last lecture: – within a dielectric medium, displacement D = E = o E + P , and if the permittivity = r o is known, D and E can be calcu- lated from free surface charge ρ s or volume charge ρ in the region without resorting to P . – on surfaces separating perfect dielectrics, ˆ n · ( D +- D- ) = 0 typ- ically, while ˆ n · D + = ρ s on a conductor-dielectric interface (with ˆ n pointing from the conductor toward the dielectric). ˆ n D + D- – Gauss’s law ∇· D = ρ (and its integral counterpart) includes only the free charge density on its right side, which is typically zero in many practical problems. – once D and E have been calculated (typically using the boundary condition equations), polarization P can be obtained as P = D- o E if needed. These rules will be used in the examples in this section. 1 z x E = 18ˆ x E = 18ˆ x E = 3ˆ x = o = o = r o Example 1: A perfect dielectric slab having a finite thickness W in the x direction is surrounded by free space and has a constant electric field E = 18ˆ x V/m in its exterior. Induced polarization of bound charges inside dielectric reduces the electric field strength inside the slab from 18ˆ x V/m to E = 3ˆ x V/m. What are the displacement field D and polarization P outside and inside the slab, and what are the dielectric constant r and electric susceptibility χ e of the slab? Solution: Displacement field outside the slab, where = o , must be D = o E = ˆ x 18 o C m 2 . The outside polarization P is of course zero. Boundary conditions at the interface of the slab with free space require the continuity of normal component of D and tangential component of E — both of these conditions would be satisfied if we were to take D = ˆ x 18 o C/m 2 also within the dielectric slab. Thus, with E = 3ˆ x V/m inside the slab, the condition D = slab E within the slab requires that slab = 6 o ....
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This note was uploaded on 01/22/2011 for the course ECE 410 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08