# 329lect09 - 9 Static fields in dielectric media •...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

## 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.

### Page1 / 8

329lect09 - 9 Static fields in dielectric media •...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online