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# Lecture 9 - 9 Static fields in dielectric media Summarizing...

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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

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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?
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