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Conductors and dielectrics in an electric field

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  • Electric field strength near the surface of a conductor in vacuum: $$E_n = \frac{\sigma}{{\varepsilon}_0}$$
  • Flux of polarization P across a closed surface: $$\oint P\, dS=-q',$$ where q' is the algebraic sum of bound charges enclosed by this surface.
  • Vector D and Gauss's theorem for it:$$D=\varepsilon E+P, \oint D\, dS=q,$$where q is the algebraic sum of extraneous charges inside a closed surface.
  • Relations at the boundary between two dielectrics:$$P_{2n}- P_{1n}=-{\sigma}',D_{2n}-D_{1n}=\sigma, E_{2\tau}=E_{1\tau}$$where a' and a are the surface densities of bound and extraneous charges, and the unit vector n of the normal is directed from medium 1 to medium 2.
  • In isotropic dielectrics:$$P=x{\varepsilon}_0 E, D=\varepsilon {\varepsilon}_0 E, \varepsilon =1+x.$$
  • In the case of an isotropic uniform dielectric filling up all the space between the equipotential surfaces:$$E=\frac{E_0}{\varepsilon}.$$

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