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Electrostatic boundary conditions at a conductor

A Gaussian pillbox gives

(E_{out} - E_{in}) \cdot n = \frac{σ}{ϵ _{0}} .

Since

E_{in} = 0

, the surface charge density is

σ = ϵ_{0} E_{out} \cdot n

.

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- Surface charge density Electrostatic boundary conditions at a conductor 29

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Electrostatic boundary condition