“Gauss’s theorem”的概念、定义、翻译、参考文献-科学参考

Gauss’s theorem

Electronics and Electrical Engineering

The normal electric field strength, E, over a closed surface containing electric charges is given by
$\int E . d S = \frac{Σ q}{ε_{0}}$
where dS is a small element of area on the surface S, ε₀ is the permittivity of free space, and Σq the total charge enclosed within the surface.
If the volume enclosed by the surface contains a distributed charge density, ρ_e, Gauss’s theorem becomes
$\int E . d S = (\frac{1}{ε_{0}}) \int ρ_{e} dτ$
where dτ is a small volume element. Since
$\int E . d S = \int div E dτ$
then
$div E = \frac{ρ_{e}}{ε_{0}}$
In a dielectric medium the total charge density includes an apparent charge density due to polarization of the atoms or molecules within the medium and Gauss’s theorem becomes
$div D = ρ_{e}$
where D is the electric displacement. This is one of Maxwell’s equations.
Two main conclusions can be drawn from Gauss’s theorem. Firstly, the electric field inside a hollow conductor containing no charge is zero, the enclosed space being at the same potential as the conductor: electrical apparatus can therefore be shielded from the effect of external low-frequency electric fields by surrounding it with an earthed conductor. Secondly, any excess static charge on a conductor must reside on the outer surface.

单词	Gauss’s theorem
释义	Gauss’s theorem Electronics and Electrical Engineering The normal electric field strength, E, over a closed surface containing electric charges is given by $\int E . d S = \frac{Σ q}{ε_{0}}$ where dS is a small element of area on the surface S, ε₀ is the permittivity of free space, and Σq the total charge enclosed within the surface. If the volume enclosed by the surface contains a distributed charge density, ρ_e, Gauss’s theorem becomes $\int E . d S = (\frac{1}{ε_{0}}) \int ρ_{e} dτ$ where dτ is a small volume element. Since $\int E . d S = \int div E dτ$ then $div E = \frac{ρ_{e}}{ε_{0}}$ In a dielectric medium the total charge density includes an apparent charge density due to polarization of the atoms or molecules within the medium and Gauss’s theorem becomes $div D = ρ_{e}$ where D is the electric displacement. This is one of Maxwell’s equations. Two main conclusions can be drawn from Gauss’s theorem. Firstly, the electric field inside a hollow conductor containing no charge is zero, the enclosed space being at the same potential as the conductor: electrical apparatus can therefore be shielded from the effect of external low-frequency electric fields by surrounding it with an earthed conductor. Secondly, any excess static charge on a conductor must reside on the outer surface.
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