Electric Field of Point Charge

索引电场概念

HyperPhysics ***** 电学和磁学

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Potential of conducting sphere

Electric Field of Conducting Sphere

导体球的电场

The electric field of a conducting sphere with charge Q can be obtained by a straightforward application of Gauss' law. Considering a Gaussian surface in the form of a sphere at radius r > R , the electric field has the same magnitude at every point of the surface and is directed outward. The electric flux is then just the electric field times the area of the spherical surface.

带电荷量为Q的导体球的电场可通过直接应用高斯定律获得。考虑一个半径为r > R的球形高斯面，高斯面上每一点的电场大小相同，方向向外。因此，电通量就是电场强度乘以球面的面积。

The electric field is seen to be identical to that of a point charge Q at the center of the sphere. Since all the charge will reside on the conducting surface, a Gaussian surface at r< R will enclose no charge, and by its symmetry can be seen to be zero at all points inside the spherical conductor

电场被看到与位于球心的点电荷Q的电场相同。由于所有电荷都将分布在导体表面，位于r < R的高斯面将不包含任何电荷，且由于其对称性，可看出在球形导体内部的所有点处电场均为零。

Point charge

点电荷

Sphere of uniform charge

均匀电荷球

导体球的电势

Fields for other charge geometries

其他电荷几何形状的场

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HyperPhysics ***** 电学和磁学

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Charged conducting sphere

Electric Field: Sphere of Uniform Charge

电场：均匀电荷的球域

The electric field of a sphere of uniform charge density and total charge charge Q can be obtained by applying Gauss' law. Considering a Gaussian surface in the form of a sphere at radius r > R, the electric field has the same magnitude at every point of the surface and is directed outward. The electric flux is then just the electric field times the area of the spherical surface.

一个均匀带电密度且总电荷为Q的球体的电场可通过应用高斯定律得到。考虑一个半径为r > R的球形高斯面，高斯面上每一点的电场大小相同，方向向外。因此，电通量就是电场与球面面积的乘积。

The electric field outside the sphere (r > R)is seen to be identical to that of a point charge Q at the center of the sphere.

在球体外（r > R）的电场看起来与球心处一个点电荷Q的电场相同。

For a radius r < R, a Gaussian surface will enclose less than the total charge and the electric field will be less. Inside the sphere of charge, the field is given by:

对于半径 r < R 的情况，高斯面将包围的总电荷少于全部电荷，因此电场会更小。在带电球体内，电场由下式给出：

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Point charge

点电荷

带电导体球

Fields for other charge geometries

其他电荷几何形状的场

索引电场概念

HyperPhysics ***** 电学和磁学

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Field outside charged sphere

Inside a Sphere of Charge

在带电球体内

The electric field inside a sphere of uniform charge is radially outward (by symmetry), but a spherical Gaussian surface would enclose less than the total charge Q. The charge inside a radius r is given by the ratio of the volumes:

带电球体内电场方向径向向外（由对称性决定），但一个球形高斯面所包围的电荷量小于总电荷Q。半径为r处的电荷量由体积比给出：

The electric flux is then given by

电通量则由以下公式给出

and the electric field is

并且电场是

Note that the limit at r= R agrees with the expression for r >= R. The spherically symmetric charge outside the radius r does not affect the electric field at r. It follows that inside a spherical shell of charge, you would have zero electric field.

注意当r=R时的极限与r≥R时的表达式一致。位于半径r之外的球形电荷不对r处的电场产生影响。因此，在带电球壳内部，电场为零。

带电球体外的电场

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HyperPhysics ***** 电学和磁学

R Nave