A new method to calculate the electric field inside a spherical shell with surface charge σ = σ _o  cos θ in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical problem. For a flat surface of uniform charge density, the electric field normal to the surface is shown to be proportional to the solid angle subtended by the surface only.

中文翻译：

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一种利用立体角计算电场的新方法

提出了一种根据立体角计算具有表面电荷σ = σ _o  cos  θ的球壳内电场的新方法。无需调用通常用于此经典问题的特殊函数即可轻松执行积分。对于电荷密度均匀的平坦表面，垂直于表面的电场仅与表面所对的立体角成正比。