Gauss's equation, commonly known as Gauss's Law, is one of the fundamental equations in electromagnetism. It's part of Maxwell's equations and describes the relationship between electric flux through a closed surface and the electric charge enclosed within that surface. The law states that the electric flux is proportional to the enclosed charge.
高斯定律的积分形式表明，通过任何闭合曲面的电通量等于被包围的电荷除以真空介电常数。左边表示电场与面积元矢量的点积的面积分。右边显示被包围的电荷除以介电常数ε₀。
高斯定律的微分形式表明电场的散度等于电荷密度除以真空介电常数。散度描述了电场在某点的发散程度。正电荷处电场向外发散，散度为正；负电荷处电场向内汇聚，散度为负。这个形式更适合分析连续分布的电荷。
高斯定律在实际应用中非常重要。对于球对称的电荷分布，我们可以选择同心球面作为高斯面。由于对称性，电场在球面上处处相等且垂直于表面。通过高斯定律可以直接得出库仑定律的形式。这种方法在分析导体、电容器和电磁屏蔽等问题中都有广泛应用。