Gaussian Surfaces

Part of the power of Gauss' law in evaluating electric fields is that it applies to any surface. It is often convenient to construct an imaginary surface called a Gaussian surface to take advantage of the symmetry of the physical situation.

If the symmetry is such that you can find a surface on which the electric field is constant, then evaluating the electric flux can be done by just multiplying the value of the field times the area of the Gaussian surface.

Conductor at Equilibrium

For a conductor at equilibrium: 对于处于平衡状态的导体：

1. The net electric charge of a conductor resides entirely on its surface. (The mutual repulsion of like charges from Coulomb's Law demands that the charges be as far apart as possible, hence on the surface of the conductor.)

2. The electric field inside the conductor is zero. (Any net electric field in the conductor would cause charge to move since it is abundant and mobile. This violates the condition of equilibrium: net force = 0.)

3. The external electric field at the surface of the conductor is perpendicular to that surface. (If there were a field component parallel to the surface, it would cause mobile charge to move along the surface, in violation of the assumption of equilibrium.)

Electric Field: Conductor Surface

The fact that the conductor is at equilibrium is an important constraint in this problem. It tells us that the field is perpendicular to the surface, because otherwise it would exert a force parallel to the surface and produce charge motion. Likewise it tells us that the field in the interior of the conductor is zero, since otherwise charge would be moving and not at equilibrium. 导体处于平衡状态这一事实是本题的重要约束条件。它告诉我们电场垂直于表面，否则电场将沿着表面施加力，导致电荷运动。同样，它也告诉我们导体内部的电场为零，否则电荷将运动，而无法处于平衡状态。

Examining the nature of the electric field near a conducting surface is an important application of Gauss' law. Considering a cylindrical Gaussian surface oriented perpendicular to the surface, it can be seen that the only contribution to the electric flux is through the top of the Gaussian surface. The flux is given by 考察导体表面附近的电场性质是高斯定律的重要应用。考虑一个垂直于表面的圆柱形高斯面，可以发现高斯面上的电通量仅通过顶部贡献。电通量由以下公式给出： and the electric field is simply 并且电场 simply 是 While strictly true only for an infinite conductor, it tells us the limiting value as we approach any conductor at equilibrium. 虽然严格来说仅适用于无限大导体，但它告诉我们接近平衡状态下的任何导体的极限值。