Electrostatic Shielding of a Charged Conducting Sphere by a Fine-Mesh Grounded Screen

The physical system considered is a charged conducting sphere held at a fixed absolute potential via a battery or some other power source. Another sphere, concentric with and larger than the first, is fabricated out of a fine-mesh screen and this outer screen is grounded. The objective is to calculate the effectiveness of the screen in reducing the electrostatic field at points outside of the system. A derivation based on elementary principles of electrostatics will show that the shielding effectiveness of the screen can be expressed in terms of the separation between the two spheres and another quantity, represented in the paper by B, that is an intrinsic property of the screen. Approximations will be used that require the screen to have a mesh size that is fine compared to other dimensions of the system. In particular, characteristic distances between mesh wires must be smaller (by an amount that was not numerically evaluated in this paper) than the separation between the charged sphere and the spherical screen shield. For a sufficiently simple mesh weave, B can be calculated. More generally, B for a given screen can be measured by measuring the capacitance per unit area and separation between a flat piece of the screen and a parallel metal plate. This method of measuring B is described in the report.