Analytical Expression of the Electric Field Induced by Uniformly Charged 3D Plates

Abstract

This paper establishes the analytical expression of the electric field induced by a uniformly charged plate (parallelepiped), which is useful for describing more complex configurations by addition of uniformly charged parallelepiped. Examples of applications involve capacitors (electrical engineering) and electrochemotherapy (medicine). The asymptotic behavior, at the origin and far away from the plates, is firstly discussed, followed by a comparison with an existing software, and finally the electric field (vector field and magnitude) is shown for two 3D orthogonal plates with equal or opposite charge density.