This paper presents a derivation for a general formula relating the first derivative of the electric-field intensity in any direction to the first derivative of the direction cosines in the orthogonal direction. A restricted form of the formula valid only in the direction of the field lines was first stated by Thomson, and later proved by others. The general form proved here promises to be useful in other attempts to apply techniques of differential geometry to the rapid solution of field problems.
Related links
Details
Title
Generalized formula for the first derivative of the electric-field intensity
Publication Details
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, Vol.47(5), pp.3682-3685