Application of a generalized Leibniz rule for calculating electromagnetic fields within continuous source regions
Article first published online: 7 DEC 2012
This paper is not subject to U.S. copyright. Published in 1991 by the American Geophysical Union.
Volume 26, Issue 1, pages 183–190, January-February 1991
How to Cite
1991), Application of a generalized Leibniz rule for calculating electromagnetic fields within continuous source regions, Radio Sci., 26(1), 183–190, doi:10.1029/89RS03057.(
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 27 SEP 1989
- Manuscript Received: 5 FEB 1989
In deriving the electric and magnetic fields in a continuous source region by differentiating the vector potential, Yaghjian (1985) explains that the central obstacle is the dependence of the integration limits on the differentiation variable. Since it is not mathematically rigorous to assume the curl and integral signs are interchangeable, he uses an integration variable substitution to circumvent this problematic dependence. Here, we present an alternative derivation, which evaluates the curl of the vector potential volume integral directly, retaining the dependence of the limits of integration on the differentiation variable. It involves deriving a three-dimensional version of Leibniz' rule for differentiating an integral with variable limits of integration, and using the generalized rule to find the Maxwellian and cavity fields in the source region.