Application of a generalized Leibniz rule for calculating electromagnetic fields within continuous source regions

Journal Article · Fri Feb 01 00:00:00 EST 1991 · Radio Science; (USA)

DOI:https://doi.org/10.1029/89RS03057· OSTI ID:5751286

Silberstein, M ^[1]

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1. USAF, Rome Air Development Center, Hanscom AFB, MA (USA)

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, an alternative derivation is presented, 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. 7 refs.

• OSTI ID: 5751286
• Journal Information: Radio Science; (USA), Vol. 26; ISSN 0048-6604
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ELECTROMAGNETIC FIELDS
CALCULATION METHODS
ELECTRIC FIELDS
INTEGRAL EQUATIONS
MAGNETIC FIELDS
MATHEMATICAL OPERATORS
MAXWELL EQUATIONS
POLARIZATION
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
657000* - Theoretical & Mathematical Physics