Electromagnetic Fields Excited in Volumes with Spherical Boundaries by Yuriy M. Penkin & Victor A. Katrich & Mikhail V. Nesterenko & Sergey L. Berdnik & Victor M. Dakhov

Author:Yuriy M. Penkin & Victor A. Katrich & Mikhail V. Nesterenko & Sergey L. Berdnik & Victor M. Dakhov
Language: eng
Format: epub
ISBN: 9783319978192
Publisher: Springer International Publishing

4.1 Radiation Fields of Dipoles Located on Perfectly Conducting Sphere

4.1.1 Fields of Radial Electric Dipole

Consider a perfectly conducting sphere, excited by radially oriented elementary electric dipole located in an isotropic homogeneous medium (Fig. 3.​1). The sphere radius is R and medium parameters are and . The density of the dipole current is defined by (4.1) under conditions and . Then, using the expressions (1.​45) for the Green’s tensor components and the functions (3.​7), we can write, in accordance with (1.​30), the radial component of the electric Hertz vector in the form (3.​17) with the complex amplitude .

The magnetic fields can be conveniently found if the Hertz vector of the electric type is used, while the electric fields can found using the magnetic Hertz vector. Hereafter, we will follow this choice. Of course, expressions for all other components of the electromagnetic field can be easily determined.

According to (1.​8), the components of the magnetic field and can be determined using the formulas (2.​14), and the field is zero, since the exciting field is of the electric type. Expressions for and can be written as,

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