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By Klaus Kark

ISBN-10: 3834802166

ISBN-13: 9783834802163

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Example text

8). 44) B (U) BM (U) e M P eM 2 SU gegeben mit U als radialem Abstand von der z-Achse. Berechnen Sie die Divergenz div B . 1. Damit wird die Divergenz eines in Zylinderkoordinaten gegebenen Vektorfelds B (U, M , z ) : div B § w w · 1 w ¨¨ e U ¸ ˜ BU eU (M)  BM e M (M)  Bz e z . 45) Bevor die Skalarprodukte ausgeführt werden können, müssen zuerst die partiellen Ableitungen berechnet werden. 46) w e U wBM w e M wBz § wBU · 1  e M ˜ ¨¨   e U  BU e M  BM e z ¸¸ . 1 noch eleganter schreiben kann: div B 3 w § h1 h2 h3 · 1 Bi ¸ .

5 Kartesische11, kreiszylindrische und sphärische Koordinaten [Wol68] sowie ihre Einheitsvektoren Rechtssysteme kartes. Koordinaten œ Zylinderkoordinaten œ Kugelkoordinaten x y z U cos M U sin M z r sin - cos M r sin - sin M r cos - ex e U cos M  e M sin M e r sin - cos M  e - cos - cos M  e M sin M ey e U sin M  e M cos M e r sin - sin M  e - cos - sin M  e M cos M ez ez e r cos -  e - sin - x2  y2 U r sin - M M z r cos - e x cos M  e y sin M eU e r sin -  e - cos -  e x sin M  e y cos M eM eM ez ez e r cos -  e - sin - arctan 0 d M  2S y x z x2  y2  z2 arctan x2  y2 z arctan 0 d M  2S 0d-dS y x U2  z 2 r U z - arctan M M e x sin - cos M  e y sin - sin M  e z cos- eU sin -  e z cos- er e x cos - cosM  e y cos- sin M  e z sin - eU cos-  e z sin - e- eM eM  e x sin M  e y cosM 11 René Descartes (1596-1650), lat.

3. 6 Rand- und Stetigkeitsbedingungen 43 Dabei ist J F eine in der Grenzfläche induzierte elektrische Flächenstromdichte, die in A m gemessen wird und U ist eine in C m 2 gemessene influenzierte elektrische FlächenladungsF dichte. An der Oberfläche eines idealen elektrischen Leiters stehen also elektrische Feldlinien senkrecht, während magnetische Feldlinien parallel verlaufen müssen, sodass auf einer metallischen Wand stets E2 ˜ B 2 0 gilt. Diese Tatsache kann mit Hilfe der lokalen Flächennormalen n wie folgt ausgedrückt werden: n u E2 0 n ˜ B2 0.

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Antennen und Strahlungsfelder by Klaus Kark


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