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Wellengleichung für das magnetische Feld

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Exercise

https://texercises.com/exercise/wellengleichung-fur-das-magnetische-feld/

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Exercise:
Zeige dass sich aus der vierten und dritten Maxwell-Gleichung im Vakuum unter Verwung der zweiten Maxwell-Gleichung eine Wellengleichung für das magnetische Feld ergibt.

Solution:
Wir nen mit der vierten Maxwell-Gleichung im Vakuum: nabla times vecB mu_ varepsilon_ fracpartial vecEpartial t We den Rotationsoperator an: nabla times nabla times vecB mu_ varepsilon_ nabla times fracpartial vecEpartial t mu_ varepsilon_ fracpartialpartial t nabla times vecE Setze die dritte Maxwell-Gleichung ein: mu_ varepsilon_ fracpartialpartial t left-fracpartial vecBpartial t right -mu_ varepsilon_ fracpartial^ vecBpartial t^ Verwe die Vektoridentität: nabla times nabla times vecB nabla nabla vecB - nabla^ vecB Da im Vakuum gilt: nabla vecB folgt: - nabla^ vecB - mu_ varepsilon_ fracpartial^ vecBpartial t^ quad Rightarrow quad boxed nabla^ vecB mu_ varepsilon_ fracpartial^ vecBpartial t^

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Maxwell-Gleichungen by uz

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Tags	elektromagnetismus, maxwell-gleichung, physik
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Difficulty	(6, default)
Points	4 (default)
Language	(Deutsch)
Type	Show
Creator	uz
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