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TOPIC: Lignes de champ

Lignes de champ 2 years 2 months ago #619

Deux lignes de champ peuvent-elles se croiser ?

Raisonnons par l'absurde pour répondre à la question.

Supposons qu'il existe deux lignes de champ qui se croisent en un point.
Ce point appartient donc à deux lignes de champ.
Par définition de la ligne de champ, en ce point, chaque ligne de champ est tangente à un vecteur champ dont l'origine est ce point.
Cela veut dire qu'en ce point, nous avons deux vecteurs champ de directions différentes.
Hors, on sait que le champ en un point est la somme vectorielle de tous les vecteurs champ en ce point.
Autrement dit, en ce point, nous devrions avoir une ligne de champ tangente à la résultante de ces vecteurs champ, ce qui est une contraction.

Il n'est donc pas possible que deux lignes de champ se croisent.
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