论电磁学中高斯定理的谬误 (Argumentum the False of Gauss Theorem in the Electromagnetism)

Abstract

Chinese Abstract: 本文的立意非常简单和明确，即数学命题的最基本规律。任何一个数学命题：其计算出来的结果都要符合“验根”的要求；即每道数学命题中，根据题设的要求得出的计算或推理结果，不能与题设条件相矛盾，否则，结果就不正确。这是数学的基本规律。 在高斯的电通量定理中，高斯的电通量定理是根据库仑定律经二重积分推导出来的。无论是根据库仑定律还是高斯定理进行计算都能得出如下的计算或推理结果：一、两个点电荷不能相互靠近，否则其相互作用力理论上会达到无穷大，其相互作用的关系是与距离的平方成反比；二、线电荷与点电荷之间的距离也不能为零，否则也是相互间的作用力理论上会达到无穷大，其相互作用的关系是与距离的一次方成反比；三、点电荷与平面电荷的关系则是一个常数，即点电荷与平面电荷的作用关系与距离无关。这就产生了一个天大的矛盾：即，如果我们在平面电荷的平面上取一个点A，那么这个点A上的电荷就是明显的经典的点电荷，再经这个所取的点电荷A点，在平面电荷的平面上作一条直线BC，直线BC经过A点；那么这条直线BC在这个平面电荷的平面上，而在这条直线BC上的电荷则又是一条经典的线电荷。那么，通过刚才在平面电荷的平面上所取的点电荷的点A，作一条垂直于平面电荷的平面的直线AD，垂线AD与平面电荷的平面相交于A点。由此可得如下结果：平面电荷外的那个点电荷D点与平面上的无论是点电荷A点电荷，还是D点电荷与经过垂直点A点的平面电荷上的线电荷BC，都是不能相互靠近的，其作用的关系与距离的二次方或一次方成反比。也就是说当距离AD为零时，其中，D点电荷与A点电荷，或D点电荷与BC线电荷之间的作用力理论上会达到无穷大。这就形成了用高斯定理本身产生的自相矛盾的情况出现。由此充分说明高斯的电通量定理是谬误的。　 高斯是一个伟大的数学家和物理学家，在数学和物理学史上，做出的巨大贡献是有目共睹的，所有后人都尊敬他。但这并不能说明高斯的电通量定理就是正确的，真理就是真理，这里所提出的高斯的电通量定理的谬误，并非要违逆高斯这位伟人的本人，而是只就真理说真理而己。 高斯的电通量定理自相矛盾的结果，其原因是在进行数学分析和推导过程中，二重积分在纽曲空间里的积分偏差所致；得出要解决这一矛盾，就必须要产生一门新的数学领域：纽曲空间微积分。

English Abstract: Conception of this paper is very simple and clear, that is the most basic laws of mathematical propositions. Any of a mathematical proposition: the results should be in line with its calculated “test root” requirements; namely in every math proposition, calculation or reasoning out the results according to the conditions set title, that can’t be inconsistent with the title set conditions, otherwise, the results is not correct. This is the basic law of mathematics.

Electric flux in Gauss theorem, Gauss’s electric flux theorem is derived according to Coulomb’s law by double integral. Whether it is calculated according to Coulomb’s law or Gauss theorem can draw the following calculation or reasoning results: One, two point charges can not be close be each other, otherwise, the interaction force could theoretically reach infinity. The interaction is inversely proportional to the relationship between the square of the distance. Two, the distance between the line charge and point charge can not be zero also, otherwise, the interaction force between them also will reach the theoretically infinity, the relationship of the interaction is inversely proportional to the one square of the distance. Three, point charge and the flat charge of relations is a constant, that point charge and a flat charge effect relationship has nothing to do with the distance. This creates a big contradiction: namely if we take a point A in the plane of the plane of the charge, then the charge on the point A is the obvious classic point charge, if we taken through the point A of the point charge, make a straight line BC on the plane in the plane of the charge, the straight line through the point of BC; then this straight line BC in the plane of the plane of the charge, and the charge on this line BC is one of the classic line charge. Well then, just through the taken in the plane of the charge A point charge, make a straight line AD perpendicular to the plane of the plane of the charge, the vertical AD intersects with the plane of the plane of the charge at point A. This gave the following results: The point charge D outside of the plane of the plane of the charge whether it is with the A point charge or the line charge BC in the plane of the plane of the charge, they are not close the each other, the interaction relationship between them is inversely proportional to the square of the distance or one time square distance. That is when the distance AD is zero, thereinto, point charge D and point charge A, or point charge D and the line charge BC, the force between the charges will reach theoretically infinite. This is creates a paradox in itself generated Gauss theorem, thus speaks the Gauss electric flux theorem is fallacious.

Gauss is a great mathematician and physicist all over the world, in the history of mathematics and physics, he made a great contribution is obvious, all descendants are respected him. But this does not explain the Gauss electric flux theorem is correct, because truth is just truth, here Gauss electric flux theorem presented is fallacy, it is not to defy the great man Gauss himself. It is just to the truth say the truth.

Gauss electric flux theorem is self-contradictiory results, the reason is that during the course of mathematical analysis and derivation, integral bias due to double integral in the curved space; come to resolve this contradiction, it is necessary to generate a new field of mathematics: calculus in the curved space.

Note: Downloadable document is available in Chinese.

Keywords: Electric field, magnetic field, dielectric flux, gauss theorem, coulombs law

JEL Classification: 0441.1-2