Gauss Theorem Because the magnetic field lines are always closed curves, any magnetic field lines that enter a closed surface will definitely come out from the inside of the surface, otherwise it will not be closed. If the outward normal direction is defined for a closed surface, the magnetic flux entering the surface is negative and the magnetic flux coming out is positive, then the total magnetic flux passing through the closed surface can be zero. This law is similar to Gauss theorem in electric field, so it is also called Gauss theorem. Compared with Gauss theorem of electrostatic field, there are essential differences between them. In the electrostatic field, due to the existence of independent charges in nature, electric field lines have a starting point and an ending point. As long as there is a net positive charge (or negative charge) on the closed surface, the electric flux passing through the closed surface is not equal to zero, that is, the electrostatic field is the active area. In the magnetic field, because there is no single magnetic pole in nature, the N pole and the S pole cannot be separated, and the magnetic induction line is a closed line with no head and no tail, so the magnetic flux passing through any closed surface must be equal to zero. The flux of electric field E (vector) through any closed surface, that is, the integral of the surface is equal to 4π times of the total charge surrounded by the surface. Formula expression: ∫ (e da) = 4 π * s (ρ dv) Gauss theorem: The total number of power lines passing through a closed surface is proportional to the amount of charge surrounded by the closed surface. In other words, the area fraction of the electric field intensity on the closed surface is directly proportional to the amount of charge surrounded by the closed surface. Gauss summation: For arithmetic progression A 1, A2, A3...an, Sn = A1+A2+A3+...+An = (A1+An) * n/2 Gauss Theorem 2: Every rational integral equation f(x)=0 has at least. Inference: the unary equation f (x) = a _ 0xn+a _1x (n-1)+...+a _ (n-1) x+a _ n = 0 must have n roots and only n roots (including imaginary roots).

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