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Gauss's law for gravity is often more convenient to work from than Newton's law. [1] The form of Gauss's law for gravity is mathematically similar to Gauss's law for electrostatics, one of Maxwell's equations. Gauss's law for gravity has the same mathematical relation to Newton's law that Gauss's law for electrostatics bears to Coulomb's law.
In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem , and it relates the distribution of electric charge to the resulting electric field .
Gauss published the first and second proofs of the law of quadratic reciprocity on arts 125–146 and 262 of Disquisitiones Arithmeticae in 1801. In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it ...
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
Any inverse-square law can instead be written in a Gauss's law-type form (with a differential and integral form, as described above). Two examples are Gauss's law (in electrostatics), which follows from the inverse-square Coulomb's law, and Gauss's law for gravity, which follows from the inverse-square Newton's law of universal gravitation. The ...
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x 4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x 4 ≡ p (mod q) to that of x 4 ≡ q (mod p).
It is an arbitrary closed surface S = ∂V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss's law for magnetism, or Gauss's law for gravity) by performing a surface integral, in order to calculate the total amount of the source quantity enclosed; e.g., amount of ...
In particular, it represents lines of inverse-square law force. The extension of the above considerations confirms that where B is to H, and where J is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that E is to D i.e. B parallels with E, whereas H parallels with D.