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Gauss's and law
These orbits were stabilized in the model by the fact that when an electron moved farther from the center of the positive cloud, it felt a larger net positive inward force, because there was more material of opposite charge, inside its orbit ( see Gauss's law ).
Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.
: ( Gauss's law )
: ( Gauss's law for magnetism )
) Of the four equations, two of them, Gauss's law and Gauss's law for magnetism, describe how the fields emanate from charges.
Gauss's law describes the relationship between an electric field and the electric charges that cause it: The electric field points away from positive charges and towards negative charges.
Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current.
Gauss's law for magnetism states that there are no " magnetic charges " ( also called magnetic monopoles ), analogous to electric charges.
If they did exist, both Gauss's law for magnetism and Faraday's law would need to be modified, and the resulting four equations would be fully symmetric under the interchange of electric and magnetic fields ; see magnetic monopoles for details.
and Gauss's law,
For nonlinear medium Gauss's law does not imply that the identity
The absence of net charge and momentum would follow from accepted physical laws ( Gauss's law and the non-divergence of the stress-energy-momentum pseudotensor, respectively ), if the universe were finite.
* Gauss's law for gravity
Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the relationship between the distribution of electric charge in space and the resulting electric field.
While Columb's law ( as given above ) is only true for stationary point charges, Gauss's law is true for all charges either in static or in motion.
Gauss's law is one of Maxwell's equations governing electromagnetism.
Gauss's law allows the E-field to be calculated in terms of a continuous distribution of charge density
Gauss's law applies to, and can be used with any physical quantity that acts in accord to, the inverse-square relationship.
* Gauss's law
* Gauss's law

Gauss's and gives
Using Gauss's theorem and Poisson's equation gives
Gauss's inequality gives an upper bound on the probability that a value lies more than any given distance from its mode.
Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue.

Gauss's and between
The suitability of Stirling's, Bessel's and Gauss's formulae depends on 1 ) the importance of the small accuracy gain given by average differences ; and 2 ) if greater accuracy is necessary, whether the interpolated point is closer to a data point or to a middle between two data points.
It follows from an application of Gauss's Lemma that if A is the norm of then the distance, induced by the metric, between two close enough points on the curve γ, say γ ( t < sub > 1 </ sub >) and γ ( t < sub > 2 </ sub >), is given by
The definition of electrostatic potential, combined with the differential form of Gauss's law ( above ), provides a relationship between the potential Φ and the charge density ρ:
That is, in a manner described by Gauss's law, assuming no dielectric between the plates:
Using an imaginary pillbox, it is possible to use Gauss's law to explain the relationship between electric displacement and free charge.

Gauss's and electric
This quantity arises in Gauss's law-which states that the flux of the electric field E out of a closed surface is proportional to the electric charge Q < sub > A </ sub > enclosed in the surface ( independent of how that charge is distributed ), the integral form is:
By way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
Gauss's law can be used to demonstrate that all electric fields inside a Faraday cage have an electric charge.
Gauss's law can be stated using either the electric field E or the electric displacement field D. This section shows some of the forms with E ; the form with D is below, as are other forms with E.
Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form.
If the electric field is known everywhere, Gauss's law makes it quite easy, in principle, to find the distribution of electric charge: The charge in any given region can be deduced by integrating the electric field to find the flux.
Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can ( see Gauss's law for magnetism ).

Gauss's and flux
Gauss's law for magnetism, which is one of the four Maxwell's equations, states that the total magnetic flux through a closed surface is equal to zero.
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a result that relates the flow ( that is, flux ) of a vector field through a surface to the behavior of the vector field inside the surface.
Indeed, if V is any smooth region, then by Gauss's law the flux of the electrostatic field E is equal to the charge enclosed ( in appropriate units ):
In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding to Gauss's law.
* Gauss's Law: The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.

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