The c.s.g. unit of magnetic flux density (or magnetic induction), equal to 1 maxwell per square centimeter, or 10-4 tesla.
Named after the German mathematician and physicist Carl Friedrich Gauss (1777-1855).
Gauss's law for electricity
qânun-e Gauss dar barq
Fr.: loi de Gauss en électricité
The total electric flux ψ out of an arbitrary closed surface in free space is equal to the net charge within the surface divided by the → permittivity. In differential form: ∇ . E = ρ/ε0, where ρ is the → charge density and ε0 the permittivity. The integral form of the law: ∫E . dS = Q/ε0 (closed surface integral). This is one of the four → Maxwell's equations.
→ gauss; → law; → electricity.
Gauss's law for magnetism
qânun-e Gauss dar meqnâtmandi
Fr.: loi de Gauss en magnétisme
The → magnetic flux through an arbitrary closed surface equals zero. Mathematically, in differential form: ∇ . B = 0 and in integral form: ΦB = ∫B.dS = 0 (closed surface integral). This is one of the four → Maxwell's equations. This law expresses the fact that there are no free magnetic poles (→ monopoles) in nature and that all the lines of force of a magnetic field are closed curves.
Fr.: lemme de Gauss
If a → polynomial with → integer coefficients can be → factorized into polynomials with → rational number coefficients, it can be factorized using only integers.
Fr.: théorème de Gauss
The total normal induction over any closed surface drawn in an electric field is equal to 4π times the total charge of electricity inside the closed surface. Gauss's theorem applies also to other vector fields such as magnetic, gravitational, and fluid velocity fields. The theorem can more generally be stated as: the total flux of a vector field through a closed surface is equal to the volume → integral of the vector taken over the enclosed volume. Also known as → divergence theorem, Ostrogradsky's theorem, and Gauss-Ostrogradsky theorem.
Of or relating to Carl Friedrich Gauss or his mathematical theories of magnetism, electricity, astronomy, or probability. → Gaussian distribution; → Gaussian profile.
vâbâžeš-e Gaussi (#)
Fr.: distribution gaussienne
A theoretical frequency distribution for a set of variable data, usually represented by a bell-shaped curve with a mean at the center of the curve and tail widths proportional to the standard deviation of the data about the mean.
→ Gaussian; → distribution.
Fr.: élimination de Gauss
A method of solving a matrix equation of the form A x = b, where A is a matrix and x and b are vectors. The process consists of two steps, first reducing the elements below the diagonal to 0 and second, back substituting to find the solutions.
→ Gaussian; → elimination.
Fr.: fonction de Gauss
The function e-x2, whose integral in the interval -∞ to +∞ gives the → square root of the → number pi: ∫e-x2dx = √π. It is the function that describes the → normal distribution.
Gaussian gravitational constant
pâyâ-ye gerâneši-ye Gauss
Fr.: constante gravitationnelle de Gauss
The constant, denoted k, defining the astronomical system of units of length (→ astronomical unit), mass (→ solar mass), and time (→ day), by means of → Kepler's third law. The dimensions of k2 are those of Newton's constant of gravitation: L 3M -1T -2. Its value is: k = 0.01720209895.
→ Gaussian; → gravitational; → constant.
Fr.: entier de Gauss
A → complex number whose → real and → imaginary parts are both integers.
Fr.: profile gaussien
The shape of a curve representing a normal distribution.
Math.: The condition of having → Gaussian distribution. The extent to which something is Gaussian.