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One difference between the Gaussian and SI systems is in the factor 4π in various formulas that relate the quantities that they define. With SI electromagnetic units, called rationalized, [3] [4] Maxwell's equations have no explicit factors of 4π in the formulae, whereas the inverse-square force laws – Coulomb's law and the Biot–Savart law – do have a factor of 4π attached to the r 2.
Planck units is system of geometrized units in which the reduced Planck constant is included in the list of defining constants. It is based on only properties of free space rather than of any object or particle. Stoney units is a system of geometrized units in which the Coulomb constant and the elementary charge are included.
Then let E 1 denote the set of global units ε that map to U 1 via the diagonal embedding of the global units in E. Since E 1 is a finite-index subgroup of the global units, it is an abelian group of rank r 1 + r 2 − 1. The p-adic regulator is the determinant of the matrix formed by the p-adic logarithms of the generators of this group.
Dirichlet's unit theorem shows that the unit group has rank 1 exactly when the number field is a real quadratic field, a complex cubic field, or a totally imaginary quartic field. When the unit group has rank ≥ 1, a basis of it modulo its torsion is called a fundamental system of units. [1]
Coherence may be restored, without changing the units, by choosing k = 3.6; then the kilometre per hour is a coherent derived unit, with 1 kmph = 1 m/s, and the metre per second is a non-coherent derived unit, with 1 m/s = 3.6 m/s. A definition of a physical quantity is a statement that determines the ratio of any two instances of the quantity.
When that multiplier is one, the unit is called a coherent derived unit. For example, the coherent derived SI unit of velocity is the metre per second, with the symbol m/s. [1]: 139 The base and coherent derived units of the SI together form a coherent system of units (the set of coherent SI units). A useful property of a coherent system is ...
It is not defined for ratios of quantities of other kinds. Within the ISQ, all levels are treated as derived quantities of dimension 1. [citation needed] Several units for levels are defined by the SI and classified as "non-SI units accepted for use with the SI units". [4] An example of level is sound pressure level, with the unit of decibel.
Centimetre–gram–second system of units; CGS system of units; Chinese units of measurement; Coherence (units of measurement) Comparison of the imperial and US customary measurement systems; Composition of Yards and Perches; Conventional electrical unit