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68-388: ε r − 1 ε r + 2 = N α 3 ε 0 {\displaystyle {\frac {\varepsilon _{\mathrm {r} }-1}{\varepsilon _{\mathrm {r} }+2}}={\frac {N\alpha }{3\varepsilon _{0}}}} where In the case that the material consists of a mixture of two or more species,

136-438: A magnetic field identical to that generated by a very small current loop. However, an electron's magnetic dipole moment is not due to a current loop, but to an intrinsic property of the electron. The electron may also have an electric dipole moment though such has yet to be observed (see electron electric dipole moment ). A permanent magnet, such as a bar magnet, owes its magnetism to the intrinsic magnetic dipole moment of

204-447: A convention of normalizing quantities with respect to some system of natural units . For example, in particle physics a system is in use where every quantity is expressed by only one unit of energy, the electronvolt , with lengths, times, and so on all converted into units of energy by inserting factors of speed of light c and the reduced Planck constant ħ . This unit system is convenient for calculations in particle physics , but

272-407: A different unit of mass so that the formula for 𝜆′ is invalid. The unit of mass was chosen to remove powers of ten from contexts in which they were considered to be objectionable (e.g., P = VI and F = qE ). Inevitably, the powers of ten reappeared in other contexts, but the effect was to make the familiar joule and watt the units of work and power respectively. The ampere-turn system

340-454: A dipole can be found from the gradient of this potential: This is of the same form of the expression for the magnetic field of a point magnetic dipole, ignoring the delta function. In a real electric dipole, however, the charges are physically separate and the electric field diverges or converges at the point charges. This is different to the magnetic field of a real magnetic dipole which is continuous everywhere. The delta function represents

408-463: A molecule has a charge distribution) is caused by an electric field external to ρ . This field may, for instance, originate from an ion or polar molecule in the vicinity of ρ or may be macroscopic (e.g., a molecule between the plates of a charged capacitor ). The size of the induced dipole moment is equal to the product of the strength of the external field and the dipole polarizability of ρ . Dipole moment values can be obtained from measurement of

476-518: A molecule's dipole is an electric dipole with an inherent electric field that should not be confused with a magnetic dipole , which generates a magnetic field. The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and, as a consequence, dipole moments are measured in the non- SI unit named debye in his honor. For molecules there are three types of dipoles: More generally, an induced dipole of any polarizable charge distribution ρ (remember that

544-507: A non-degenerate state (see degenerate energy level ) is given as the expectation (average) value of the dipole operator, where | S ⟩ {\displaystyle |\,S\,\rangle } is an S -state, non-degenerate, wavefunction, which is symmetric or antisymmetric under inversion: I | S ⟩ = ± | S ⟩ {\displaystyle {\mathfrak {I}}\,|\,S\,\rangle =\pm |\,S\,\rangle } . Since

612-416: A positive charge and toward a negative charge. When placed in a homogeneous electric or magnetic field , equal but opposite forces arise on each side of the dipole creating a torque τ }: for an electric dipole moment p (in coulomb-meters), or for a magnetic dipole moment m (in ampere-square meters). The resulting torque will tend to align the dipole with the applied field, which in

680-576: A separate abbreviation "esu", and similarly with the corresponding symbols. In another variant of the CGS system, electromagnetic units ( EMU ), current is defined via the force existing between two thin, parallel, infinitely long wires carrying it, and charge is then defined as current multiplied by time. (This approach was eventually used to define the SI unit of ampere as well). The EMU unit of current, biot ( Bi ), also known as abampere or emu current ,

748-458: A system of units of electromagnetism, in which the dimensions of all electric and magnetic quantities are expressible in terms of the mechanical dimensions of mass, length, and time, is traditionally called an 'absolute system'. All electromagnetic units in the CGS-ESU system that have not been given names of their own are named as the corresponding SI name with an attached prefix "stat" or with

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816-423: A way that the product remains a positive constant.) For the magnetic (dipole) current loop, the magnetic dipole moment points through the loop (according to the right hand grip rule ), with a magnitude equal to the current in the loop times the area of the loop. Similar to magnetic current loops, the electron particle and some other fundamental particles have magnetic dipole moments, as an electron generates

884-450: A zero permanent dipole. This fact follows quantum mechanically from the inversion symmetry of atoms. All 3 components of the dipole operator are antisymmetric under inversion with respect to the nucleus, where p {\displaystyle {\mathfrak {p}}} is the dipole operator and I {\displaystyle {\mathfrak {I}}} is the inversion operator. The permanent dipole moment of an atom in

952-444: Is a special aspect of electromagnetism units. By contrast it is always correct to replace, e.g., "1 m" with "100 cm" within an equation or formula.) Lack of unique unit names leads to potential confusion: "15 emu" may mean either 15 abvolts , or 15 emu units of electric dipole moment , or 15 emu units of magnetic susceptibility , sometimes (but not always) per gram , or per mole . With its system of uniquely named units,

1020-470: Is a variant of the metric system based on the centimetre as the unit of length , the gram as the unit of mass , and the second as the unit of time . All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways in which the CGS system was extended to cover electromagnetism . The CGS system has been largely supplanted by the MKS system based on

1088-531: Is applicable to gases such as N 2 , CO 2 , CH 4 and H 2 at sufficiently low densities and pressures. For example, the Clausius–Mossotti relation is accurate for N 2 gas up to 1000 atm between 25 °C and 125 °C. Moreover, the Clausius–Mossotti relation may be applicable to substances if the applied electric field is at a sufficiently high frequencies such that any permanent dipole modes are inactive. The Lorentz–Lorenz equation

1156-521: Is constructed in a similar way by considering magnetomotive force and magnetic field strength to be electrical quantities and rationalizing the system by dividing the units of magnetic pole strength and magnetization by 4 π . The units of the first two quantities are the ampere and the ampere per centimetre respectively. The unit of magnetic permeability is that of the emu system, and the magnetic constitutive equations are B = (4 π /10) μ H and B = (4 π /10) μ 0 H + μ 0 M . Magnetic reluctance

1224-500: Is for many gases, the equation reduces to: or simply This applies to gases at ordinary pressures. The refractive index n of the gas can then be expressed in terms of the molar refractivity A as: where p is the pressure of the gas, R is the universal gas constant , and T is the (absolute) temperature, which together determine the number density N . Centimetre%E2%80%93gram%E2%80%93second system of units The centimetre–gram–second system of units ( CGS or cgs )

1292-572: Is given a hybrid unit to ensure the validity of Ohm's law for magnetic circuits. In all the practical systems ε 0 = 8.8542 × 10 A⋅s/(V⋅cm), μ 0 = 1 V⋅s/(A⋅cm), and c = 1/(4 π × 10 ε 0 μ 0 ). There were at various points in time about half a dozen systems of electromagnetic units in use, most based on the CGS system. These include the Gaussian units and the Heaviside–Lorentz units . In this table, c = 29 979 245 800

1360-436: Is impractical in other contexts. Dipole In physics , a dipole (from Ancient Greek δίς ( dís )  'twice' and πόλος ( pólos )  'axis') is an electromagnetic phenomenon which occurs in two ways: Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the electric dipole moment points from

1428-494: Is less straightforward. Formulas for physical laws of electromagnetism (such as Maxwell's equations ) take a form that depends on which system of units is being used, because the electromagnetic quantities are defined differently in SI and in CGS. Furthermore, within CGS, there are several plausible ways to define electromagnetic quantities, leading to different "sub-systems", including Gaussian units , "ESU", "EMU", and Heaviside–Lorentz units . Among these choices, Gaussian units are

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1496-508: Is similar to the Clausius–Mossotti relation, except that it relates the refractive index (rather than the dielectric constant) of a substance to its polarizability . The Lorentz–Lorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz , who published it in 1869, and the Dutch physicist Hendrik Lorentz , who discovered it independently in 1878. The most general form of

1564-473: Is the atomic number of the i  th nucleus. The dipole observable (physical quantity) has the quantum mechanical dipole operator : Notice that this definition is valid only for neutral atoms or molecules, i.e. total charge equal to zero. In the ionized case, we have where r c {\displaystyle \mathbf {r} _{c}} is the center of mass of the molecule/group of particles. A non-degenerate ( S -state) atom can have only

1632-546: Is the numeric value of the speed of light in vacuum when expressed in units of centimetres per second. The symbol "≘" is used instead of "=" as a reminder that the units are corresponding but not equal . For example, according to the capacitance row of the table, if a capacitor has a capacitance of 1 F in SI, then it has a capacitance of (10   c ) cm in ESU; but it is incorrect to replace "1 F" with "(10   c ) cm" within an equation or formula. (This warning

1700-524: Is therefore defined as follows: The biot is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one centimetre apart in vacuum , would produce between these conductors a force equal to two dynes per centimetre of length. Therefore, in electromagnetic CGS units , a biot is equal to a square root of dyne: The unit of charge in CGS EMU is: Dimensionally in

1768-521: Is valid in SI should also be valid in the system. For example, since electric field strength is voltage per unit length, its unit is the volt per centimetre, which is one hundred times the SI unit. The system is electrically rationalized and magnetically unrationalized; i.e., 𝜆 = 1 and 𝜆′ = 4 π , but the above formula for 𝜆 is invalid. A closely related system is the International System of Electric and Magnetic Units, which has

1836-564: The American Physical Society and the International Astronomical Union . SI units are predominantly used in engineering applications and physics education, while Gaussian CGS units are still commonly used in theoretical physics, describing microscopic systems, relativistic electrodynamics , and astrophysics . The units gram and centimetre remain useful as noncoherent units within

1904-450: The CGS system of units the Clausius–Mossotti relation is typically rewritten to show the molecular polarizability volume α ′ = α 4 π ε 0 {\displaystyle \alpha '={\tfrac {\alpha }{4\pi \varepsilon _{0}}}} which has units of volume [m]. Confusion may arise from the practice of using

1972-420: The dielectric constant . Some typical gas phase values given with the unit debye are: Potassium bromide (KBr) has one of the highest dipole moments because it is an ionic compound that exists as a molecule in the gas phase. The overall dipole moment of a molecule may be approximated as a vector sum of bond dipole moments . As a vector sum it depends on the relative orientation of the bonds, so that from

2040-441: The electrostatic units variant of the CGS system, (CGS-ESU), charge is defined as the quantity that obeys a form of Coulomb's law without a multiplying constant (and current is then defined as charge per unit time): The ESU unit of charge, franklin ( Fr ), also known as statcoulomb or esu charge , is therefore defined as follows: two equal point charges spaced 1 centimetre apart are said to be of 1 franklin each if

2108-400: The farad (capacitance), ohm (resistance), coulomb (electric charge), and henry (inductance) are consequently also used in the practical system and are the same as the SI units. The magnetic units are those of the emu system. The electrical units, other than the volt and ampere, are determined by the requirement that any equation involving only electrical and kinematical quantities that

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2176-503: The metre , kilogram , and second, which was in turn extended and replaced by the International System of Units (SI). In many fields of science and engineering, SI is the only system of units in use, but CGS is still prevalent in certain subfields. In measurements of purely mechanical systems (involving units of length, mass, force , energy , pressure , and so on), the differences between CGS and SI are straightforward:

2244-451: The unit-conversion factors are all powers of 10 as 100 cm = 1 m and 1000 g = 1 kg . For example, the CGS unit of force is the dyne , which is defined as 1 g⋅cm/s , so the SI unit of force, the newton ( 1 kg⋅m/s ), is equal to 100 000  dynes . On the other hand, in measurements of electromagnetic phenomena (involving units of charge , electric and magnetic fields, voltage , and so on), converting between CGS and SI

2312-499: The volt and the ampere as the units of voltage and current respectively. Doing this avoids the inconveniently large and small electrical units that arise in the esu and emu systems. This system was at one time widely used by electrical engineers because the volt and ampere had been adopted as international standard units by the International Electrical Congress of 1881. As well as the volt and ampere,

2380-444: The z -axis. Then, The field itself is a vector quantity: where This is exactly the field of a point dipole, exactly the dipole term in the multipole expansion of an arbitrary field, and approximately the field of any dipole-like configuration at large distances. The vector potential A of a magnetic dipole is with the same definitions as above. The electrostatic potential at position r due to an electric dipole at

2448-455: The CGS-EMU system, charge q is therefore equivalent to M L . Hence, neither charge nor current is an independent physical quantity in the CGS-EMU system. All electromagnetic units in the CGS-EMU system that do not have proper names are denoted by a corresponding SI name with an attached prefix "ab" or with a separate abbreviation "emu". The practical CGS system is a hybrid system that uses

2516-472: The Hermitian adjoint I ∗ {\displaystyle {\mathfrak {I}}^{*}\,} may be moved from bra to ket and then becomes I ∗ ∗ = I {\displaystyle {\mathfrak {I}}^{**}={\mathfrak {I}}\,} . Since the only quantity that is equal to minus itself is the zero, the expectation value vanishes, In

2584-518: The Lewis structures for the resonance forms of ozone which show a positive charge on the central oxygen atom. An example in organic chemistry of the role of geometry in determining dipole moment is the cis and trans isomers of 1,2-dichloroethene . In the cis isomer the two polar C−Cl bonds are on the same side of the C=C double bond and the molecular dipole moment is 1.90 D. In the trans isomer,

2652-615: The Lorentz–Lorenz equation is (in Gaussian-CGS units) where n is the refractive index, N is the number of molecules per unit volume, and α m {\displaystyle \alpha _{\mathrm {m} }} is the mean polarizability. This equation is approximately valid for homogeneous solids as well as liquids and gases. When the square of the refractive index is n 2 ≈ 1 {\displaystyle n^{2}\approx 1} , as it

2720-631: The SI removes any confusion in usage: 1 ampere is a fixed value of a specified quantity, and so are 1 henry , 1  ohm , and 1 volt. In the CGS-Gaussian system , electric and magnetic fields have the same units, 4 π 𝜖 0 is replaced by 1, and the only dimensional constant appearing in the Maxwell equations is c , the speed of light. The Heaviside–Lorentz system has these properties as well (with ε 0 equaling 1). In SI, and other rationalized systems (for example, Heaviside–Lorentz ),

2788-420: The SI system, as with any other prefixed SI units. In mechanics, the quantities in the CGS and SI systems are defined identically. The two systems differ only in the scale of the three base units (centimetre versus metre and gram versus kilogram, respectively), with the third unit (second) being the same in both systems. There is a direct correspondence between the base units of mechanics in CGS and SI. Since

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2856-415: The accurate description of such effects falls outside of classical electromagnetism). A theoretical magnetic point dipole has a magnetic field of exactly the same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the (vector) area of

2924-425: The case of an electric dipole, yields a potential energy of The energy of a magnetic dipole is similarly In addition to dipoles in electrostatics, it is also common to consider an electric or magnetic dipole that is oscillating in time. It is an extension, or a more physical next-step, to spherical wave radiation. In particular, consider a harmonically oscillating electric dipole, with angular frequency ω and

2992-430: The case of open-shell atoms with degenerate energy levels, one could define a dipole moment by the aid of the first-order Stark effect . This gives a non-vanishing dipole (by definition proportional to a non-vanishing first-order Stark shift) only if some of the wavefunctions belonging to the degenerate energies have opposite parity ; i.e., have different behavior under inversion. This is a rare occurrence, but happens for

3060-533: The dipole moment information can be deduced about the molecular geometry . For example, the zero dipole of CO 2 implies that the two C=O bond dipole moments cancel so that the molecule must be linear. For H 2 O the O−H bond moments do not cancel because the molecule is bent. For ozone (O 3 ) which is also a bent molecule, the bond dipole moments are not zero even though the O−O bonds are between similar atoms. This agrees with

3128-406: The dipole moment is zero because the two C−Cl bonds are on opposite sides of the C=C and cancel (and the two bond moments for the much less polar C−H bonds also cancel). Another example of the role of molecular geometry is boron trifluoride , which has three polar bonds with a difference in electronegativity greater than the traditionally cited threshold of 1.7 for ionic bonding . However, due to

3196-454: The electron. The two ends of a bar magnet are referred to as poles (not to be confused with monopoles , see Classification below) and may be labeled "north" and "south". In terms of the Earth's magnetic field, they are respectively "north-seeking" and "south-seeking" poles: if the magnet were freely suspended in the Earth's magnetic field, the north-seeking pole would point towards the north and

3264-528: The electrostatic force between them is 1 dyne . Therefore, in CGS-ESU, a franklin is equal to a centimetre times square root of dyne: The unit of current is defined as: In the CGS-ESU system, charge q is therefore has the dimension to M L T . Other units in the CGS-ESU system include the statampere (1 statC/s) and statvolt (1  erg /statC). In CGS-ESU, all electric and magnetic quantities are dimensionally expressible in terms of length, mass, and time, and none has an independent dimension. Such

3332-425: The equilateral triangular distribution of the fluoride ions centered on and in the same plane as the boron cation, the symmetry of the molecule results in its dipole moment being zero. Consider a collection of N particles with charges q i and position vectors r i . For instance, this collection may be a molecule consisting of electrons, all with charge − e , and nuclei with charge eZ i , where Z i

3400-409: The excited H-atom, where 2s and 2p states are "accidentally" degenerate (see article Laplace–Runge–Lenz vector for the origin of this degeneracy) and have opposite parity (2s is even and 2p is odd). The far-field strength, B , of a dipole magnetic field is given by where Conversion to cylindrical coordinates is achieved using r = z + ρ and where ρ is the perpendicular distance from

3468-408: The existence of magnetic monopoles has never been experimentally demonstrated. A physical dipole consists of two equal and opposite point charges: in the literal sense, two poles. Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A point (electric) dipole is the limit obtained by letting

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3536-572: The field of science. Starting in the 1880s, and more significantly by the mid-20th century, CGS was gradually superseded internationally for scientific purposes by the MKS (metre–kilogram–second) system, which in turn developed into the modern SI standard. Since the international adoption of the MKS standard in the 1940s and the SI standard in the 1960s, the technical use of CGS units has gradually declined worldwide. CGS units have been deprecated in favor of SI units by NIST , as well as organizations such as

3604-400: The formulae expressing the laws of mechanics are the same in both systems and since both systems are coherent , the definitions of all coherent derived units in terms of the base units are the same in both systems, and there is an unambiguous relationship between derived units: Thus, for example, the CGS unit of pressure, barye , is related to the CGS base units of length, mass, and time in

3672-443: The general adoption of centimetre, gram and second as fundamental units, and to express all derived electromagnetic units in these fundamental units, using the prefix "C.G.S. unit of ...". The sizes of many CGS units turned out to be inconvenient for practical purposes. For example, many everyday objects are hundreds or thousands of centimetres long, such as humans, rooms and buildings. Thus the CGS system never gained wide use outside

3740-554: The loop. Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration. This is simply one term in the multipole expansion when the total charge ("monopole moment") is 0—as it always is for the magnetic case, since there are no magnetic monopoles. The dipole term is the dominant one at large distances: Its field falls off in proportion to ⁠ 1 / r ⁠ , as compared to ⁠ 1 / r ⁠ for

3808-683: The most common today, and "CGS units" is often intended to refer to CGS-Gaussian units. The CGS system goes back to a proposal in 1832 by the German mathematician Carl Friedrich Gauss to base a system of absolute units on the three fundamental units of length, mass and time. Gauss chose the units of millimetre, milligram and second. In 1873, a committee of the British Association for the Advancement of Science , including physicists James Clerk Maxwell and William Thomson recommended

3876-447: The nature of the constants that appear in these formulas. This illustrates the fundamental difference in the ways the two systems are built: In each of these systems the quantities called "charge" etc. may be a different quantity; they are distinguished here by a superscript. The corresponding quantities of each system are related through a proportionality constant. Maxwell's equations can be written in each of these systems as: In

3944-412: The negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges. (To be precise: for the definition of the dipole moment, one should always consider the "dipole limit", where, for example, the distance of the generating charges should converge to 0 while simultaneously, the charge strength should diverge to infinity in such

4012-429: The next ( quadrupole ) term and higher powers of ⁠ 1 / r ⁠ for higher terms, or ⁠ 1 / r ⁠ for the monopole term. Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. Such is the case with polar compounds like hydrogen fluoride (HF), where electron density is shared unequally between atoms. Therefore,

4080-400: The origin is given by: where p is the (vector) dipole moment , and є 0 is the permittivity of free space . This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential Φ( r ). If the source of Φ( r ) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ( r ). The electric field from

4148-525: The product of the wavefunction (in the ket) and its complex conjugate (in the bra) is always symmetric under inversion and its inverse, it follows that the expectation value changes sign under inversion. We used here the fact that I {\displaystyle {\mathfrak {I}}} , being a symmetry operator, is unitary : I − 1 = I ∗ {\displaystyle {\mathfrak {I}}^{-1}={\mathfrak {I}}^{*}\,} and by definition

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4216-566: The right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by i in the following form: ε r − 1 ε r + 2 = ∑ i N i α i 3 ε 0 {\displaystyle {\frac {\varepsilon _{\mathrm {r} }-1}{\varepsilon _{\mathrm {r} }+2}}=\sum _{i}{\frac {N_{i}\alpha _{i}}{3\varepsilon _{0}}}} In

4284-491: The same way as the SI unit of pressure, pascal , is related to the SI base units of length, mass, and time: Expressing a CGS derived unit in terms of the SI base units, or vice versa, requires combining the scale factors that relate the two systems: The conversion factors relating electromagnetic units in the CGS and SI systems are made more complex by the differences in the formulas expressing physical laws of electromagnetism as assumed by each system of units, specifically in

4352-400: The separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field. Although there are no known magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as electrons (although

4420-429: The shorter name "molecular polarizability" for both α {\displaystyle \alpha } and α ′ {\displaystyle \alpha '} within literature intended for the respective unit system. The Clausius–Mossotti relation assumes only an induced dipole relevant to its polarizability and is thus inapplicable for substances with a significant permanent dipole . It

4488-477: The south-seeking pole would point towards the south. The dipole moment of the bar magnet points from its magnetic south to its magnetic north pole . In a magnetic compass , the north pole of a bar magnet points north. However, that means that Earth's geomagnetic north pole is the south pole (south-seeking pole) of its dipole moment and vice versa. The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical spin since

4556-451: The strong field pointing in the opposite direction between the point charges, which is often omitted since one is rarely interested in the field at the dipole's position. For further discussions about the internal field of dipoles, see or Magnetic moment § Internal magnetic field of a dipole . Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from

4624-532: The unit of current was chosen such that electromagnetic equations concerning charged spheres contain 4 π , those concerning coils of current and straight wires contain 2 π and those dealing with charged surfaces lack π entirely, which was the most convenient choice for applications in electrical engineering and relates directly to the geometric symmetry of the system being described by the equation. Specialized unit systems are used to simplify formulas further than either SI or CGS do, by eliminating constants through

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