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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.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
The gauss (symbol: G, sometimes Gs) is a unit of measurement of magnetic induction, also known as magnetic flux density. The unit is part of the Gaussian system of units, which inherited it from the older centimetre–gram–second electromagnetic units (CGS-EMU) system.
Coulomb's law in the CGS-Gaussian system takes the form =, where F is the force, q G 1 and q G 2 are the two electric charges, and r is the distance between the charges. This serves to define charge as a quantity in the Gaussian system.
For example, the CGS unit of force is the dyne, which is defined as 1 g⋅cm/s 2, so the SI unit of force, the newton (1 kg⋅m/s 2), 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 is less ...
Then, if the total flux is known, the field itself can be deduced at every point. Common examples of symmetries which lend themselves to Gauss's law include: cylindrical symmetry, planar symmetry, and spherical symmetry. See the article Gaussian surface for examples where these symmetries are exploited to compute electric fields.
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).
The equations given above for the electric potential (and all the equations used here) are in the forms required by SI units. In some other (less common) systems of units, such as CGS-Gaussian, many of these equations would be altered.