In this page, constants , c and e are in SI units and they all have exact values; the dimensionless constant α has the relative uncertainty of 0.15 ppb according to CODATA-2018.
In natural units:
- length and time are represented as the reciprocal of energy:
- force is represented as the square of energy:
- velocity is dimensionless
Therefore, the relations among SI, Gaussian and natural units for length, force and velocity are: [1]
The dimension of electric charge can be determined by Coulomb's law in different unit systems:
Apply (1) and (2) on (4), (5) and (6): [2,3]
The dimension of magnetic B field can be determined by Lorentz force in different unit systems:
Apply (2), (3) and (7) on (8), (9) and (10): [2]
- For mechanic quantities, SI and Gaussian unit superscripts are omitted, because both SI and Gaussian share the same dimension, e.g. force is LMT-2.
- Here are the calculations.
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