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Home Q & A Board Science-Related Homework Help Physics
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datboililp datboililp
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11 years ago
I know the conversion factor is ? 3.33564×10^?10, but how do you derive the conversion factor?
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micooomicooo
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11 years ago
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11 years ago
The esu is the cgs systems unit of charge while the Coulomb is the SI unit of charge. The esu is defined directly in the cgs system where as the Coulomb is derived in SI.

The equation is:

1 esu = 0.1 A m / c

where c is the speed of light.

This works out to be:

1 esu = 0.1 (C/s) * m / (299,792 m/s)

or

1 esu = 3.334564e-10 C

You might wonder how the speed of light came into all this. The cgs system assumes that the permitivity of free space is dimensionless and ignores the magnetic permiability of free space. Where as the SI gives both units. These two quantities are related to each other by the equation:

\epsilon_0 * \mu_0 = 1/c^2

So when converting from defined cgs to derived SI the speed of light shows up as a consequence of adding units to the permitivity of free space and taking into to account the magnetic permiability of free space.
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