How do you convert electrostatic unit of charge (esu) to coulomb (C)?

Question

I know the conversion factor is ≈ 3.33564×10^−10, but how do you derive the conversion factor?

Answer 1

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.

Answer 2

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RE:
How do you convert electrostatic unit of charge (esu) to coulomb (C)?
I know the conversion factor is ≈ 3.33564×10^−10, but how do you derive the conversion factor?

Answer 3

Esu Unit

Answer 4

The statcoulomb is defined as the charge that placed on two point particles 1cm apart results in a force of 1 dyne.

You can work this out directly in the MKS system:

dyne = g(cm)/s^2 = q^2/(4piE0(cm)^2) or

q = sqrt(4piE0(cm)^3(g)/s^2) = 3.33E-10C

Answer 5

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