What Are the Correct Units of Coulomb's Constant?

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The discussion revolves around the units of Coulomb's constant as it relates to Coulomb's Law and the permittivity of free space, ε0. Participants are exploring the dimensional analysis of these units within the context of electrostatics.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning whether the units of Coulomb's constant can be directly derived from the units of ε0, which are given as F/m. Some suggest that it might be F-1m based on the relationship ke = 1/(4∏ε0). Others introduce the idea of expressing ε0 in terms of basic SI units, leading to further exploration of dimensional analysis.

Discussion Status

The discussion is active, with multiple interpretations being explored regarding the units of Coulomb's constant. Some participants have provided insights into the derivation of units, while others are questioning the assumptions made about the relationships between the constants involved.

Contextual Notes

There is a focus on the definitions and relationships between various physical constants, particularly in the context of electrostatics. Participants are considering the implications of using different unit systems and the foundational definitions of the units involved.

ZedCar
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Coulomb's constant, which appears in Coulomb's Law, contains ε0.

The units of ε0 being F/m

Are the units of Coulomb's constant therefore F/m ?

Thank you.
 
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ZedCar said:
Coulomb's constant, which appears in Coulomb's Law, contains ε0.

The units of ε0 being F/m

Are the units of Coulomb's constant therefore F/m ?

Thank you.

I would have thought F-1m since ke = 1/(4∏εo)
 
ZedCar said:
Coulomb's constant, which appears in Coulomb's Law, contains ε0.

The units of ε0 being F/m

Are the units of Coulomb's constant therefore F/m ?

Thank you.

Yes, but farad can be derived from the basic units of the SI system, so the unit of ε0 is A2s4kg-1m-3 in terms of the basic SI units.

ehild
 
PeterO said:
I would have thought F-1m since ke = 1/(4∏εo)

For parallel plate capacitors, C=εA/d (A is the surface of the plates, d is the distance between them) so farad=[ε]m.

ehild
 

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