What is the Dimension of Electric Charge?

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Discussion Overview

The discussion revolves around the dimensional analysis of electric charge, specifically questioning the definition of its dimension as "M^(1/2)*L^(3/2)*T^(-1)" as presented in a German Wikipedia article. Participants explore the implications of this definition in relation to Coulomb's Law and the nature of electric charge as a fundamental property.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that the dimension of electric charge is defined as "M^(1/2)*L^(3/2)*T^(-1)" according to a German Wikipedia source, questioning the fundamental nature of electric charge.
  • Another participant explains that this dimension arises from Coulomb's Law, which relates charge to force, mass, length, and time.
  • A participant seeks clarification on whether this definition implies that Coulomb's Constant is dimensionless.
  • There is a suggestion that defining electric charge in this way may be misleading, as it treats charge as a mechanical unit while other electromagnetic quantities depend on its definition.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the dimensional definition of electric charge, with some questioning its validity and others defending its basis in Coulomb's Law. The discussion remains unresolved regarding the interpretation of electric charge as a fundamental property versus a derived quantity.

Contextual Notes

Participants highlight the dependence of electromagnetic quantities on the definition of electric charge, indicating that the discussion may be limited by assumptions about the nature of charge and the systems of units used.

azabak
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If you search electric charge on the German Wikipedia (search electric charge on Wikipedia and click on the "Deutsch" blue link on the left side) its dimension is defined as "M^(1/2)*L^(3/2)*T^(-1)". I always thought of electric charge as fundamental property that by definition has its own dimension "Q". Could someone please explain me this?
azabak
 
Last edited:
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This comes about by defining the unit of charge using Coulomb's Law: two charges, each with one unit of charge, separated by one unit of distance, exert one unit of force on each other. Combine this with the definition of the unit of force in terms of units of mass, length and time.
 
Is this the definition of electric charge? If so it makes the Coulomb's Constant dimensionless.
 
azabak said:
Is this the definition of electric charge?

It's a definition of electric charge.
If so it makes the Coulomb's Constant dimensionless.

Yes, in such a system of units. See for example

http://en.wikipedia.org/wiki/Gaussian_units
 
I think this definition is, somehow, misleading assuming electric charge as a mechanical unit since all other electromagnetic quantities depend on the definition of electric charge.
 

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