What is the Dimension of Electric Charge?

AI Thread Summary
The dimension of electric charge is defined as "M^(1/2)*L^(3/2)*T^(-1)" according to the German Wikipedia, which contrasts with the common notion of charge having its own dimension "Q." This definition arises from Coulomb's Law, where the unit of charge is linked to force, mass, and distance. The discussion highlights that this interpretation could render Coulomb's Constant dimensionless, raising questions about the mechanical nature of electric charge. Some participants argue that this definition may be misleading, as it suggests that electric charge is a fundamental mechanical unit, while other electromagnetic quantities rely on its definition. The conversation emphasizes the complexity of defining electric charge within the framework of physics.
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
 
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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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