Help: From Ampere to Coulomb in SI units

In summary, the conversation discusses the choices made when defining SI units, including the value of 1 Ampere and the constant for the force between parallel conductors. The Coulomb's law and its connection to the definition of Ampere is also mentioned, along with potential changes to the definitions in the future for historical reasons.
  • #1
Sunfire
221
4
Hello,

Could someone help me finish this train of thought? This is how we think in SI units:

First, just because we like the value of 1 Ampere as it is now, we choose the force between two parallel conductors to be exactly

2×10[itex]^{-7}[/itex]N= const ×[itex]\frac{1A×1A}{1m}[/itex]

Then, purely as choice, we decide to formulate a constant from the above relation

μ[itex]_{0}[/itex]=4π×10[itex]^{-7}[/itex] N/A^2

Next comes the Coulomb's law. Why do we choose the Coulomb constant to involve the [itex]\epsilon_{0}[/itex] from the expression c[itex]^{2}[/itex]=[itex]\frac{1}{\epsilon_{0}\mu_{0}}[/itex]? Why not choose something else?

Is this tied to the definition of Ampere?

Thanks.
 
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  • #2
These days, the Ampere is defned by the force law - so it is the amount of current that gets you 2x10-7N of force between wires 1m apart.

Normally we'd want to make the force 1N for the definition, that would make the Ampere very large indeed. The funny number was selected for historical reasons.

http://en.wikipedia.org/wiki/Ampere

The Coulomb is defined in terms of the Amp - yes.
This is likely to get reversed in 2014... with the Coulomb getting defined as a specific number of elementary charges and the Amp being defined as 1 C/s.
Then people will ask - "why that exact number" and the reason will be "historical" ... i.e. so that values don't get thrown too far off what people expect. [I mean - the kinds of values that people feel are comfortable to use.]
 
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Related to Help: From Ampere to Coulomb in SI units

What is the difference between Ampere and Coulomb in SI units?

Ampere and Coulomb are both units of measurement for electric current in the International System of Units (SI). The main difference between them is that Ampere measures the flow of electric charge, while Coulomb measures the actual amount of electric charge. In simpler terms, Ampere is a measure of how fast the charge is moving, while Coulomb is a measure of the total charge.

How do you convert Ampere to Coulomb?

To convert from Ampere to Coulomb, you can use the formula Q = I x t, where Q is the electric charge in Coulomb, I is the electric current in Ampere, and t is the time in seconds. For example, if you have an electric current of 2 Ampere for 5 seconds, the conversion would be: Q = 2 A x 5 s = 10 C. Therefore, 2 Ampere is equivalent to 10 Coulomb.

Why is Coulomb the preferred unit for electric charge?

Coulomb is the preferred unit for electric charge because it is a more precise and accurate measurement than other units, such as the unit of electric charge in the CGS system (statcoulomb). Coulomb is also the base unit for electric charge in the SI system, making it easier to convert between different units of electric charge.

Can you explain the relationship between Ampere and Coulomb?

The relationship between Ampere and Coulomb is based on the definition of electric current, which is the rate of flow of electric charge. One Ampere is equal to one Coulomb of electric charge passing through a given point in one second. In other words, Ampere and Coulomb are directly proportional to each other, with a conversion factor of 1 Ampere = 1 Coulomb/second.

What are some real-life applications of Ampere and Coulomb in SI units?

Ampere and Coulomb have many practical applications, such as in electrical engineering, electronics, and physics. They are used to measure and describe the flow of electric current in circuits, the charge of particles in an atom, and the strength of an electric field. These units are also essential in the development and use of electrical devices, such as batteries, motors, and generators.

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