Why is μ0 assigned an exact value in SI units?

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Discussion Overview

The discussion centers around the assignment of an exact value to the permeability of free space (μ0) in SI units and the implications of this assignment on other physical constants, particularly in relation to the speed of light and the definition of the meter. Participants explore the theoretical and practical aspects of defining these constants within the framework of SI units.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the rationale behind assigning μ0 an exact value, suggesting it should be experimentally derived like other constants.
  • Another participant argues that since the meter is defined in terms of the speed of light, μ0 can be set to an exact value by manipulating the definition of the Tesla, making its assigned value arbitrary.
  • A different participant challenges the assertion that the meter is defined in terms of the speed of light, stating that μ0 has SI base units without proportionality, implying limited room for manipulation.
  • In response, a participant clarifies that the meter has indeed been defined based on the speed of light since 1983, suggesting that this definition allows for the manipulation of μ0 through the unit of Tesla.
  • Another participant acknowledges the earlier confusion regarding the manipulation of units, noting that adjusting the Ampere also affects μ0.
  • One participant supports the claim that the meter's definition ties it to the speed of light, reinforcing the argument made by another participant.

Areas of Agreement / Disagreement

Participants express disagreement regarding the definition of the meter and its implications for μ0. Some assert that the meter is defined in terms of the speed of light, while others contest this view, leading to an unresolved discussion on the nature of these definitions and their consequences.

Contextual Notes

The discussion highlights potential misunderstandings regarding the definitions of SI units and their interdependencies, particularly concerning the roles of μ0, ε0, and the speed of light. There are unresolved aspects related to the manipulation of units and the implications of these definitions on physical constants.

A. Turner
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Hello all,

While I understand the significance of natural units, I am wondering why, in SI units, we are able to assign μ0 an exact value. The speed of light is experimentally determined in m/s, and given the relationship derived from Maxwell's equations, we know that c^2 = 1/√(ε0μ0). Thus by assigning μ0 an exact value of 4π*10^-7 in SI units, we are also defining the value of ε0. Thus we have defined the proportionality of charge to force in SI units -- which should be an experimentally derived value. So where am I going wrong here?

It must be that we are not actually 'choosing' the value of μ0. But then how is it exact in SI?

Thanks
 
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Since the meter is defined in terms of the speed of light, the numerical value of c is exact. Since c^2 = 1/√(ε0μ0), that means that we can choose a definition of the unit of magnetic field (Tesla) such that μ0 is exact and ε0 is exact. μ0 is just a proportionality factor in the Biot-Savart law, so by manipulating the value of the Tesla, we can set μ0 to any number we choose. The value of 4π*10^-7 is arbitrary.
 
Khashishi said:
Since the meter is defined in terms of the speed of light, the numerical value of c is exact. Since c^2 = 1/√(ε0μ0), that means that we can choose a definition of the unit of magnetic field (Tesla) such that μ0 is exact and ε0 is exact. μ0 is just a proportionality factor in the Biot-Savart law, so by manipulating the value of the Tesla, we can set μ0 to any number we choose. The value of 4π*10^-7 is arbitrary.

I don't believe the meter is defined in terms of the speed of light? Other natural units are, but not the meter. Furthermore, mu naught has SI base units without any added proportionality, so I don't see how there is room for manipulation.
 
You believe wrong. As of 1983, the meter is defined as the distance light travels in vacuum in 1/299792458 of a second. In other words, m = c*s/299792458

The base units are the room for manipulation. As I said, the value of Tesla was manipulated.
 
Khashishi said:
You believe wrong. As of 1983, the meter is defined as the distance light travels in vacuum in 1/299792458 of a second. In other words, m = c*s/299792458

The base units are the room for manipulation. As I said, the value of Tesla was manipulated.

Ah okay, thank you so much!
 
Ah right, I said the Tesla was manipulated, but adjusting the Ampere has the same effect.
 
A. Turner said:
I don't believe the meter is defined in terms of the speed of light?
Khashishi is correct. The meter is defined as the distance that makes c equal to a certain exact number.
 

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