Why is μ0 assigned an exact value in SI units?

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SUMMARY

The discussion centers on the assignment of an exact value to μ0 (the permeability of free space) in SI units, specifically 4π x 10^-7 N/A². Participants clarify that this value is not arbitrary but is defined through the relationship c² = 1/√(ε0μ0), where c is the speed of light, which is also defined exactly. The manipulation of the unit of magnetic field (Tesla) or the unit of electric current (Ampere) allows for μ0 and ε0 to be defined precisely, establishing a proportionality in electromagnetic equations.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with SI units, particularly Tesla and Ampere
  • Knowledge of the relationship between electric and magnetic fields
  • Basic concepts of natural units in physics
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  • Research the derivation of Maxwell's equations
  • Study the implications of defining the meter in terms of the speed of light
  • Explore the Biot-Savart law and its applications
  • Learn about the historical context of SI unit definitions and their evolution
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Physicists, electrical engineers, and students studying electromagnetism who seek to understand the foundational principles of SI units and their interrelationships.

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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