# Why is μ0 assigned an exact value in SI units?

• A. Turner
In summary: However, in 1983, an amendment to the International Treaty on Weights and Measures defined the meter as the distance light travels in vacuum in 1/299792458 of a second. This means that the value of c can be manipulated according to the needs of science.
A. Turner
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

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.

## 1. Why is μ naught defined?

μ naught, also known as the permeability of free space, is defined to provide a numerical value for the strength of the magnetic field in a vacuum. This allows for precise calculations and measurements in the field of electromagnetism.

## 2. What is the significance of μ naught?

The value of μ naught, which is approximately 4π x 10^-7 N/A^2, is a fundamental constant in physics. It relates the magnetic field strength to the electric current and is used in various equations to describe electromagnetic phenomena.

## 3. How was μ naught originally determined?

μ naught was first calculated by the physicist James Clerk Maxwell in the mid-19th century through his famous equations of electromagnetism. It was later experimentally measured by scientists such as Joseph Henry and Wilhelm Weber.

## 4. Can the value of μ naught change?

No, the value of μ naught is considered a fundamental constant and is not dependent on any external factors. It is a fixed value that remains the same in all areas of the universe.

## 5. How does μ naught relate to other physical constants?

μ naught is related to other fundamental constants such as the speed of light, electric charge, and Planck's constant. It is used in the calculation of other physical quantities and plays a crucial role in our understanding of the fundamental laws of nature.

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