# Why can we define μ naught?

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1. Aug 6, 2015

### 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

2. Aug 6, 2015

### Khashishi

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.

3. Aug 6, 2015

### A. Turner

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.

4. Aug 6, 2015

### Khashishi

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.

5. Aug 6, 2015

### A. Turner

Ah okay, thank you so much!

6. Aug 6, 2015

### Khashishi

Ah right, I said the Tesla was manipulated, but adjusting the Ampere has the same effect.

7. Aug 6, 2015

### Staff: Mentor

Khashishi is correct. The meter is defined as the distance that makes c equal to a certain exact number.

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