What's the physical interpretation of ##\mu_0## and ##\varepsilon_0##?

In summary: This means that the flux through a particular area can be determined by solving the flux equation for that area. This opens up a lot of possibilities for using Maxwell's equations in ways that were not possible before.In summary, the physical interpretations of ##\mu_0## and ##\varepsilon_0##, the magnetic permeability and electric permittivity of vacuum, can't be directly measured. However, they can be indirectly measured through the effects they have on other physical quantities. In CGS units, there is only one arbitrary constant, the speed of light in a vacuum, which depends on the units of length and time. This makes Maxwell's equations more flexible since you can choose any combination of E to
  • #1
HakimPhilo
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What are the physical interpretations of ##\mu_0## and ##\varepsilon_0##, the magnetic permeability and electric permittivity of vacuum? Can these be directly measured? How?
 
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  • #2
They are basically artifacts of the units that we use for the magnetic field and the electric field. In Gaussian units, in vacuum, they don't exist at all. Look at Maxwell's equations in Gaussian units.
 
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  • #3
Rather than "they don't exist at all", you mean they are "1" don't you?
 
  • #4
HallsofIvy said:
Rather than "they don't exist at all", you mean they are "1" don't you?
That is a dimensionless 1, which can always be factored out or in. So I don't think there much of a difference between being a dimensionless factor 1 and not existing.

In SI units for Newtons 2nd law (f=ma) would you say the conversion factor between N and kg m/s^2 doesn't exist or is 1? I think either way is equivalent.
 
  • #5
I would say it was 1. To say a conversion factor "doesn't exist", to me, would imply that you can't convert one to the other.
 
  • #6
The key difference between CGS units and SI units is that SI invented an extra independent base unit (the ampere) which is logically unnecessary, and CGS units did not. Since the physics doesn't depend on the units, there is necessarily an extra non-dimensionless constant in SI units to mop up the extra unit.

So in SI units you have two "arbitrary units conversion factors" ##\mu_0## and ##\epsilon_0##, and an equation giving the speed of light in a vacuum in terms of the two factors.

In CGS you only have one "arbitrary constant" which depends on the units of length and time, namely the speed of light.

EDIT: this crossed with Hall's previous post, but IMO the point is that in CGS units there is nothing to convert. As an example, the units of electrical resistivity are just seconds-1, not something derived from amperes. Similarly the units of electrical capacitance in CGS are just centimeters.
 
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HallsofIvy said:
I would say it was 1. To say a conversion factor "doesn't exist", to me, would imply that you can't convert one to the other.
Fair enough. As long as you are consistent between Newton's 2nd law in SI units and Maxwells equations in Gaussian I think it is fine.
 
  • #8
Where SI starts showing a potential logical advantage over Gaussian units is that ##\mu_0## and ##\varepsilon_0## become no longer constants but vectors or tensors when dealing with media. Outside of a vacuum, magnetic permeability and electric permittivity vary continuously. They are the basis for most optical equations.

This means too that the possibilities for solutions to the Maxwell equations is increased. You may choose any combination of E to D or B to H variables using ##\mu## and ##\varepsilon## as conversion factors. Maxwell determined that there is a fundamental difference between a force intensity and a flux amount (the difference between E and D and subsequently B and H) that is defined in geometric terms.

##B = \mu H##
##D = \varepsilon E##
 
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1. What are ##\mu_0## and ##\varepsilon_0##?

##\mu_0## and ##\varepsilon_0## are the vacuum permeability and vacuum permittivity, respectively. They are fundamental constants that describe the properties of empty space in electromagnetism.

2. Why do we need ##\mu_0## and ##\varepsilon_0## in electromagnetism?

##\mu_0## and ##\varepsilon_0## are necessary in electromagnetism because they relate the electric and magnetic fields to one another. They also help to define the speed of light and the behavior of electromagnetic waves.

3. How are ##\mu_0## and ##\varepsilon_0## related to each other?

##\mu_0## and ##\varepsilon_0## are related by the speed of light, c, in a vacuum. This relationship is expressed as ##c^2 = 1/(\mu_0 \varepsilon_0)##. In other words, the product of ##\mu_0## and ##\varepsilon_0## determines the speed at which electromagnetic waves travel through empty space.

4. What are the units of ##\mu_0## and ##\varepsilon_0##?

##\mu_0## has units of henries per meter (H/m), while ##\varepsilon_0## has units of farads per meter (F/m). These units reflect the relationship between electric and magnetic fields in free space.

5. How were ##\mu_0## and ##\varepsilon_0## first determined?

The values of ##\mu_0## and ##\varepsilon_0## were first determined experimentally by James Clerk Maxwell in the 1860s. He used a series of equations to calculate the speed of electromagnetic waves, which led to the discovery of the relationship between ##\mu_0## and ##\varepsilon_0## and the speed of light.

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