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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?
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.HallsofIvy said:Rather than "they don't exist at all", you mean they are "1" don't you?
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.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.
##\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.
##\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.
##\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.
##\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.
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.