The Connection Between Electric and Magnetic Constants Explained

[PhDorBust]

Both the electric constant and magnetic constant are the product of rationalized units and hold no physical significance.

How can they have no physical significance yet have such an elegant relation to the speed of light?

 

[Bob S]

The constants ε_o Farads per meter and μ_o Henrys per meter are a consequence of selecting rationalized MKS units. But their units, Farads and Henrys per meter have important effects:

SQRT[μ_o/ε_o] = 377 ohms, the same "ohms" as a resistor, because capacitors and inductors store electric and magnetic fields, which are important in electric circuits.

SQRT[1/μ_oε_o] = 2.9979 x 10⁸ meters per second (speed of light).

Even if we set their values to 1, and revalue many fundamental constants (ohms, speed of light (meaning the meter if we hold the second fixed), amps, volts, Tesla, Farad, Newton (defined through the Lorentz force), etc., etc., their units will remain.

Bob S

 

[PhDorBust]

The constants ε_o Farads per meter and μ_o Henrys per meter are a consequence of selecting rationalized MKS units. But their units, Farads and Henrys per meter have important effects:

SQRT[μ_o/ε_o] = 377 ohms, the same "ohms" as a resistor, because capacitors and inductors store electric and magnetic fields, which are important in electric circuits.

SQRT[1/μ_oε_o] = 2.9979 x 10⁸ meters per second (speed of light).

Even if we set their values to 1, and revalue many fundamental constants (ohms, speed of light (meaning the meter if we hold the second fixed), amps, volts, Tesla, Farad, Newton (defined through the Lorentz force), etc., etc., their units will remain.

Bob S

I'm afraid I don't follow. I understand these electric and magnetic constants to simply be constants of proportionality from electric units to mechanical ones. And the attached constants like 1/4pi are merely for simplicity. This would be fine except for their relation to the speed of light. I understand that for the speed of light eqn, the units work out to m/s... but how do constants come to equal it?

What was derived from what?

 

[Bob S]

What was derived from what?

The second came first, followed by the cubit (then meter and the foot). Then kilogram (or it could have been a stone or a pound), then "g" and Newtons, then volt (from Volta cells), amp, then ohm, Gauss etc, etc.

Now (I believe) a Newton is defined as the force between two conductors each 1 meter long and x? cm apart and carrying 1 amp. We could set all the important constants to 1, but problems arise if we set the speed of light to 1, and not change the definition of a second, for example. We would have a nanometer stick in common usage (the speed of light is about 30 cm/nanosecond).

Bob S

 

[Phrak]

Both the electric constant and magnetic constant are the product of rationalized units and hold no physical significance.

How can they have no physical significance yet have such an elegant relation to the speed of light?

Hold on. As Bob was trying to explain it, I think, both mu₀ and eplison₀ have physical significance. We can use these values to calculate physically significant things like the speed of light in a vacuum and how electrical circuits will behave. Their exact values, in some given units, are the result of the way in which we people define things like distance and units of electric current.

If these humanly defined units have physical significance, so do the values of vacuum permeability and permissively.

What do you mean by physical significance?

Edit: I take it all back. Anyone who would talk to you about physics using the word 'significance' is not talking physics but gibberish where words are held in common but their meanings are ephemeral and moving targets, evolving with personal taste. The word 'significance' has no physical significance. :-d

 

[PhDorBust]

It seems like these rationalized factors like 1/4pi for coulomb's law were implemented after the fact of Maxwell's equations so that the relation did exist elegantly?

 

[PhDorBust]

It seems like these rationalized factors like 1/4pi for coulomb's law were implemented after the fact of Maxwell's equations so that the relation did exist elegantly?

Wikipedia states that the electric constant describes no physical property and is simply a measurement-system constant. How does it describe the speed of light then?

 

[Bob S]

Wikipedia states that the electric constant describes no physical property and is simply a measurement-system constant. How does it describe the speed of light then?

In an earlier post I stated that the ratio of μ_o and ε_o had the units of ohms², and the product had the units of velocity^-2. Ohms of course are the basis for electrical engineering, and velocity for the speed of light. If μ_o and ε_o are simply constants, then if we set these constants to one (both their values and their units), can we then say that the resistance of a 1-ohm resistor equals the speed of light? This would make physics really simple, wouldn't it. Everybody could then claim to be a physicist.

Bob S