# I What was the value of the permeability constant in 1865?

#### avicenna

What is the value of the permeability constant in 1865, the time when Maxwell's theory was first published? What was the experimental method used to determine the constant. Who did the experiment.

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Mentor

#### avicenna

https://en.wikipedia.org/wiki/Oliver_Heaviside
Nothing there.

It is said Maxwell discovered that the speed of radiation v = 1/√(μ₀ ε₀) and v happened to be near the known speed of light then. So in 1865, there should be an accepted value of μ₀. But google gives no clue at all. Why so difficult to trace history of permeability constant?

#### jtbell

Mentor
Maxwell didn't actually use the equation $v = \frac 1 {\sqrt {\mu_0 \epsilon_0}}$. That equation uses SI units which hadn't been codified in Maxwell's day. He used a different set of units, and indeed different names for many electromagnetic quantities. The equation we use nowadays should be considered a modern "translation" or "interpretation" of Maxwell's calculations. For what it's worth, you can see what Maxwell actually wrote when he calculated the theoretical speed of his electromagnetic waves:

https://en.wikisource.org/wiki/Page:Philosophical_magazine_23_series_4.djvu/38

#### avicenna

Maxwell didn't actually use the equation $v = \frac 1 {\sqrt {\mu_0 \epsilon_0}}$. That equation uses SI units which hadn't been codified in Maxwell's day. He used a different set of units, and indeed different names for many electromagnetic quantities. The equation we use nowadays should be considered a modern "translation" or "interpretation" of Maxwell's calculations. For what it's worth, you can see what Maxwell actually wrote when he calculated the theoretical speed of his electromagnetic waves:

https://en.wikisource.org/wiki/Page:Philosophical_magazine_23_series_4.djvu/38
OK. The original derivation of radiation speed is too difficult for me. I don't really know how our modern EM speed derivation may be related or compared to Maxwell's original.

#### tech99

Gold Member
OK. The original derivation of radiation speed is too difficult for me. I don't really know how our modern EM speed derivation may be related or compared to Maxwell's original.
In the cgs system in use at that time (and also when I was at school) there are two sets of units, emu and esu. The emu is current (charge x velocity) necessary to produce a force of 1 dyne between two conductors, and the esu is the charge necessary to produce a force of 1 dyne between two charges, all spaced 1cm. For a vacuum, permeability and permittivity were defined as 1. Maxwell noticed that the ratio of these two units was about equal to 3 x 10^8 m/s, which is c.

#### avicenna

In the cgs system in use at that time (and also when I was at school) there are two sets of units, emu and esu. The emu is current (charge x velocity) necessary to produce a force of 1 dyne between two conductors, and the esu is the charge necessary to produce a force of 1 dyne between two charges, all spaced 1cm. For a vacuum, permeability and permittivity were defined as 1. Maxwell noticed that the ratio of these two units was about equal to 3 x 10^8 m/s, which is c.
Great! Very helpful. Though I don't understand it now, this is the hint if I want to investigate further. I do know that the force between currents in conductors is related to the magnetic field and thus to permeability. The other is simply related to permittivity.

"What was the value of the permeability constant in 1865?"

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