On Physical Lines of Force: elasticity, density and the speed of light

In summary, Maxwell discusses the ratio of m to mu in different substances, which has a value of 6 to 5 in a medium where elasticity is dependent on forces between pairs of particles. He also presents a wave equation for transverse vibrations in this medium, where the speed of propagation is proportional to the square root of tension and inversely proportional to the square root of linear mass. He derives this equation using the model of particles connected by springs, with the assumption that elasticity is due entirely to forces between pairs of particles. The numerical values for elasticity and density are not mentioned, but they may be related to modern equations for electric and magnetic constants.
  • #1
Dunnis
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Maxwell: -"The ratio of m to mu varies in different substances; but in a medium whose elasticity depend entirely upon forces acting between pairs of particles, this ratio is that of 6 to 5, and in this case E^2= Pi*m"

Q1: What is this 6:5 ratio and how did he make that conclusion?

Q2: What is the importance of "depend entirely... pairs of particles"?



Maxwell: -"To find the rate of propagation of transverse vibrations through the elastic medium, on the supposition that its elasticity is due entirely to forces acting between pairs of particles

[PLAIN]https://www.physicsforums.com/latex_images/26/2647530-2.png

where 'm' is the coefficient of transverse elasticity, and 'p' is the density."

Q3: Again this "entirely due to pairs of particles", what is he talking about, is he saying photons are made of particle pairs, or is he describing aether as something like Dirac Sea made of electron-positron pairs, or what?

Q4: Where did he get numerical values for this elasticity 'm' and density 'p', are those two the same numbers as electric and magnetic constant in modern equations?

Q5: Did anyone notice his original "wave equation" is nothing else but the 'wave equation for vibrating string': -"The speed of propagation of a wave in a string (v) is proportional to the square root of the tension of the string (T) and inversely proportional to the square root of the linear mass (μ) of the string:

[PLAIN]https://www.physicsforums.com/latex_images/26/2647530-3.png

". - http://en.wikipedia.org/wiki/Vibrating_string
 
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  • #2
What are the E and m in the E^2 = pi*m?

"Pairs of particles." The wave equation is often derived using the model of a chain of particles all connected to their neighbors using springs. When he says connected as paris of particles he probably is referring to the fact that the equation assumes a rather pedestrian situation like this (as opposed to something that may have different symmetries of springiness in different direction, etc...)

Did anyone notice his original "wave equation" is nothing else but the 'wave equation for vibrating string

Yep, the derivations are extremely similar. One case you look at particles vertically displaced from their neighbours (restoring force in the small oscillation limit of T*theta) and in the other case you look at particles horizontally displaced from their neighbours (restoring force of k*x)

Hope that was of help. The parts I didn't respond to I don't know how to.
 
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1. What is the concept of "Physical Lines of Force"?

Physical Lines of Force is a concept in physics that explains the behavior of physical forces such as elasticity, density, and the speed of light. It suggests that these forces can be represented by imaginary lines that connect objects and particles, and these lines determine how the forces interact with each other.

2. How does elasticity affect Physical Lines of Force?

Elasticity refers to the ability of a material to return to its original shape after being deformed by an external force. In the context of Physical Lines of Force, elasticity plays a significant role in determining the strength and direction of the lines connecting objects, as well as the overall behavior of the forces between them.

3. What is the relationship between density and Physical Lines of Force?

Density is a measure of how much mass is contained in a given volume of a substance. In the context of Physical Lines of Force, density affects the strength and direction of the lines connecting objects, as well as the overall behavior of the forces between them. Objects with higher density will have stronger lines of force connecting them, while objects with lower density will have weaker lines.

4. How does the speed of light play a role in Physical Lines of Force?

The speed of light is a fundamental physical constant that determines the maximum speed at which energy, information, or matter can travel. In the context of Physical Lines of Force, it affects the strength and direction of the lines connecting objects, as well as the overall behavior of the forces between them. The speed of light also plays a crucial role in the concept of electromagnetic waves, which are a type of Physical Line of Force.

5. Is the concept of Physical Lines of Force widely accepted in the scientific community?

Yes, the concept of Physical Lines of Force is widely accepted in the scientific community and has been studied extensively in the fields of physics and mechanics. The concept was first introduced by Michael Faraday in the 19th century and has been further developed and refined by other scientists over the years. It continues to be a fundamental concept in understanding the behavior of physical forces.

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