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Elasticity and resistance are universal terms regarding electromagnetism!


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Do you know what elasticity is? I will tell you in short.
Imagine two rubber rods, equal in dimensions, but they are made from different types of rubber. The different types of rubber have different elasticity.
Imagine one has to bend both rods to an equal extent (figure below):


Let’s say the grey rubber is more elastic than the black rubber. Therefore, you have to apply less force to bend the grey rod than to bend the black rod to the same extent (pictured on the right in the figure above).

Instead of bending them, let’s say you have to twist them to the same extent. What does it mean “to the same extent” in this case? If you twist them by applying force with both hands, then it means, for example, that you have to turn the rod with the left hand for 90 degrees and also with the right hand for 90 degrees. So, you will twist both rods to the same extent (i.e. 180 degrees). (note: you can turn only one hand for 180 degrees. The result is the same.)
You will do that also easier with the grey rod than with the black rod.

Now, imagine two rubber rods, both are made from the same type of rubber and both are equally long, but the one rod is thicker than the other. The thinner rubber rod is more elastic than the thicker rubber rod. You will have to apply less force for the thinner rod to twist it (or to bend it) to the same extent.

Yet another case: you have two rubber rods, both are made from the same type of rubber, both equally thick, but the one rod is longer than the other rod. The longer rubber rod is more elastic than the shorter. You will have to apply less force to twist the longer rod.

So, you see that the elasticity of a rubber rod depends on the material, on the length and on the thickness (i.e. the cross sectional area):


k - coefficient of elasticity
L - the length of the rod
A - cross sectional area of the rod

But look, we can always speak of the opposite (reciprocal) of a certain quantity. For example, the opposite of speed is slowness (1/v). The cheetah is the world champion in speed, but the snail is the world champion in slowness. Its slowness is 115 s/m.

Similarly, instead of elasticity of the rubber rod, we can speak of its reciprocal quantity. What quantity would that be? It would be resistivity. Instead of saying a rod is more elastic, we could also say it is less resistive and vice versa (less elastic corresponds to the more resistive).

You are probably asking yourself, what all this has to do with electromagnetism? Look, more than a hundred years ago Oliver Heaviside introduced the term “elastance” as the inverse of capacitance. He made an analogy of a capacitor as a spring, which was not a very good comparison. A true comparison is twisting and untwisting of a rubber rod. If you connect a capacitor to a battery, then the EM-forces of the dielectric get twisted. The process of twisting is actually an electric current through the dielectric in one direction. If you disconnect the capacitor and then connect it to a resistor, the process of untwisting in the dielectric begins (the energy stored in the twist is being released). It is actually an electric current in the opposite direction. The greater the resistance of the resistor is, the slower is the process of untwisting.

So, the dielectric of the capacitor is, in a sense, a rubber rod.
For the capacitance of a capacitor applies the equation:


For the elasticity/elastance of a capacitor would apply the reciprocal equation:


If you compare it to the first equation about the elasticity of the rubber rod, you will notice that they are the same. The length of the rubber rod corresponds to the “d” of the dielectric.

Instead of capacitance of a capacitor, we can speak of resistance of a capacitor. So, instead of capacitance/elastance, we can speak of resistance/elasticity. Why would we do that? Because we can apply the same concept to an inductor.

Just as there is twisting and untwisting of the EM-forces in the dielectric of a capacitor, there is also twisting and untwisting of the EM-forces in the (ferromagnetic) core of an inductor. The difference between the two is in that, that in the first case the dominance is on the electric forces, while in the second case the dominance is on the magnetic forces.

The inductance of a ferromagnetic core is:


The number μ (mu) is called magnetic permeability. It corresponds to the resistivity of the rubber as material. The number A is the cross sectional area of the core, while l is the length of the core.

So, the elasticity of the ferromagnetic core will be:


Oliver Heaviside didn’t coin an opposite term for the inductance as he did it for the capacitance. If he did it, then it should have been the same as for the capacitance.

I can also speak about resistance vs elasticity regarding the flow of electric current through the metals, but I will do it in another post. Here I will only say that silver and copper are electrically the most elastic metals, that is, they conduct the electric current the best.

As you can see, resistance and elasticity are universal terms regarding electromagnetism. They can be applied to conductors, dielectrics (capacitors) and ferromagnetics (inductors).

See also:
What is electric current?

Pinna Brelstaff optical illusion recurs in mechanics and electromagnetism!


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