Dec 9, 2011 · This relates the two constants $\epsilon_0$ and $\mu_0$ by the following argument: Consider two charged parallel lines. They repel electrostatically by an amount determined by the field of a charged line at distance r from the center: $\rho\over 2\pi \epsilon_0 r$, so they get pushed apart by a force f per unit length which is equal to:

Jul 22, 2020 · I was reading some information about the constant of electromagnetism $\epsilon_0$ $[\frac{C^2}{N\cdot M^2}]$ and according to my understanding it is the amount how much electric field is permitted in the space (vacuum). I do not understand this idea so much and I would like for an example in real life when the $\epsilon_0$ plays role.

Maxwell relates the electric permitivity to magnetic permeability in the vacuum, $\mu_{0}=\frac{1}{\epsilon_{0}c^{2}}$ which is given a value of $\mu_{0}=4\pi\times10^{-7}H/m$ in SI units. The 'reason' for the "$4\pi$" appearing here and in Coulomb's constant (believe it or not) so that Maxwell's equations can be written without any $4\pi ...

May 28, 2020 · I find Jackson’s table as baffling as Wikipedia’s. I used to teach electromagnetism from Jackson but that was when his book used Gaussian units. From my point of view, there is no $\epsilon_0$ in Gaussian EM and it has no “value” in Gaussian units. To convert equations from SI to Gaussian one replaces $1/4\pi\epsilon_0$ with $1 ...

Edit 2: I was under the impression that $\epsilon_0$ is defined to make Gauss's law simpler. I voted this ...

What does all that have to do with $\epsilon_0$? Well, by induction we have that $\omega,\omega^\omega,\omega^{\omega^\omega},\ldots$ are all countable, and there are only countably many of those. From this we have that $\epsilon_0$ is also countable. It is a large countable ordinal. Now we can continue by induction, what is $\epsilon_1$?

Oct 5, 2017 · This is described by the variable $\epsilon = \epsilon_0 \epsilon_r$, where $\epsilon_r$ is the relative permittivity, which is one or greater. It is important to realize that there are many other possible equations of state that relate the movement of …

Apr 6, 2016 · The $\epsilon_0$ and $\mu_0$ are coefficients in the microscopic Maxwell equations, which describe the fundamental behaviour of light in vacuum. This particular simple and straightforward description of light present for example in the quantum electrodynamics or in quantum chemical calculations (for example time-dependent density functional ...

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Jun 7, 2017 · So in the past few months when trying to learn about the properties of the fixed points in ordinals as I move from $0$ to $\epsilon_{\epsilon_0}$ I noticed when moving from $\epsilon_n$ to the next one $\epsilon_{n+1}$, the operation …