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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.

shreder
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2 Answers2

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It doesn’t have any physical significance. It is nothing more than an ugly artifact of SI units. In other unit systems, such as Gaussian units, it doesn’t exist and “vacuum permittivity” isn’t even a meaningful concept.

More generally, no physical constant with dimensions has physical meaning, because its value depends on arbitrarily chosen units. As a simple example, what is significant about the speed of light is not its particular value but that it isn’t zero, isn’t infinite, and is much larger than other speeds we typically observe. Dimensionless ratios of other speeds to the speed of light are what have physical significance.

For more information, see the question Dimensionless constants in physics.

G. Smith
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Imagine a positive charge placed in vacuum, we can understand its lines of forces are directed outward (because it is positive charge) with equal distances between them, now the amount of how easily the electric field lines go through this space is determined by the value of the $\epsilon_0$

Sagigever
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  • Do you think that the value of $\epsilon_0$ tells us that field lines go through vacuum very easily, or with great difficulty, or something in between? And please explain why you think that. – G. Smith Jul 22 '20 at 18:27
  • Actually that's not correct: the CGS units have no $\epsilon_0$ in them so the number of electric field lines cannot be determined by $\epsilon_0$ else this would be a unit-dependent quantity, i.e. the number of field lines would depend on the choice of units rather than only the size of the source. – ZeroTheHero Jul 22 '20 at 18:39
  • The number of field lines is infinite. – G. Smith Jul 22 '20 at 18:44