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What is the Vacuum Permeability (Magnetic Constant)?

Answer #1

Level 2 (without higher mathematics)
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The vacuum permeability is a physical constant and is written as \( \mu_0 \) (pronounced: "Mu zero"). It has the following value:

Value of the vacuum permeability
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  • The unit of \(\mu_0\) is, for example, volt-second per ammeter or Henry per meter:

    Unit of the magnetic vacuum permeability
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  • The vacuum permeability occurs in the equations that have to do with magnetic fields. For example, in the Biot-Savart law or in the wave equation for electromagnetic waves.

  • The vacuum permeability, for example, determines how strongly two current-carrying wires attract or repel each other.

    Attractive Lorentz force - two current-carrying conductors of the same direction
    Two current-carrying wires attracting each other.
    Repulsive Lorentz force - two conductors with current flowing in opposite directions
    Two repulsive current-carrying wires.
  • The vacuum permeability, together with the vacuum permittivity \(\varepsilon_0\), determines how large the speed of light \(c\) should be in a vacuum:

    Vacuum permeability is the reciprocal of the vacuum permittivity and speed of light squared
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  • Vacuum permeability describes how good the magnetic fields can penetrate the vacuum.

  • The magnetic field constant also determines how strongly the vacuum can be magnetized. If we want to know how strongly other substances can be magnetized, then we can calculate their permeability \(\mu\):

    Formula for permeability of a material
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    Here \(\mu_{\text r}\) is the relative permeability and varies from material to material. The relative permeability value describes whether the material is diamagnetic, paramagnetic or ferromagnetic. Iron, for example, has a value of \(\mu_{\text r} = 300 \) to \(\mu_{\text r}= 10\, 000\) depending on the temperature and is very easy to magnetize.

The vacuum permeability can be measured, for example, with the help of two long current-carrying wires which are at a distance \(r\) from each other. For this purpose, the attractive force \(\class{green}{F}\) of two wires is measured, through which (in each) the current \(\class{blue}{I}\) flows:

Magnetic force (Lorentz force) on a current-carrying conductor
One of the two wires.
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A more precise way to determine the vacuum permeability experimentally is to measure the fine structure constant \(\alpha\) and then use the following equation:

Determine vacuum permeability by using the fine structure constant
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Here \(h\) is the Planck's constant, \(e\) is the elementary charge, and \(c\) is the speed of light.