Mu Naught Value: Definition, Units and Calculation

Mu naught or vacuum permeability of free space is a physical constant. It is the measure of the amount of resistance that is offered against the formation of the magnetic field in a vacuum. Mu naught is represented as μ₀. 

The value of mu naught is given by μ₀ = 4\(\pi\) × 10^-7 H/m.

Key Terms: Mu naught value, Permeability of Free space, Magnetic Field, Physical Constant, Henry, Micrometer, Electromagnetism, Permeability

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What is the Value of Mu Naught? 

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Mu naught value or μ₀  represents the permeability of free space.  It has an exactly defined value till 20 May 2019 but on 20 May 2019, the value of mu naught was revised. There was a revision to the SI system that took place on 20 May 2019.

• It is the value of the measured amount of resistance that is given against the formation of the magnetic field.
• Mu naught is the permeability constant of the vacuum in the magnetic field.
• Mu naught is a physical constant that is often used in electromagnetism.
• The sign μ is a Greek alphabet that is used to represent mu in physics.
• The value of Mu naught is equal to μ₀ = 4\(\pi\) × 10^-7 H/m.
• The approximated value of Mu naught is equal to 12.57 ×10^-7 H/m.

• Mu naught is also the proportionality constant between the free space permeability and the magnetic field strength in any of the mediums.
• As per the revised SI, the vacuum permeability is no longer a constant. It becomes a value that is needed to determine the experimentally.

The recently measured value is: 4π × 10000000008220 × 10^-7H•m¹

The video below explains this:

Mu Naught value Detailed Video Explanation:

Also Read:

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Mu Naught Unit 

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Mu naught is measured in H/m or Henry per meter.

• To represent the magnetic permeability in a vacuum we used to write using the Greek alphabet that is μ. 
• The sign μ is an abbreviation of the unit micron(s) or micrometer(s).
• Both of these are referred to as a unit of displacement that is equal to 0.000001-meter or 0.001 mm (millimeter).
• The dimensional unit of Mu Naught is M¹L¹T^-2A^-2.

1μ (micrometer) = 0.000001 meter

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Calculation of Mu Naught 

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To calculate the Mu naught value or the permeability of free space first, we need to know the magnitude and the direction. The force per unit length is represented by F on the electric current. It is given by the product of current and magnetic density.

The formula for force is: F = I × B

If there are two conductors or currents then one is I₁ and the other is I₂. They are r distance apart. If we suppose that I₁ produces a magnetic field B₁ then as per the third law of Newton it is said that each object has an equal and opposite direction. According to this, the force of the wire will be the same and in the opposite direction to the other one.

The magnitude of the force is: I₁ is B = μ × I₁2πr

As we already know that F = I × B

The force that will be experienced would be I₂ × B

So, when we place the value of B in it, then it will be F = μ × I₁ × I₂ 2πr

If this experiment is carried out in a vacuum then μ₀ = μ

The distance, r is assumed as 1 meter

Let’s calculate between these two wires

F = μ₀2π

On substituting, we get,

F = 4π ×10^-7 N/m or 4π ×10^-7 Wb A^-1 m^-1

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Things to Remember 

• The value of Mu naught is equal to μ₀ = 4pi × 10^-7Hm.
• Mu naught value or μ₀ is the permeability constant of the vacuum in the magnetic field.
• Mu naught is a physical constant that is often used in electromagnetism. 
• Mu naught value is the measurement of the resistance amount that is offered against the formation of the magnetic field.
• Mu naught value is calculated using Henry per meter.
• The sign μ is an abbreviation of the unit micron(s) or micrometer(s). Both of these are referred to as a unit of displacement that is equal to 0.000001-meter or 0.001 mm(millimeter).

Also Read: