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Question: The unit of permeability of vacuum (\({{\mu }_{0}}\) ) is ____________ A) \(\dfrac{N}{{{A}^{2}}}\)...

The unit of permeability of vacuum (μ0{{\mu }_{0}} ) is ____________
A) NA2\dfrac{N}{{{A}^{2}}}
B) NA\dfrac{N}{A}
C) NA
D) JA2\dfrac{J}{{{A}^{2}}}

Explanation

Solution

The system of units is different for different countries and some of the different systems of units are the CGS system of units, the FPS system of units, the MKS system of units and the SI system of units. The SI system of units is internationally accepted and MKS is a system of units. In the SI unit system there are seven SI base units and three supplementary units.

Complete step-by-step solution:
Permeability is defined as the measure of the ability of the material to allow the formation of magnetic lines of force.
Permeability of vacuum is defined as magnetic permeability in a classical vacuum and vacuum permeability is derived from the production of magnetic field by an electric current or by a moving electric charge and in all other formulas for a magnetic field production in a vacuum.
Permeability of vacuum is called as permeability constant and μ0=4π×10−7Hm−1{{\mu }_{0}}=4\pi \times {{10}^{-7}}H{{m}^{-1}} .
As we all known that B=μ02π×iRB=\dfrac{{{\mu }_{0}}}{2\pi }\times \dfrac{i}{R}
Where B= Magnetic flux density.
R=Radius
I=current
On rearranging the above equation
μ0=2π×B×Ri{{\mu }_{0}}=\dfrac{2\pi \times B\times R}{i}
Therefore the unit of μ0=B×Ri{{\mu }_{0}}=\dfrac{B\times R}{i}
Magnetic flux density is measured in tesla and in SI units it is equal to newton per meter per ampereNA−1m−1N{{A}^{-1}}{{m}^{-1}} . Radius is measured in meter (m) and SI unit of current is amperes (A).
2π2\pi which is dimensionless.
After substituting their respective units
μ0=NA−1m−1×meterA{{\mu }_{0}}=\dfrac{N{{A}^{-1}}{{m}^{-1}}\times meter}{A}
μ0=newtonampere2=NA2{{\mu }_{0}}=\dfrac{newton}{amper{{e}^{2}}}=\dfrac{N}{{{A}^{2}}}
So the correct option is A.

Note: Electric permittivity in free space(ε0)({{\varepsilon }_{0}}) is the ability of a material to permit electric fields which in turn relates to permittivity. Electric permittivity of free space is a constant of proportionalityε0=1c2μ0{{\varepsilon }_{0}}=\dfrac{1}{{{c}^{2}}{{\mu }_{0}}}. System of measurement is a collection of units of measurement .Each units which will have a universally recognized size.