Question

The SI unit of magnetic permeability is
(A). $Wb{m}^{-2}{A}^{-1}$
(B). $Wb{m}^{-1}A$
(C). $Wb{m}^{-1}{A}^{-1}$
(D). $Wbm{A}^{-1}$

Answer 1

Hint: In order to find the SI unit of magnetic permeability, first we will understand what is magnetic permeability, and then we will try to find out the SI unit by using a relation with the help of known SI units of different physical quantities.

Complete step-by-step answer:
First of all let us understand about Magnetic permeability, So that it helps us better in solving the question .
Magnetic permeability can be defined as the ratio of the magnetic flux density to the magnetic field intensity. It is a scalar quantity and denoted by the symbol $\mu$ . Physically it indicates the ease with which magnetic fields can create more or higher magnetic force, So if a material has low magnetic permeability it will generate less magnetic force whereas if magnetic permeability is high it’ll generate high magnetic force.
Mathematically it can be written as $\mu ={\displaystyle \frac{B}{H}}$
Where B = magnetic flux density and H= magnetic field intensity.
And we also know that magnetic field intensity (H) is equal to $H={\displaystyle \frac{Idl\sin \theta }{r^2}}$
Now we will recall the SI units of all the measurable quantities, we have
SI unit of magnetic flux density(B) is ${\displaystyle \frac{Wb}{m^2}}$
And SI unit of magnetic field intensity(H) is ${\displaystyle \frac{Am}{m^2}}$
Substituting these values of magnetic flux density and magnetic field intensity in the relation of magnetic permeability i.e. $\mu ={\displaystyle \frac{B}{H}}$
SI unit of magnetic permeability is:
$$\begin{gathered} \mu ={\displaystyle \frac{\text{SI unit of B}}{\text{SI unit of H}}} \\ \Rightarrow \mu ={\displaystyle \frac{\left({\displaystyle \frac{Wb}{m^2}}\right)}{\left({\displaystyle \frac{Am}{m^2}}\right)}} \\ \Rightarrow \mu ={\displaystyle \frac{\left({\displaystyle \frac{Wb}{m^2}}\right)}{\left({\displaystyle \frac{Am}{m^2}}\right)}} \\ \Rightarrow \mu ={\displaystyle \frac{Wb}{Am}} \\ \Rightarrow \mu =Wb/m/A \end{gathered}$$
Therefore, The SI unit of Magnetic Permeability is $Wb{m}^{-1}{A}^{-1}\text{ or }Wb{A}^{-1}{m}^{-1}$
Hence, the correct answer is option C.


Note: Terms such as permeability, susceptibility etc., must be well known as they are also related to Electric field and Potential. Definitions are also asked in some of the competitive exams. So it’s recommended to have a grip on them as well.