Question

The value of \[\mu \] is \[4\pi \times {{10}^{-7}}\text{ H}{{\text{m}}^{-1}}\].
A.) True
B.) False

Answer 1

Hint: Permeability in electromagnetism will lead to the answer. Permeability of free space and permeability of a specific medium can be the same or different.

Complete step by step answer:
Permeability of free space \[{{\mu }_{0}}\] is a physical constant extensively used in electromagnetism. Permeability is the measurement of the resistance of a material against the formation of a magnetic field. We can measure the degree of magnetization as a response to the applied magnetic field with this physical quantity. Henry per meters as well as Newtons per ampere squared have been used as the unit of permeability. The permeability of free space or magnetic constant\[{{\mu }_{0}}\] is the amount of resistance in the vacuum when a magnetic field is applied. It is a well-defined value.
\[{{\mu }_{0}}=4\pi \times {{10}^{-7}}\text{ H}{{\text{m}}^{-1}}\]
Relative permeability is normally represented by \[{{\mu }_{r}}\]. It is the ratio between the permeability of a specific medium (\[\mu \]) and the permeability of a free space (\[{{\mu }_{0}}\]).
\[{{\mu }_{r}}=\dfrac{\mu }{{{\mu }_{0}}}\]
So, the question will be correct only if the relative permeability is one. Otherwise it will be false. However, permeability of free space is always a constant value.

Additional information: To define electromagnetism, we need permeability. If we are dealing with an isotropic medium then the permeability will be a scalar. If it is anisotropic, then permeability will become a tensor.
\[\mu =\dfrac{B}{H}\] is an important equation in electromagnetism. Here B is the magnitude of magnetic induction and H is the intensity of magnetic field. It’s dimensional formula is \[\left[ \text{ML}{{\text{T}}^{-2}}{{\text{A}}^{-2}} \right]\].

Note: Don’t get confused with permeability and permeability of free space. \[\mu ={{\mu }_{0}}\]only if \[{{\mu }_{r}}=1\].