Question

The dimensional formula for magnetic permeability $\mu $ is
$\begin{align}
  & A.\left[ ML{{T}^{-2}}{{A}^{-2}} \right] \\
 & B.\left[ {{M}^{0}}{{L}^{-1}}T \right] \\
 & C.\left[ {{M}^{0}}{{L}^{2}}{{T}^{-2}}{{A}^{-2}} \right] \\
 & D.\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-2}} \right] \\
\end{align}$

Answer 1

Hint: Magnetic permeability is described as the ratio of the magnetic induction to the magnetic intensity. It is given as a scalar quantity and denoted by the notation$\mu $. Magnetic permeability is used to measure a substance’s opposition to the magnetic field or it is the measure of the degree to which a magnetic field can enter through a substance.

Complete step by step solution:
First of all, let us discuss the magnetic permeability of a material. It is given as the ratio of the magnetic induction and magnetic intensity. The larger the magnetic permeability of the substance, the larger is the conductivity for magnetic lines of force. This is true in the reverse direction also. The magnetic permeability of a substance notates the easiness with which an external magnetic field can produce a higher magnetic force of attraction in the substance.
Therefore we can write that, the dimension of magnetic induction$B$can be written as
$\left[ B \right]=\left[ M{{T}^{-2}}{{A}^{-1}} \right]$
And also the magnetic field intensity is having a dimensional formula which is given as,
$\left[ H \right]=\left[ {{M}^{0}}{{L}^{-1}}A \right]$
Taking the ratio of both of these quantities will give the dimension of magnetic permeability,
That is,
\[\left[ \mu \right]=\dfrac{\left[ B \right]}{\left[ H \right]}=\dfrac{\left[ M{{T}^{-2}}{{A}^{-1}} \right]}{\left[ {{M}^{0}}{{L}^{-1}}A \right]}\]
Simplifying will give,
\[\left[ \mu \right]=\left[ ML{{T}^{-2}}{{A}^{-2}} \right]\]
Therefore the correct answer is option A.

Note: The performance of moving a coil or a loop of wire placed in a magnetic field induces a voltage in the coil with the magnitude of this created induced voltage proportional to the speed or velocity of the motion of the magnet known as magnetic induction. Magnetic field strength which is also known as magnetic intensity or magnetic field intensity is the part of the magnetic field occurring in a substance that develops due to an external current.