Question

The SI unit of magnetic permeability is
a) $A m^{-1}$
b) $A m^{-2}$
c) $H m^{-2}$
d) $H m^{-1}$

Answer 1

Magnetic permeability benefits us to estimate the resistance of the material to the magnetic field, or it estimates the range to which magnetic field can enter through a material. We write formulas for self-inductance and try to evaluate the value of magnetic permeability. After putting down the units of all terms, we get the unit of magnetic permeability.

Complete step-by-step solution:
The symbol $\mu$ denotes magnetic permeability.
The formula of self-inductance-
$L = \dfrac{\mu N_{1} N_{2} A}{l}$
$\mu = \dfrac{L l}{ N_{1} N_{2} A }$
Where, $\mu$ is magnetic permeability.
L is the self-inductance.
$N_{1}$ is the number of turns in the first coil.
$N_{2}$ is the number of turns in the second coil.
A is the area of cross-section.
Unit of self-inductance, L is Henry, H.
Unit of length, l is metre, m and area, A is $m^{2}$.
$\mu = \dfrac{H \times m}{ m^{2}}= H m^{-1}$
Option (d) is correct.

Additional Information The variation of magnetic permeability, depending on the intensity of the applied magnetic field, also has a pretty important role. With the increase of stresses, it rises in weak magnetic fields and decreases in strong fields. Permeability depends on various factors, such as the material's nature, position in the medium, humidity, temperature, and applied force frequency.

Note: If the material has more excellent magnetic permeability, higher will be the conductivity for force magnetic lines. Magnetic permeability is constantly positive and can change with a magnetic field. It helps in determining how much magnetic flux the material can support, which will move into it. More to note, the reverse of magnetic permeability is magnetic reluctivity.