Question

The unit for permeability is
A) Wb/At m
B) At/m
C) At/Wb
D) Wb

Answer 1

Magnetic permeability is the property of a material that is equal to the magnetic flux density (B) established within the material by a magnetizing field divided by the magnetic field strength( H)of the magnetizing field.
Magnetic permeability (μ) is thus defined as $\mu = \dfrac{B}{H}$
Therefore, units of B and H will give the value of the unit of magnetic permeability.

Complete Solution:
The S.I. unit of Magnetic Flux is Weber(Wb) and the S.I. unit of Magnetic field strength (H) is given by Ampere/Metre i.e. (A/m)
Now, the magnetic permeability is given by-
$\mu = \dfrac{B}{H} = \dfrac{{Wb}}{{A/m}}$
$\mu = Wb/A{\text{ }}m$
Hence, the unit of magnetic permeability is $Wb/A{\text{ }}m$.

Option A is correct.

Additional Information:
Magnetic flux density (B) is a measure of the actual magnetic field within a material considered as a concentration of magnetic field lines, or flux, per unit cross-sectional area.
Magnetic field strength (H) is a measure of the magnetizing field produced by electric current flow in a coil of wire.
Magnetic permeability is defined as the ratio of the magnetic flux density to the magnetic intensity. It is a scalar quantity and denoted by the symbol $\mu$. Magnetic permeability helps us to measure a substance resistance to the magnetic field or measure of the degree to which magnetic fields can penetrate through a substance.

Note: In cgs unit, the permeability B/H of space is dimensionless and has a value of 1.
In mks and SI units, B and H have different dimensions, and the permeability of free space (symbolized ${\mu _0}$) is defined as equal to $4\pi \times {10^{ - 7}}$ weber per ampere-metre.