Question

Observe the given figure. At what value of H is the permeability the greatest?

A) H = 0.6 kA/m
B) H = 0.06 kA/m
C) H = 6 kA/m
D) H = 60 kA/m

Answer 1

Hint: First, we will find out the relation between the permeability and magnetic flux density and field intensity. Then from the formula, we can check the proportionality of the permeability with the field intensity which will give us the answer required.

Complete step by step solution:
A magnetization curve determines the relation between magnetic induction, B and field intensity, H. The field intensity is generally taken along the abscissa while the magnetic induction along the ordinate of the magnetization graph.
The permeability is basically the property of a material to let pass the magnetic lines of force. It is directly proportional to the number of magnetic field lines passing through it and if the material is present in the vacuum, then its permeability is denoted by $\mu_0$.
The magnetic permeability is given by the ratio of flux density and the field intensity of a material. Mathematically, it can be expressed as,
$\mu =\dfrac{B}{H}$ ………. (i)
Generally, we use in equations the relative permeability of a material which is the ratio of permeability of a medium to that of vacuum and is given by
$\mu_r =\dfrac{\mu}{\mu_0} \implies \mu = {\mu_0}{\mu_r}$
So, now we can write the equation (i) as,
$\mu_r =\dfrac{1}{\mu_0}\left(\dfrac{B}{H}\right)$
So, we can clearly see that, for maximum permeability, the value of H should be minimum and thus from the options, minimum value of the field intensity is 0.06 kA/m.

Hence, option B is the correct answer.

Note: Another approach to solve this question can be by finding the slope of the curve as it gives the value of permeability. So, the point with maximum slope will give the point of maximum permeability.