Question

When a piece of a ferromagnetic substance is put in a uniform magnetic field, the flux density inside it is 4 times the flux density away from the piece. The magnetic permeability of the material is:
A) $1$
B) $2$
C) $3$
D) $4$

Answer 1

Remember, the concept of permeability i.e. the ratio of total magnetic field inside the material and magnetic field outside the material is known as permeability. Thus, we will use the formula of permeability here to get the required solution.

Formula used:
Here, we will use the formula of magnetic permeability, which is given by
${\mu _r} = \dfrac{B}{{{B_0}}}$
Where, ${\mu _r}$ is the permeability, $B$ is the total field inside the material and ${B_0}$ is the magnetic outside the material.

Complete step by step solution:
Let us first define the terms mentioned in the question,
FERROMAGNETIC SUBSTANCES: Ferromagnetic substances are defined as the substances which are strongly attracted by the external magnetic field. These substances contain magnetic properties even if the external magnetic field is removed.
Iron and Nickel are the two common examples of ferromagnetic substances.

FLUX DENSITY: Flux density is defined as the area in which the magnetic field is concentrated.

MAGNETIC PERMEABILITY: Magnetic permeability is defined as the property, which indicates how easily a material is magnetised.
Now, in the question, we are given that
Flux density inside = $4*$ (flux density away from the piece)
Therefore using formula of permeability,
${\mu _r} = \dfrac{B}{{{B_0}}}$
$\Rightarrow \dfrac{{4B}}{{{B_0}}}$
$\Rightarrow 4$
Therefore, we can say that when a piece of a ferromagnetic substance is put in a uniform magnetic field, the flux density inside it is 4 times the flux density away from the piece then, the magnetic permeability of the material is 4.

Additional Information:
Now, let us talk about ferromagnetism.
Ferromagnetism is a physical phenomenon in which electrically uncharged materials strongly attract others. Certain materials showing properties of ferromagnetism are: iron, cobalt, nickel and some other compounds.
Nowadays, ferromagnetic substances are used in a variety of substances, which are useful in everyday life i.e. electric motors and generators, transformers, telephones, and loudspeakers.

Note: We are all aware of the classification of materials i.e. diamagnetic, paramagnetic and ferromagnetic. But there exist many other materials i.e. ferromagnetic, anti-ferromagnetic, spin glass etc. these materials have properties which are exotic and mysterious.