Question

A rod of cross-sectional area $10c{m^2}$ is placed with its length parallel to a magnetic field of intensity${10^3}A{m^{ - 1}}$, the flux through the rod is ${10^4}wb$. Then the permeability of material of the rod is:
(A) ${10^4}wb/Am$
(B) ${10^3}wb/Am$
(C) ${10^2}wb/Am$
(D) $10wb/Am$

Answer 1

We are given here with the area of the cross section of the rod, the magnetic field intensity and the flux through the rod and are asked to find the permeability of material of the rod. Thus, we will use the formula of magnetic field which includes these parameters.

Formulae used:
$\phi = BA$
Where, $\phi$ is the magnetic flux through the material, $B$ is the magnetic field and $A$ is its cross-sectional area.
$B = \mu H$
Where, $\mu$ is the permeability of the material and $H$ is the magnetic field intensity through the material.

Complete step by step solution:
Here,
We are given that,
$\phi = {10^4}wb$
$H = {10^3}A{m^{ - 1}}$
And
$A = 10c{m^2} = 10 \times {10^{ - 4}}{m^2} = {10^{ - 3}}{m^2}$
Now,
We know,
$\phi = BA \Rightarrow B = \dfrac{\phi }{A}$
But,
$B = \mu H$
Thus, we can say
$\dfrac{\phi }{A} = \mu H$
After further rearrangements, we get
$\mu = \dfrac{\phi }{{AH}}$
Putting in the values
$\mu = \dfrac{{{{10}^4}}}{{{{10}^{ - 3}} \times {{10}^3}}}wb/Am$
After calculations, we get
$\mu = {10^4}wb/Am$

Hence, the correct answer is (A).

Additional Information
The physical significance of permeability is the extent to which a material can enhance a magnetic field passing through it. It is the qualitative measure of the ability of a material to enhance a magnetic field. On the basis of this parameter, materials can be further classified into three types:
1. Paramagnetic: Has a constant relative permeability slightly greater than$1$.
2. Diamagnetic: Has a constant relative permeability slightly lower than$1$.
3. Ferromagnetic: Does not have a constant relative permeability.

Note: We got the answer to be a very high value, thus the material cannot be classified into neither paramagnetic nor a diamagnetic. It could possibly be a ferromagnetic material.