The permeability of a metal is $0.1256 \ TmA^{-1}$. Its relative permeability will be (Given: $\frac{\mu_0}{4 \pi} = 10^{-7} \ SI \ unit$,$\pi = 3.14$).

What is the magnetic susceptibility of a medium if its relative permeability is $0.85$?

$A$ solenoid has a core of a material with relative permeability $400$. The windings of the solenoid are insulated from the core and carry a current of $2 \; A$. If the number of turns is $1000$ per metre,calculate $(a) \; H$,$(b) \; M$,$(c) \; B$ and $(d)$ the magnetising current $I_m$.

The magnetic induction and the intensity of the magnetic field inside an iron core of an electromagnet are $1 \ Wb \ m^{-2}$ and $150 \ A \ m^{-1}$,respectively. The relative permeability of iron is $(\mu_0 = 4 \pi \times 10^{-7} \ H \ m^{-1})$.

An iron rod of volume $10^{-4} \, m^3$ and relative permeability $1000$ is placed inside a long solenoid wound with $5 \, \text{turns/cm}$. If a current of $0.5 \, A$ is passed through the solenoid, then the magnetic moment of the rod is .... $A m^2$.

The percentage increase in magnetic field $(B)$ when the space within a current-carrying solenoid is filled with magnesium (magnetic susceptibility $\chi_{mg} = 1.2 \times 10^{-5}$) is: