If the magnetizing field on a ferromagnetic material is increased,its permeability

Write the equation of the magnetic field obtained in the core of a solenoid in the form of $\vec{H}$ and $\vec{M}$.

$A$ magnetizing field of $100 \,A/m$ produces a magnetic flux of $2.4 \times 10^{-5} \,Wb$ in an iron bar of cross-sectional area $0.3 \,cm^2$. The magnetic permeability of the iron bar in the $SI$ unit is

Which of the following relations is incorrect?
$(a) \ B = \mu_0(H + I)$
$(b) \ B = \mu_0(H + \chi_m)$
$(c) \ \mu_r = 1 + \chi_m$
$(d) \ \chi_m = I / H$
(Here,$I =$ intensity of magnetization and $H =$ magnetising field)

Oersted is a unit of

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 .... $A m^2$.