The $S.I.$ unit of magnetic permeability is

The relation between total magnetic field $(B)$, magnetic intensity $(H)$, permeability of free space $(\mu_0)$, and susceptibility $(\chi)$ 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)

An iron rod of cross-sectional area $0.2 \, cm^2$ is subjected to a magnetizing field intensity of $1600 \, A \cdot m^{-1}$. If the magnetic flux produced in the rod is $2.4 \times 10^{-5} \, Wb$, what is the magnetic susceptibility of the material of the rod?

An iron bar having a cross-sectional area of $2 \times 10^{-5} \ m^2$ and a magnetising field of $2400 \ A/m$ produces a magnetic flux of $2.4 \pi \times 10^{-5} \ Wb$. What will be the value of permeability $(\mu)$ and susceptibility $(\chi)$ of the bar? (Given $\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A$)

What are the dimensions of $\chi$,the magnetic susceptibility? Consider an $H$-atom. Guess an expression for $\chi$,up to a constant,by constructing a quantity of dimensions of $\chi$ out of parameters of the atom: $e, m, v, R$ and $\mu_0$. Here,$m$ is the electronic mass,$v$ is electronic velocity,$R$ is Bohr radius. Estimate the number so obtained and compare with the value of $|\chi| \approx 10^{-5}$ for many solid materials.