An iron rod is placed parallel to a magnetic field of intensity $H = 2000 \text{ A/m}$. The magnetic flux through the rod is $\phi = 6 \times 10^{-4} \text{ Wb}$ and its cross-sectional area is $A = 3 \text{ cm}^2$. The magnetic permeability $\mu$ of the rod in $\text{Wb/A} \cdot \text{m}$ is:

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 $(\mu_0 = 4 \pi \times 10^{-7} \ H \ m^{-1})$.

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.

$A$ bar magnet having length $5 \ cm$ and area of cross-section $4 \ cm^{2}$ has a magnetic moment of $2 \ Am^{2}$. If the magnetic susceptibility is $5 \times 10^{-6}$,the magnetic intensity will be:

The relationship between the magnetic susceptibility $(\chi)$ and the magnetic permeability $(\mu)$ is given by (where $\mu_0$ is the permeability of free space and $\mu_{r}$ is relative permeability).

$ \chi_{1} $ and $ \chi_{2} $ are the magnetic susceptibilities of a paramagnetic material at temperatures $ T_{1} \ K $ and $ T_{2} \ K $ respectively. Then: