The relation between the magnetic susceptibility $\chi$ and the relative magnetic permeability $\mu_r$ is:

Define magnetisation $(M)$ and give its unit and dimension.

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

Give the unit and dimensional formula of magnetisation.

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.

The space inside a straight current-carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to $1.2 \times 10^{-5}$. What is the fractional increase in the magnetic field inside the solenoid with respect to the magnetic field when air is the medium inside the solenoid?