# What are the dimensions of χ,

Question:

What are the dimensions of χ, the magnetic susceptibility? Consider an H-atom. Guess an expression for χ, up to a constant by constructing a quantity of dimensions of χ, out of parameters of the atom: e, m, v, R and μ0. 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 | χ| equivalent to 10-5 for many solid materials.

Solution:

χm = I/H = intensity of magnetisation/magnetising force

χ is dimensionless as I and H has the same units

χ = 10-4