Discussion
The dimensions of \(\frac{mB}{kT}\) where m is the magnetic moment, B, the magnetic flux density, k, Boltzmann constant and T, the absolute temperature are:
Answer: E
\(\frac{mB}{kT}\) is dimensionless: \(M^{0}L^{0}T^{0}\).
The energy of a magnetic dipole in a field is \(U = -mB\), so mB has the dimensions of energy. kT is also an energy (the thermal energy scale). Their ratio is a pure number, as it must be in expressions like the Langevin function for paramagnetism.
Every other option carries non-zero powers of M, L or T, which a ratio of two energies cannot have.
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