Consider a large collection of magnetic dipoles, each with a magnetic moment of m= J/T constrained to point either up or down. (The unit 'T' here is Tesla.) The energy of each dipole in a field H is just +mH (if down) or -mH (if up).

a) Suppose % of the dipoles point up in thermal equilibrium. What is the ratio of the Boltzmann factors for up and down dipoles?

Ratio =

b) At temperature = ^oC, what magnetic field strength is required to align the dipoles so that xx% point up?

H = T

c) At what temperature would a field of T (the strength of the Earth's field) line up xx% of the dipoles?

T = K