The magnetisation of two dimensional hole systems in the quantum Hall regime has been studied using a highly-sensitive torsion balance magnetometer. In a time varying magnetic field eddy currents are induced which become large around integer and fractional filling factors where ρ_xx takes a very low value. The sweep rate and temperature dependence of these induced currents are in good agreement with the model of quantum Hall effect breakdown proposed recently by Matthews et al. This model also allows comparison between the energy gap at different filling factors and so provides a measurement of the fractional quantum Hall effect energy gap, Δ_1/3, and the spin split energy gap, g*μ_BB.