  We report on the development of an induction based low temperature high
frequency ac susceptometer capable of measuring at frequencies up to 3.5 MHz
and at temperatures between 2 K and 300 K. Careful balancing of the detection
coils and calibration have allowed a sample magnetic moment resolution of
$5\times10^{-10} Am^2$ at 1 MHz. We will discuss the design and
characterization of the susceptometer, and explain the calibration process. We
also include some example measurements on the spin ice material CdEr$_2$S$_4$
and iron oxide based nanoparticles to illustrate functionality.
