We derive expressions for the magnetic flux in a circular loop due to eddy currents and thermal noise in coaxial metallic disks. The eddy currents are induced by an applied field that changes sinusoidally in time. We give expressions for the eddy current noise when the frequency of the applied field is very low as well as when it is very high. We combine these expressions to obtain one that is valid over the whole frequency range. The theoretical results agree well with experimental ones obtained by means of a superconducting quantum interference device (SQUID) magnetometer system. We also studied the flux due to thermal noise; again, the theoretical results show fair agreement with the experimental ones.