We have used magnetic particles to study specific binding of prostate specific antigen (PSA) to the surfaces of the bioparticles. The used particles have a mean diameter of about 130 nm and are placed in phosphate buffer saline (PBS). Each particle is composed of clusters of magnetic single domains of magnetite, which are covered with dextran. Changes in surface chemistry of the particles give rise to a change in the hydrodynamic volume of the particles. The later is mirrored by the changed frequency response of the complex magnetic susceptibility of a fluid containing these particles. Using ordinary induction coils and the lock-in amplifier technique it is possible to measure the complex magnetic susceptibility of the particle solution in a frequency range from about 10 Hz up to 10 kHz. From the measurement of the complex susceptibility versus the excitation frequency (both at the excitation frequency as well as at higher harmonics) we have shown that it is possible to quantitatively study the binding of PSA to the surfaces of the magnetic particles and thus to determine the PSA concentration in solution containing known concentration of nanoparticles functionalised with a monoclonal PSA antibody. Our method allows to perform an immunoassay in a single step and is much faster and cheaper compared to conventional ELISA procedures.