In this study, we derived the equations describing the dynamics of a magnetic fluid in crossed magnetic fields (bias and alternating probe fields), considering the field dependence of the relaxation times, interparticle interactions, and demagnetizing field has been derived. For a monodisperse fluid, the dependence of the output signal on the bias field and the probe field frequency was constructed. Experimental studies were conducted in a frequency range up to 80 kHz for two samples of fluids based on magnetite nanoparticles and kerosene. The first sample had a narrow particle size distribution, low-energy magneto dipole interactions, and weak dispersion of dynamic susceptibility. The second sample had a broad particle size distribution, high-energy magneto dipole interactions, and strong dispersion of dynamic susceptibility. In the first case, the bias field led to the appearance of short chains. In the second case, we found quasi-spherical clusters with a characteristic size of 100 nm. The strong dependence of the output signal on the particle size allowed us to use the crossed field method to independently estimate the maximum diameter of the magnetic core of particles.