In the context of biomagnetism, a magnetically shielded room (MSR) is designed for shielding against external magnetic fields. Recently, several applications, such as combined structural magnetic resonance imaging (MRI) and functional magnetoencephalography (MEG), have emerged that require applying relatively strong magnetic fields inside the MSR. These magnetic fields induce eddy currents and magnetize the MSR walls that are made of materials with high permeability and conductivity. These eddy currents and magnetization generate secondary magnetic fields inside the room that disturb, e.g., combined MEG-MRI by affecting sample spins and by exceeding the available dynamic range of the magnetic field sensors. In this work, static and dynamic magnetic fields applied inside an MSR are studied both theoretically and experimentally. Using a spherical model, analytical expressions are derived for the amplitudes and time constants of the various secondary magnetic field modes. These predictions are validated by comparison with experimental measurements in a rectangular MSR. The results of this study facilitate, e.g., the design of coils compatible with an MSR; a self-shielded coil is presented that decreases the secondary magnetic fields to a small fraction.