Plasma wakefield acceleration (PWFA) is a promising tool for acceleration of charged particles to high energies at relatively small lengths. Knowledge about the structure of the electromagnetic field produced by the driver bunch in plasma plays the essential role for the realization of this accelerating scheme. Constant external magnetic field which can be used for focusing the driver bunch affects the field structure essentially because plasma acquires both anisotropy and gyrotropy. However, the field in the latter case has not been practically investigated until present. Here we study the field produced by point charge and small bunch moving in cold magnetized plasma along the external magnetic field. We note the singular behavior of some components of the wave field produced by point charge near the charge trajectory. We also analyze the influence of the external magnetic field and bunch size on the field components.