if we take an very small point source of EM wave, we will find that the EM wave is polarized. How does the polarization vary depending on which point of the sphere ? Polarization is always shown along one axis, but in a real 3D spherical wave it's impossible to keep a transversal EM field vector without changing its direction EDIT: My question comes from optics, if the image of a point is formed from constructive interference, then for such interference to occur, the polarization must have a specific configuration in 3D
The E and B vectors of a spherical EM wave lie in a plane normal to the direction of the propagation of the wave and their magnitude and direction (within that plane), at any point in space, are randomly changing with time.
The source of such wave could be considered a point source only in a sense that it is small relative to the distances at which the wave is evaluated. The source has to contain a large number of incoherent radiators to ensure a uniform distribution of radiation in all directions.
We can also loosely say that the EM spherical wave is unpolarized, such as EM radiation from a light bulb or a star, keeping in mind that it is in fact always polarized, but the polarization is randomly changing.
You can find more details on this topic in this post.