Initially, the observer is at rest relative to a static charge. A static charge produces only an electric field in its own rest frame. So, the observer at rest experiences an electric field.
When the observer starts moving away from the static charge, the charge is now moving relative to the observer.
According to the principles of electromagnetism and special relativity:
1. Electric Field: A charge always has an electric field, regardless of its state of motion or the observer's state of motion. The magnitude and direction of this electric field might change depending on the relative velocity (due to Lorentz transformation of fields), but it will still be present.
2. Magnetic Field: A moving charge constitutes an electric current, and an electric current produces a magnetic field. From the perspective of the moving observer, the static charge appears to be moving (in the opposite direction to the observer's motion). Therefore, this (relatively) moving charge will produce a magnetic field as measured by the moving observer.
So, when the observer moves relative to the charge, they will experience both an electric field and a magnetic field.
\[ \boxed{\text{Electric and magnetic field}} \]