Final answer:
Yes, it is possible for an electron to be affected by a magnetic field but not by an electric field if the electron moves perpendicular to the magnetic field with the electric field parallel to it, as the electric force would not act on the electron in this arrangement.
Step-by-step explanation:
An electron can indeed be affected by an external magnetic field but not by an external electric field if it moves in a specific way relative to these fields. According to physics, the force exerted by a magnetic field on a moving charge not only depends on the presence of the field but also the velocity of the charge and its angle relative to the field. Specifically, the magnetic force is perpendicular to the direction of the velocity of the charged particle and to the magnetic field, and it is proportional to the magnitude of the charge, the magnitude of the velocity, and the magnitude of the magnetic field.
It is possible if an electron moves perpendicular to a magnetic field and an electric field that is parallel to the magnetic field, the electric field will not exert a force. This scenario is because the magnetic force does no work on the charged particle, and thus the particle's kinetic energy and speed remain constant while its direction of motion can be changed by the magnetic field.
In simpler terms, an electron moving perpendicular to the magnetic field lines in a circular path will not be accelerated by the magnetic field because the magnetic force provides the centripetal force necessary for circular motion. However, when an electric field is parallel to the magnetic field, the electron would experience no electric force due to its perpendicular motion, thus fulfilling the conditions asked in the question.