Final answer:
Yes, an electron will move under the influence of an electromagnetic field with its motion governed by the Coulomb force in the case of an electric field, and the Lorentz force in a magnetic field.
Step-by-step explanation:
The question asks whether an electron, which has a negative charge, will move in an electromagnetic field under the Coulomb force. The answer to this question is True. An electron will indeed move under the influence of an electromagnetic field through both the electric and magnetic components of the field. In an electric field, the electron will experience a force due to the field acting on its charge, which according to Coulomb's law is proportional to the charge on the electron and the strength of the electric field. The direction of the force is opposite to the field direction, as the electron has a negative charge.
In a magnetic field, a moving charged particle such as an electron will experience a force as well, known as the Lorentz force. The direction of this force is perpendicular to both the velocity of the electron and the magnetic field. This response to the field dynamics is why we can observe phenomena such as the auroras, where charged particles from the sun are deflected by Earth's magnetic field, and the operation of equipment like cathode-ray tubes, where electron beams are steered by magnetic fields.