The effect of a field on the velocity of an electron depends on the type of field and the nature of the interaction between the electron and the field. Here are two common scenarios:
Electric Field: When an electron is subjected to an electric field, it experiences a force known as the electric force. The electric force exerted on the electron depends on the strength and direction of the electric field. If the electric field is uniform and directed along the path of the electron, the force will accelerate the electron in the direction of the field. The acceleration of the electron will cause its velocity to change over time. The magnitude and direction of the electron's velocity will depend on the properties of the field and the electron's initial conditions (such as its initial velocity).
Magnetic Field: In the presence of a magnetic field, an electron experiences a force known as the magnetic force. The magnetic force on an electron is perpendicular to both the velocity of the electron and the magnetic field direction (according to the right-hand rule). This force can cause the electron to move in a curved path, altering its velocity. The magnitude and direction of the electron's velocity will depend on the strength and orientation of the magnetic field, as well as the initial conditions of the electron.
It's important to note that the effect of a field on the velocity of an electron is not limited to these two scenarios. Electrons can also interact with other types of fields, such as gravitational fields or electromagnetic fields, which can lead to further changes in their velocities. The specific effects will depend on the properties of the field and the electron's characteristics.