The electrons move with constant average velocity to the left as shown in the diagram above. The current density is a vector pointing towards the right. Let the normal to the cross-sectional area point towards the right. A, where n e is the number of free electrons per unit volume. It is their average speed, as they move along the wire.
Particles accelerate when they acted on by forces.
E is acting on the particle and it accelerates. To produce an electric field, something has to do work and separate charges. Such a device is called an emf . Examples of an emf are a battery or a power supply. The emf separates charges by moving electrons internally from its positive to its negative terminal.