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How does an electric field cause electrons to develop a drift velocity?

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density current: descent to the ocean floor — density current Diagram showing the behaviour of a density current as it descends to the seafloor.

When an electric field is applied to a conducting material, it exerts a force on the free electrons within it, pulling them in the direction opposite to the field due to their negative charge.1

As these electrons accelerate under the influence of the electric field, they do not move unimpeded; instead, they periodically collide with atoms or other imperfections within the material's crystal lattice. These frequent collisions act as a limiting factor on the electrons' motion. The combination of the continuous acceleration provided by the electric field and the recurring scattering from collisions results in the electrons maintaining a steady average velocity, which is known as the drift velocity.231

The ease with which these particles move through the material under a given electric field is defined as mobility. In this process, the energy gained by the electrons from the electric field is transferred to the material during collisions, which generates heat.1