Question

. Explain how the average velocity of free electrons in a metal at constant temperature, in an electric field, remain
constant even though the electrons are being constantly accelarated by this electric field?

Answer 1

we know that free electrons are the current carriers in a metallic conductor and these free electrons moves randomly in all directions and constantly collide with the positive ions inside the metal due to which average thermal velocity is equals to zero.
when an electric field is applied across the two ends of the metallic conductor then an electric field is set up across the two ends of the conductor and now free electron moves in a particular direction due to external electric field and get accelerated .

Answer 2

When an electric field is applied to the metal, the free electrons experience a force and are accelerated in the direction of the electric field. However, as the electrons accelerate, they also collide with other atoms and free electrons in the metal. These collisions cause the free electrons to lose some of their kinetic energy and change direction, leading to the randomization of their velocity vectors.

Despite these collisions, the electric field continues to accelerate the free electrons, and the overall direction of motion of the electrons is maintained. The average velocity of the electrons remains constant because it is a measure of the overall displacement of the electrons over time, regardless of their instantaneous speed.

Thus, the average velocity of free electrons in a metal at a constant temperature, in an electric field, remains constant because the acceleration due to the electric field is countered by the randomizing effects of collisions.

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