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

though electric field is accelerating electrons but electrons moves haphazardly in a non uniform way because of their charge .. like charge repel each other (neighbor electrons)

velocity is a vector quantity
it has both magnitude and direction
therefore if a electrons travel +x,
it will be nullified by -x because of their random movement.
hence the avg velocity remains constant

Answer 2

"We know that the electric field always accelerates an electron. Since, electrons have a negative charge therefore, they will move in a non-uniform way. The same and equal charge of electrons repel each other.

The velocity is a vector quantity, therefore, the velocity has both "magnitude and direction". It means if electron moves in +x, it will be nullified by -x because of random movement. It makes the average velocity remains constant. "