(a) Write the nature of path of free electrons in a conductor in the (i) presence of electric field (ii) absence of electric field.
(b) Between two successive collisions each free electron acquires a velocity from 0 to v where `v=(e E)/(m)tau`. What is the average velocity of a free electron in the presence of an electric field.

Explanation

(a) (i) In the presence of electric field, the paths of free electrons in a metal conductor are curved. (ii) In the absecnce of electice field, the paths of free electrons in a metal conductor are straight lines between two successive collisions.
(b) Average velocity of a free electron in the presence of electric field is `v= (eE)/(m) tau`
Where the symbols have their usual meanings. The different free electrons in a metal conductor move with differennt velocity in the presence of electric field.
(C) As the temperature of a conductor increases, the thermal speed of the electrons incereases and also the amplitude of vibration of the metal atoms/ions increases. Now thr free electrons colide more frequently with the atoms/ions of metal. As a result of it, the value of relaxation time `tau` decreases. Since average velocity `v prop tau`, so the average valocity of free electrons decreases.