$A$ uniform copper wire carries a current $i$ amperes and has $p$ carriers per meter$^3$. The length of the wire is $\lambda$ meters and its cross-section area is $s$ meter$^2$. If the charge on a carrier is $q$ coulombs,the drift velocity in $ms^{-1}$ is given by

$(a)$ Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0 \times 10^{-7} \; m^{2}$ carrying a current of $1.5 \; A$. Assume that each copper atom contributes roughly one conduction electron. The density of copper is $9.0 \times 10^{3} \; kg/m^{3}$ and its atomic mass is $63.5 \; u$.
$(b)$ Compare the drift speed obtained above with,$(i)$ thermal speeds of copper atoms at ordinary temperatures,$(ii)$ speed of propagation of electric field along the conductor which causes the drift motion.

Assertion: Free electrons always keep on moving in a conductor,even then no magnetic force acts on them in a magnetic field unless a current is passed through it.
Reason: The average velocity of free electrons is zero.

$(a)$ The electron drift speed is estimated to be only a few $mm\; s^{-1}$ for currents in the range of a few amperes. How then is current established almost the instant a circuit is closed?
$(b)$ The electron drift arises due to the force experienced by electrons in the electric field inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady average drift speed?
$(c)$ If the electron drift speed is so small,and the electron's charge is small,how can we still obtain large amounts of current in a conductor?
$(d)$ When electrons drift in a metal from lower to higher potential,does it mean that all the 'free' electrons of the metal are moving in the same direction?
$(e)$ Are the paths of electrons straight lines between successive collisions (with the positive ions of the metal) in the $(i)$ absence of electric field,$(ii)$ presence of electric field?

$A$ constant potential difference is applied between the ends of a wire. If the length of the wire is elongated to $4$ times its original length,then the drift velocity of electrons will be:

An electric current flows along an insulated strip $PQ$ of a metallic conductor. The current density in the strip varies as shown in the graph. Which one of the following statements could explain this variation?