Current density in a cylindrical wire of radius $R$ is given as $J = \begin{cases} J_0 \left( \frac{x}{R} - 1 \right) & 0 \leqslant x < \frac{R}{2} \\ J_0 \frac{x}{R} & \frac{R}{2} \leqslant x \leqslant R \end{cases}$. The current flowing in the wire is:

$A$ copper wire has a square cross-section,$2.0 \, mm$ on a side. It carries a current of $8 \, A$ and the density of free electrons is $8 \times 10^{28} \, m^{-3}$. The drift speed of electrons is equal to

Two wires each of radius of cross section $r$ but of different materials are connected together end to end (in series). If the densities of charge carriers in the two wires are in the ratio $1 : 4$,the drift velocity of electrons in the two wires will be in the ratio:

$(a)$ 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?

When current flows through a conductor,the order of magnitude of the drift velocity of electrons is

$A$. The drift velocity of electrons decreases with the increase in the temperature of a conductor.
$B$. The drift velocity is inversely proportional to the area of cross-section of a given conductor.
$C$. The drift velocity does not depend on the applied potential difference to the conductor.
$D$. The drift velocity of an electron is inversely proportional to the length of the conductor.
$E$. The drift velocity increases with the increase in the temperature of a conductor.
Choose the correct answer from the options given below: