For a cylinder of radius $R$,the current density is given by $J = J_0 \frac{r}{R}$,where $J_0$ is a constant and $r$ is the distance from the axis. Calculate the total current.

$(a)$ 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?

The drift velocity of free electrons in a conductor is $v$ when a current $i$ is flowing in it. If both the radius and current are doubled,then the drift velocity will be

The number density of free electrons in a copper conductor is $8.5 \times 10^{28} \; m^{-3}$. How long does an electron take to drift from one end of a wire $3.0 \; m$ long to its other end? The area of cross-section of the wire is $2.0 \times 10^{-6} \; m^2$ and it is carrying a current of $3.0 \; A$.

Explain the mobility of a charge carrier in a conductor and derive its equation.

Why is current not formed in solid conductors in the absence of an electric field?