In the given hollow cylindrical conductor,the current density is $J = \frac{J_0}{r^2}$,where $J_0$ is a constant and $r$ is the distance from the axis of the cylinder. If the radius of the inner surface is $a$ and the radius of the outer surface is $2a$,find the current passed through the conductor.

$A$. 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:

The current density in a cylindrical wire of radius $r = 4.0 \, mm$ is $J = 1.0 \times 10^{6} \, A/m^{2}$. The current through the outer portion of the wire between radial distances $r/2$ and $r$ is $x \pi \, A$,where $x$ is ..........

The current density in a cylindrical wire of radius $4 \; mm$ is $4 \times 10^{6} \; A \cdot m^{-2}$. The current through the outer portion of the wire between radial distance $\frac{R}{2}$ and $R$ is $\dots \; \pi \; A$.

$A$ copper wire of length $10 \, m$ and radius $(10^{-2} / \sqrt{\pi}) \, m$ has an electrical resistance of $10 \, \Omega$. The current density in the wire for an electric field strength of $10 \, V/m$ is:

Charge passing through a conductor of cross-section area $A=0.3 \,m^2$ is given by $q=3 t^2+5 t+2$ in coulomb,where $t$ is in second. What is the value of drift velocity at $t=2 \,s$ ? (Given,$n=2 \times 10^{25} / m^3$ )