$A$ cylindrical resistor is connected across a battery $\varepsilon$. The cylinder has a uniform free electron density, and the middle part of the cylinder has a larger radius as shown in the figure. Which of the following graphs represents the variation of $V_d$ (drift velocity) with respect to $x$ (distance along the length of the resistor)?

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.

Consider a conductor of length $40 \ cm$,where a potential difference of $10 \ V$ is maintained between the ends of the conductor. Find out the mobility of the electrons,provided the drift velocity of the electrons is $5 \times 10^{-6} \ m/s$.

An ionization chamber with parallel conducting plates as anode and cathode has $5 \times 10^7$ electrons and the same number of singly-charged positive ions per $cm^3$. The electrons are moving at $0.4\, m/s$. The current density from anode to cathode is $4\,\mu A/m^2$. The velocity of positive ions moving towards cathode is ............. $m/s$. [$AIPMT$ $1992$]

In a particle accelerator,a current of $500 \,\mu A$ is carried by a proton beam in which each proton has a speed of $3 \times 10^7 \,m/s$. The cross-sectional area of the beam is $1.50 \,mm^2$. The charge density in this beam (in $C/m^3$) is close to

$A$ current of $10 \,A$ is maintained in a conductor of cross-section $1 \,cm^2$. If the number density of free electrons is $9 \times 10^{28} \,m^{-3}$,the drift velocity of free electrons is .......... $m/s$.