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.

The drift velocity of the electrons in a copper wire of length $2\ m$ under the application of a potential difference of $200\ V$ is $0.5\ m/s$. Their mobility (in $m^2 V^{-1} s^{-1}$) is

$A$ conductor of length $\ell$ with a circular cross-section is shown in the figure,carrying a current $i$. The radius of the cross-section varies linearly from $a$ to $b$. Assuming $(b - a) << \ell$,calculate the current density at a distance $x$ from the left end.

$A$ current of $2 \,A$ is passing through a metal wire of cross-sectional area $2 \times 10^{-6} \,m^{2}$. If the number density of free electrons in the wire is $5 \times 10^{26} \,m^{-3}$, the drift speed of electrons is (Given, $e = 1.6 \times 10^{-19} \,C$)

$A$ silver wire of length $3 \,m$ and of cross-sectional area $6.14 \times 10^{-6} \,m^2$ carries a current of $6 \,A$. The atomic weight and density of silver are $108 \,g/mol$ and $10500 \,kg/m^3$,respectively. $A$ silver atom contributes one free electron for conduction. The Avogadro number is $6.023 \times 10^{23} /mol$. The drift velocity of electrons in silver is close to:

$A$ potential difference of $5 \,V$ is applied across a conductor of length $10 \,cm$. If the drift velocity of electrons is $2.5 \times 10^{-4} \,m/s$,then the electron mobility will be ............ $m^2 V^{-1} s^{-1}$.