The drift speed of electrons in a material is found to be $0.3 \ m s^{-1}$ when an electric field of $2 \ V m^{-1}$ is applied across it. The electron mobility (in $m^2 \ V^{-1} \ s^{-1}$) in the material is

Current density in a cylindrical wire of radius $R$ varies with radial distance as $J(r) = \beta(r + r_0)^2$. The current through the shaded section of the wire shown in the figure is:

$A$ steady current $I$ is set up in a wire whose cross-sectional area decreases in the direction of the flow of the current. Then,as we examine the narrowing region,

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 wire carrying a current of $10\,A$ with a cross-sectional area of $1\,cm^2$. If the number of electrons per unit volume is $9 \times 10^{28}\,m^{-3}$,find the drift velocity of the electrons.

Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n \propto T$,assuming $\tau$ (relaxation time of collision) and dimensions of the wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graphs is true?