$A$ charged particle having a drift velocity of $7.5 \times 10^{-4} \, m s^{-1}$ in an electric field of $3 \times 10^{-10} \, V m^{-1}$ has a mobility in $m^{2} V^{-1} s^{-1}$ of:

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:

$A$ current of $5\; A$ is passing through a non-linear magnesium wire of cross-section $0.04\; m^2$. At every point,the direction of current density is at an angle of $60^{\circ}$ with the unit vector of the area of cross-section. The magnitude of the electric field at every point of the conductor is .... $V/m$ (Resistivity of magnesium is $\rho = 44 \times 10^{-8}\, \Omega m$).

$A$ copper wire of diameter $1.02\, mm$ carries a current of $1.7\, A$. Find the drift velocity $(v_d)$ of electrons in the wire. Given $n$,the number density of electrons in copper $= 8.5 \times 10^{28} /m^3$. (Express the answer in $mm/s$)

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 ............. $m/s$. [$AIPMT$ $1992$]

Define mobility and write its $SI$ unit.