$A$ 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:

$A$ current of $1.344 \, A$ flows through a copper wire of cross-sectional area $1 \, mm^2$. If the number of free electrons per unit volume is $8.4 \times 10^{22} \, cm^{-3}$,then the drift velocity is:

Charge passing through a conductor of cross-section $0.3 \, m^2$ is given by $q = (3t^2 + 5t + 2) \, C$ where '$t$' is in seconds. The drift velocity at $t = 2 \, s$ is (Concentration of electrons in the conductor $= 2 \times 10^{25} \, m^{-3}$)

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

The lengths of two wires made of the same material are in the ratio $2:3$ and their radii are in the ratio $1:2$. If the two wires are connected in parallel to a battery,then the ratio of the drift velocities of free electrons in the two wires 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 $\dots \; \pi \; A$.