If a current of $80 \ A$ is passing through a straight conductor of length $10 \ m$,then the total momentum of electrons in the conductor is (mass of electron $= 9.1 \times 10^{-31} \ kg$ and charge of electron $= 1.6 \times 10^{-19} \ C$).

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.

Two wires each of radius of cross section $r$ but of different materials are connected together end to end (in series). If the densities of charge carriers in the two wires are in the ratio $1 : 4$,the drift velocity of electrons in the two wires will be in the ratio:

When there is an electric current through a conducting wire along its length,then an electric field must exist

$(a)$ Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0 \times 10^{-7} \; m^{2}$ carrying a current of $1.5 \; A$. Assume that each copper atom contributes roughly one conduction electron. The density of copper is $9.0 \times 10^{3} \; kg/m^{3}$ and its atomic mass is $63.5 \; u$.
$(b)$ Compare the drift speed obtained above with,$(i)$ thermal speeds of copper atoms at ordinary temperatures,$(ii)$ speed of propagation of electric field along the conductor which causes the drift motion.

Cross-sectional area of a copper wire is equal to the area of a square of length $2 \ mm$. If this copper wire draws $8 \ A$ electric current,then find the drift velocity of free electrons. The number density of electrons in the copper wire is $8 \times 10^{28} \ m^{-3}$.