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 $= 2 \times 10^{25} \, m^{-3}$)

$A$ battery is connected to a uniform resistance wire $AB$ and $B$ is earthed. Which one of the graphs below shows how the current density $J$ varies along $AB$?

$A$ beam contains $2 \times 10^8$ doubly charged positive ions per cubic centimeter,all of which are moving with a speed of $10^5 \,m/s$. The current density is ............. $A/m^2$.

Which of the following quantities does not change when a resistor connected to a battery is heated due to the current?

Derive the equation of mobility in terms of relaxation time $(\tau)$. Write its unit.

$(a)$ 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.