Electric Currents in Conductors

A steady current flows in a metallic conductor of non-uniform cross-section. Which of these qualities is constant along the conductor: current, current density, electric field, drift speed?

The earth's surface has a negative surface charge density of ${10}^{-9} {\mathrm{Cm}}^{-2}.$ The potential difference of $400 \mathrm{kV}$ between the top of the atmosphere and the surface results (due to the low conductivity of the lower atmosphere) in a current of only $1800 \mathrm{A}$ over the entire globe. If there were no mechanism of sustaining atmospheric electric field, how much time (roughly) would be required to neutralize the earth's surface? (This never happens in practice because there is a mechanism to replenish electric charges, namely the continual thunderstorms and lightning in different parts of the globe).(Radius of earth $= 6.37\times {10}^{6 }\mathrm{m}$).

The number density of free electrons in a copper conductor estimated is  $8.5\times {10}^{28} {\mathrm{m}}^{-3}$. How long does an electron take to drift from one end of a wire $3.0 \mathrm{m}$ long to its other end? The area of cross-section of the wire is  $2.0\times {10}^{-6} {\mathrm{m}}^2$ and it is carrying a current of  $3.0 \mathrm{A}$. Take, charge of electron, $e =1.6\times {10}^{-19} \mathrm{C}$.

A battery of emf $10 \mathrm{V}$ and internal resistance $3 \mathrm{\Omega }$ is connected to a resistor. If the current in the circuit is $0.5 \mathrm{A}$, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

The storage battery of a car has an emf of $12 \mathrm{V}$. If the internal resistance of the battery is $0.4 \mathrm{\Omega }$, what is the maximum current that can be drawn from the battery?