$A$ current flows in a wire of circular cross-section with the free electrons travelling with a mean drift velocity $\vec v$. If an equal current flows in a wire of twice the radius,the new mean drift velocity is:

Write Ohm's law in the form of current density (vector form).

An insulating pipe of cross-section area $A$ contains an electrolyte which has two types of ions with charges $-e$ and $+2e$. $A$ potential difference applied between the ends of the pipe results in the drifting of the two types of ions,having drift speeds $v$ (for $-e$ ion) and $v/4$ (for $+2e$ ion). Both ions have the same number density $n$. The current flowing through the pipe is:

Derive the equation of mobility in terms of electric current.

For a given electric current,the drift velocity of conduction electrons in a copper wire is $v_d$ and their mobility is $\mu$. When the current is increased at constant temperature,

$A$ current of $2\,A$ flows through a wire of cross-sectional area $25.0\,mm^2$. The number of free electrons per cubic meter is $2.0 \times 10^{28}$. The drift velocity of the electrons is $...............\times 10^{-6}\,ms^{-1}$ (given,charge on electron $= 1.6 \times 10^{-19}\,C$).