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 $\dots \; \pi \; A$.

Assertion: Free electrons always keep on moving in a conductor,even then no magnetic force acts on them in a magnetic field unless a current is passed through it.
Reason: The average velocity of free electrons is zero.

Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n \propto T$,assuming $\tau$ (relaxation time of collision) and dimensions of the wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graphs is true?

The current density in a solid cylindrical wire of radius $R$,as a function of radial distance $r$,is given by $J(r) = J_{0}(1 - \frac{r}{R})$. The total current in the radial region $r = 0$ to $r = \frac{R}{4}$ will be:

$A$ potential difference of $5 \,V$ is applied across a conductor of length $10 \,cm$. If the drift velocity of electrons is $2.5 \times 10^{-4} \,m/s$,then the electron mobility will be ............ $m^2 V^{-1} s^{-1}$.

Find the mobility of an electron in a wire if its average collision time is $9.1 \times 10^{-15} \,s$. (Charge of electron $= 1.6 \times 10^{-19} \,C$ and mass of electron $= 9.1 \times 10^{-31} \,kg$)