In a particle accelerator,a current of $500 \,\mu A$ is carried by a proton beam in which each proton has a speed of $3 \times 10^7 \,m/s$. The cross-sectional area of the beam is $1.50 \,mm^2$. The charge density in this beam (in $C/m^3$) is close to

The drift velocity of electrons for a conductor connected in an electrical circuit is $V_{d}$. The conductor is now replaced by another conductor of the same material and same length but with double the area of cross-section. The applied voltage remains the same. The new drift velocity of electrons will be

There is a current of $1.344 \, A$ in a copper wire whose area of cross-section normal to the length of the wire is $1 \, mm^2$. If the number of free electrons per $cm^3$ is $8.4 \times 10^{22}$, then the drift velocity would be

$A$ current $I$ is passing through a wire having two sections $P$ and $Q$ of uniform diameters $d$ and $d/2$ respectively. If the mean drift velocity of electrons in sections $P$ and $Q$ is denoted by $v_P$ and $v_Q$ respectively,then

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:

An ionization chamber with parallel conducting plates as anode and cathode has $5 \times 10^7$ electrons and the same number of singly-charged positive ions per $cm^3$. The electrons are moving at $0.4\, m/s$. The current density from anode to cathode is $4\,\mu A/m^2$. The velocity of positive ions moving towards cathode is ............. $m/s$. [$AIPMT$ $1992$]