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

$A$ cylindrical wire of radius $0.5 \, mm$ and conductivity $5 \times 10^{7} \, S/m$ is subjected to an electric field of $10 \, mV/m$. The expected value of current in the wire will be $x^{3} \, \pi \, mA$. The value of $x$ is ......

As shown in the figure,a current is passing through a conducting wire. The radius of the cross-section of the wire at point $A$ is $3r$ and at point $B$ is $r$. Find the ratio of the drift velocity at point $A$ to that at point $B$.

Current density in a cylindrical wire of radius $R$ varies with radial distance as $J(r) = \beta(r + r_0)^2$. The current through the shaded section of the wire shown in the figure is:

Derive the equation of mobility in terms of electric current.

$A$ silicon block at $300\,K$ has a length of $10\,cm$ and a cross-sectional area of $1 \times 10^{-4}\,m^2$. If a $2\,V$ battery is connected across its ends parallel to the length,find the current flowing through it. The electron mobility is $0.14\,m^2V^{-1}s^{-1}$ and the electron number density is $1.5 \times 10^{16}\,m^{-3}$.