The surface charge density of a conducting plate is $-2 \times 10^{-6} \ C/m^2$. An electron with energy $100 \ eV$ moves towards the plate and strikes it. What is the initial distance of the electron from the plate?

The volume charge density of a sphere of radius $6 \, m$ is $2 \, \mu C \, m^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is $.... \times 10^{10} \, N C^{-1}$. [Given: Permittivity of vacuum $\epsilon_{0} = 8.85 \times 10^{-12} \, C^{2} N^{-1} m^{-2}$]

At a distance $l$ from a uniformly charged long wire, a charged particle is thrown radially outward with a velocity $u$ in the direction perpendicular to the wire. When the particle reaches a distance $2l$ from the wire, its speed is found to be $\sqrt{2}u$. The magnitude of the velocity, when it is a distance $4l$ away from the wire is (ignore gravity)

The electric field intensity at a point at a distance $r$ from the axis of an infinitely long pipe having a linear charge density $q$ is proportional to:

$A$ uniform rod $AB$ of mass $m$ and length $l$ is hinged at its midpoint $C$. The left half $(AC)$ of the rod has linear charge density $-\lambda$ and the right half $(CB)$ has $+\lambda$,where $\lambda$ is constant. $A$ large non-conducting sheet of uniform surface charge density $\sigma$ is also present near the rod. Initially,the rod is kept perpendicular to the sheet. The end $A$ of the rod is initially at a distance $d$. Now,the rod is rotated by a small angle $\theta$ in the plane of the paper and released. The time period of small angular oscillations is:

The electric field near a conducting surface having a uniform surface charge density $\sigma$ is given by: