What is the electric field intensity at a point at a distance $r$ $(r < R)$ from the center of a charged spherical conductor of radius $R$ carrying a charge $Q$?

$A$ 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:

The electric field due to an infinitely long thin straight wire with uniform linear charge density of $2.5 \times 10^{-7} \ Cm^{-1}$ at a radial distance of $x$ from the wire is $7.5 \times 10^4 \ NC^{-1}$. Then $x=$ (in $cm$)

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 $\epsilon_{0} = 8.85 \times 10^{-12} \, C^{2} N^{-1} m^{-2}$]

An electron revolves around an infinite cylindrical wire having a uniform linear charge density of $2 \times 10^{-8} \, C \cdot m^{-1}$ in a circular path under the influence of an attractive electrostatic field,as shown in the figure. The velocity of the electron with which it is revolving is $......... \times 10^6 \, m \cdot s^{-1}$. (Given: mass of electron $= 9 \times 10^{-31} \, kg$)