The electric intensity due to an infinite cylinder of radius $R$ and having charge $q$ per unit length at a distance $r(r > R)$ from its axis is

Three infinitely long charged thin sheets are placed as shown in the figure. The magnitude of the electric field at point $P$ is $\frac{x \sigma}{\epsilon_0}$. The value of $x$ is . . . . . . . (All quantities are measured in $SI$ units).

What is the flux through a cube of side $a$ if a point charge of $q$ is at one of its corners?

The electrostatic field of a long uniformly charged wire varies with distance $r$ according to which relation?

The electric field intensity at $P$ and $Q$,in the shown arrangement,are in the ratio:

$A$ 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: