As shown in the figure,a ball $B$ is suspended by a string $S$ from a large charged plate $P$ such that it makes an angle $\theta$ with the plate. The surface charge density of the plate is proportional to which of the following?

Electric field intensity at points in between and outside two thin separated parallel sheets of infinite dimension with like charges of same surface charge density $(\sigma)$ are . . . . . . and . . . . . . respectively.

$A$ long charged cylinder of linear charge density $\lambda$ is surrounded by a hollow coaxial conducting cylinder. What is the electric field in the space between the two cylinders?

The electric field at a distance $R$ from the surface of a uniformly charged nonconducting sphere of radius $R$ is $20 \,V/m$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is $.... \,V/m$.

The electric field at a distance of $20 \ cm$ from the center of a uniformly charged dielectric sphere of radius $R = 10 \ cm$ is $100 \ V/m$. What will be the electric field $E$ at a distance of $3 \ cm$ from the center of the sphere (in $V/m$)?

$A$ 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: