$A$ thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \le r < \infty$,where $r$ is the distance from the centre of the shell?

An electrostatic field in a region is radially outward with magnitude $E = \alpha r$,where $\alpha$ is a constant and $r$ is the radial distance. The charge contained in a sphere of radius $R$ in this region (centered at the origin) is:

If the uniform surface charge density on an infinite plane sheet is $\sigma$,the electric field near the surface will be . . . . . . .

Two infinite parallel metal planes contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively,and they are separated by a small distance in air. If the permittivity of air is $\varepsilon_{0}$,then the magnitude of the field between the two planes with its direction will be:

What will be the total electric flux through the faces of a cube of side length $a$ if a charge $q$ is placed at:
$(a)$ $A$: a corner of the cube.
$(b)$ $B$: the midpoint of an edge of the cube.

$A$ charged ball $B$ hangs from a silk thread $S,$ which makes an angle $\theta$ with a large charged conducting sheet $P,$ as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to $:-$