Electric field produced due to an infinitely long straight uniformly charged wire at a perpendicular distance of $2 \ cm$ is $3 \times 10^8 \ N C^{-1}$. Then,linear charge density on the wire is . . . . . . . $(k = 9 \times 10^9 \ SI \ unit)$ (in $\mu C/m$)

$A$ non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its center is:
$(1) \text{ Increases with increase in } r \text{ for } r < R$
$(2) \text{ Decreases with increase in } r \text{ for } 0 < r < \infty$
$(3) \text{ Decreases with increase in } r \text{ for } R < r < \infty$
$(4) \text{ Is continuous at } r = R$

In a cuboid of dimension $2 L \times 2 L \times L$,a charge $q$ is placed at the centre of the surface ' $S$ ' having an area of $4 L^2$. The flux through the opposite surface to ' $S$ ' is given by

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:

The electric field intensity at a point between two parallel sheets with like charges of the same surface charge density $(\sigma)$ is:

The electric field intensity due to an infinite cylindrical thin wire having charge $q$ per unit length at a distance $r$ from its axis is