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 $\mu C/m$)

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

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder,as shown in the figure. The magnitude of the electric field at the point $P$,which is at a distance $2R$ from the axis of the cylinder,is given by the expression $\frac{23 \rho R}{16 k \varepsilon_0}$. The value of $k$ is

$A$ very long charged solid cylinder of radius 'a' contains a uniform charge density $\rho$. The dielectric constant of the material of the cylinder is $k$. What will be the magnitude of the electric field at a radial distance '$x$' $(x < a)$ from the axis of the cylinder?

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance $r$ from its centre is represented graphically by

$A$ positive charge $Q$ is placed on a conducting spherical shell with inner radius $R_1$ and outer radius $R_2$. $A$ particle with charge $q$ is placed at the center of the spherical cavity. The magnitude of the electric field at a point in the cavity,at a distance $r$ from the center,is