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

A conducting sphere of radius $R = 20$ $cm$ is given a charge $Q = 16\,\mu C$. What is $\overrightarrow E $ at centre

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 $\frac{{23\rho R}}{{16K{\varepsilon _0}}}$ .The value of $K$ is

If the total charge enclosed by a surface is zero, does it imply that the electric field everywhere on the surface is zero ? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0r^2$  ($\rho_0$  is a constant and r is measure from centre).Consider two points $A$ and $B$ at distance $x$ and $y$ respectively ($x < R, y > R$) from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then