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

An infinite line charge produces a field of $9 \times 10^4 \;N/C$ at a distance of $2\; cm$. Calculate the linear charge density in $\mu C / m$

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.

In the figure, a very large plane sheet of positive charge is shown. $P _{1}$ and $P _{2}$ are two points at distance $l$ and $2 \,l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields $E_{1}$ and $E_{2}$ at $P _{1}$ and $P _{2}$ respectively are

A solid metallic sphere has a charge $ + \,3Q$. Concentric with this sphere is a conducting spherical shell having charge $ – Q$. The radius of the sphere is $a$ and that of the spherical shell is $b(b > a)$. What is the electric field at a distance $R(a < R < b)$ from the centre