Three infinitely long charge sheets are placed as shown in the figure. The electric field at point $P$ is

Find the ratio of the electric field at points $A$ and $B$. An infinitely long uniformly charged wire with linear charge density $\lambda$ is kept along the $z$-axis.

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

$A$ long charged cylinder of linear charge density $\lambda$ is surrounded by a hollow coaxial conducting cylinder. What is the electric field in the space between the two cylinders?

Two concentric conducting thin spherical shells of radii $a$ and $b$ $(b > a)$ are given charges $Q$ and $-2Q$ respectively. The electric field along a line passing through the centre as a function of distance $(r)$ from the centre is given by:

Two infinitely long parallel conducting plates having surface charge densities $+\sigma$ and $-\sigma$ respectively,are separated by a small distance. The medium between the plates is vacuum. If $\varepsilon_0$ is the dielectric permittivity of vacuum,then the electric field in the region between the plates is