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

Electric field at a point varies as ${r^o}$ for

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 centre as a function of distance $(r)$ from centre is given by

Two infinitely long parallel wires having linear charge densities ${\lambda _1}$ and ${\lambda _2}$ respectively are placed at a distance of $R$ metres. The force per unit length on either wire will be $\left( {K = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

The electric field $\vec E = {E_0}y\hat j$ acts in the space in which a cylinder of radius $r$ and length $l$ is placed with its axis parallel to $y-$ axis. The charge inside the volume of cylinder is 

Let $\rho (r)\, = \frac{Q}{{\pi {R^4}}}\,r$ be the volume charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $'p'$ inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is