What is the flux through a cube of side $a$ if a point charge of $q$ is at one of its corners?

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2 \sigma$. The force experienced by a point charge $+q$ placed at the midpoint between the two plates will be:

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

$A$ spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

$A$ negatively charged plate has a surface charge density of $\sigma = 2 \times 10^{-6} \ C/m^2$. An electron with kinetic energy $KE = 200 \ eV$ is projected towards the plate. If the electron does not strike the plate,find the minimum initial distance $r$ in $mm$ from the plate.

Two mutually perpendicular infinitely long straight conductors carrying uniformly distributed charges of linear densities $\lambda_{1}$ and $\lambda_{2}$ are positioned at a distance $r$ from each other. Force between the conductors depends on $r$ as