An $100 \ eV$ electron is fired directly towards a large metal plate having surface charge density $-2 \times 10^{-6} \ C \ m^{-2}$. The distance from where the electron is projected,so that it just fails to strike the plate,is: (in $mm$)

Two spherical,nonconducting,and very thin shells of uniformly distributed positive charge $Q$ and radius $d$ are located a distance $10d$ from each other. $A$ positive point charge $q$ is placed inside one of the shells at a distance $d/2$ from the center,on the line connecting the centers of the two shells,as shown in the figure. What is the net force on the charge $q$?

In a cuboid of dimension $2 L \times 2 L \times L$,a charge $q$ is placed at the centre of the surface ' $S$ ' having an area of $4 L^2$. The flux through the opposite surface to ' $S$ ' is given by

The region between two concentric spheres of radii '$a$' and '$b$' (see figure) has a volume charge density $\rho = \frac{A}{r}$,where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres is constant,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

$A$ long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of the cylindrical volume is $R$. $A$ charged particle $(q)$ revolves around the cylinder in a circular path at a distance $r$ from the axis. The kinetic energy of the particle is: