$A$ and $B$ are two concentric spheres. If $A$ is given a charge $Q$ while $B$ is earthed as shown.

The electric field in a region is radially outward with magnitude $E = A r_0$. The charge contained in a sphere of radius $r_0$ centered at the origin is

$A$ large metal plate has a surface charge density of $8.85 \times 10^{-6} \ C \ m^{-2}$. An electron having initial kinetic energy of $8 \times 10^{-17} \ J$ is moving towards the center of the plate. If the electron stops just before reaching the plate,then the initial distance between the electron and the plate is [Take $\epsilon_{0} = 8.85 \times 10^{-12} \ C^{2} \ N^{-1} \ m^{-2}$]

The space between two large parallel plates is filled with a material of uniform charge density $\rho$. Assume that one of the plates is kept at $x=0$. The potential at any point $x$ between these plates is given by (where $A$ and $B$ are constants):

$A$ force of $10 \; N$ acts on a charged particle placed between two plates of a charged capacitor. If one plate of the capacitor is removed,then the force acting on that particle will be ...... $N$.

The electric potential in a region around the origin is given by $V(x) = 4x^2$. The total charge enclosed in a cube of side $1 \ m$ centered at the origin is (in Coulombs) ...