If an insulated non-conducting sphere of radius $R$ has a uniform charge density $\rho$,the electric field at a distance $r$ from the center of the sphere $(r < R)$ will be:

$A$ solid sphere of radius $r_1=1 \text{ cm}$ carries charge distributed uniformly over it with density $\rho_1=-3 \text{ C/cm}^3$. It is surrounded by a concentric spherical shell of radius $r_2=2 \text{ cm}$ carrying uniform charge density $\rho_2=0.5 \text{ C/cm}^3$. If $E_d$ denotes the magnitude of the electric field at distance $d$ from the common centre of the spheres,then

$A$ 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 $\epsilon_{0} = 8.85 \times 10^{-12} \ C^{2} \ N^{-1} \ m^{-2}$]

$A$ long cylindrical volume contains a uniformly distributed charge of density $\rho \; C m^{-3}$. The electric field inside the cylindrical volume at a distance $x = \frac{2 \varepsilon_{0}}{\rho} \; m$ from its axis is $....... V m^{-1}$.

The electrostatic field of a long uniformly charged wire varies with distance $r$ according to which relation?

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