Two parallel large thin metal sheets have equal surface charge densities $\sigma = 26.4 \times 10^{-12} \ C/m^2$ of the same sign. The electric field between these sheets is:

$A$ solid metal sphere of radius $R$ having charge $q$ is enclosed inside a concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in the figure. The approximate variation of the electric field $\overrightarrow{E}$ as a function of distance $r$ from the centre $O$ is given by:

$A$ non-conducting solid sphere of radius $R$ has a uniform volume charge density $\rho$. The electric potential at the center of the sphere is related to the potential at the surface and outside the sphere due to this uniform charge distribution.
Statement-$1$: When a charge $q$ is moved from the surface to the center of the sphere,the change in its potential energy is $q\rho R^2 / 6\varepsilon_0$.
Statement-$2$: The electric field at a distance $r$ $(r < R)$ from the center of the sphere is $\rho r / 3\varepsilon_0$.

The electric field components in the figure are $E_{x}=\alpha x^{1 / 2}, E_{y}=E_{z}=0,$ in which $\alpha=800 \; N/C \cdot m^{1/2}.$ Calculate
$(a)$ the flux through the cube,and
$(b)$ the charge within the cube. Assume that $a=0.1 \; m$.

$A$ positive charge $Q$ is placed on a conducting spherical shell with inner radius $R_1$ and outer radius $R_2$. $A$ particle with charge $q$ is placed at the center of the spherical cavity. The magnitude of the electric field at a point in the cavity,at a distance $r$ from the center,is

An early model for an atom considered it to have a positively charged point nucleus of charge $Ze$,surrounded by a uniform density of negative charge up to a radius $R$. The atom as a whole is neutral. For this model,what is the electric field at a distance $r$ from the nucleus?