An infinitely long thin straight wire has a uniform charge density of $\frac{1}{4} \times 10^{-2} \text{ C/m}$. What is the magnitude of the electric field at a distance of $20 \text{ cm}$ from the axis of the wire?

$A$ solid ball of radius $R$ has a charge density $\rho$ given by $\rho = \rho_0 \left( 1 - \frac{r}{R} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is

What will be the total electric flux through the faces of the cube of side length '$a$' if a charge '$Q$' is placed at '$B$', the midpoint of an edge of the cube (see figure)?

$A$ 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 $\rho r / 3\varepsilon_0$.

Three infinite plane sheets carrying uniform charge densities $-\sigma, 2 \sigma, 4 \sigma$ are placed parallel to the $XZ$ plane at $Y=a, 3a, 4a$ respectively. The electric field at the point $(0, 2a, 0)$ 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.