$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?

$A$ charge $17.7 \times 10^{-4} \ C$ is distributed uniformly over a large sheet of area $200 \ m^2$. The electric field intensity at a distance $20 \ cm$ from it in air will be $\left[\varepsilon_0=8.85 \times 10^{-12} \ C^2/Nm^2\right]$

Obtain Coulomb's law from Gauss's law.

In finding the electric field using Gauss's Law,the formula $|\overrightarrow{E}| = \frac{q_{enc}}{\varepsilon_{0}|A|}$ is applicable. In the formula,$\varepsilon_{0}$ is the permittivity of free space,$A$ is the area of the Gaussian surface,and $q_{enc}$ is the charge enclosed by the Gaussian surface. The equation can be used in which of the following situations?

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution,there is a finite value of electric potential at the centre of the sphere,at the surface of the sphere,and also at a point outside the sphere. The electric potential at infinity is zero.
Statement-$1$: When a charge $q$ is taken from the centre to the surface of the sphere,its potential energy changes by $\frac{q \rho R^2}{6 \epsilon_0}$.
Statement-$2$: The electric field at a distance $r (r < R)$ from the centre of the sphere is $\frac{\rho r}{3 \epsilon_0}$.

$A$ 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: